Apparatus for generating property associated with chemical product

Abstract

The invention relates to an apparatus (720) for generating a characteristic associated with a chemical product. The providing unit (721) provides an electronic structural representation comprising a) a first portion indicative of an active space and b) a second portion indicative of an inactive space. The characteristic depends on the active space and the inactive space. A determination unit (722) causes the quantum computer and / or the classical computer to generate a solution of the first portion and a solution of the second portion. A calculation unit (723) generates a solution of the electronic structure representation by combining the solution of the first portion and the solution of the second portion to generate the characteristic. The combining includes generating an interaction representation based on a reference state associated with an overlay of an electronic configuration generated based on a solution of the first portion and a solution of the second portion.

Description

Technical Field

[0001] This invention relates to an apparatus, method, and computer program product for generating properties associated with a chemical product. Further, this invention relates to a system for generating properties associated with a chemical product, the system including the apparatus. Background Technology

[0002] Quantum computers are typically a completely new type of computing system that allows the use of the special behavior of quantum mechanical systems to perform computations that ordinary computers cannot complete in any reasonable amount of time, under certain conditions. Summary of the Invention

[0003] The object of this invention is to provide apparatus, methods, systems, and computer program products that allow for improved efficiency and effectiveness in using quantum computers to compute problems related to chemical products (e.g., electronic structure problems), i.e., allowing for reduced computation time and required computational resources while achieving the same quality of results. Furthermore, the chemical industry sells chemical products with specific technical application characteristics. At the heart of any chemical product is a chemical molecule or combination of chemical molecules; for example, a chemical product comprises one or more chemical molecules that determine its properties. The properties of chemical monomers or oligomers can be determined, for example, by extrapolation, to determine the properties of chemical polymers.

[0004] Chemical products, comprising one or more types of chemical molecules, are highly complex real-world systems containing multiple interacting electrons that constitute the properties of the chemical molecules and thus the properties of the chemical products. Therefore, capturing the complexity of chemical molecules in calculations by reflecting atomic types, chemical bonds between atoms of the same and / or different types, the three-dimensional structure of the atomic arrangement, the interactions between multiple atoms in this three-dimensional arrangement, and especially the subatomic structure and electron density constituted by electrons, is extremely important. Such highly complex molecular structures are typically described through electronic structure problems, for example, using the Schrödinger equation employing Hamiltonian operators. To allow for solving such complex electronic structure problems, approximation methods can be used. However, with approximation methods, the properties derived from electronic correlations may not be adequately reflected in most systems. Therefore, it is necessary to include as many electronic correlations as possible from real-world systems to obtain results that are as close as possible to the real-world, technologically applicable properties of chemical molecules. This is particularly important for the chemical industry, which produces chemical products based on the generation, properties, and production formulations of chemical molecules to generate corresponding real-world chemical products with the corresponding properties.

[0005] Electronic structure calculations are essential in the design of experimental setups where the number of experiments producing real-world chemical molecules with desired properties often depends on the accuracy of the calculated electronic structure problem and the accuracy of the properties determined from the results. Obtaining highly accurate solutions can be NP-hard—meaning that classical computers would need decades to solve them. Therefore, generating such accurate solutions is impossible in many real-world scenarios for developing practically relevant chemical molecules with enhanced or novel properties. This leads to more intensive, inefficient laboratory work and increases the time required to develop new chemical molecules.

[0006] Given the environmental impact of chemical development and the pace at which the chemical industry must adjust its chemical framework and chemical products, it is advantageous, particularly through more accurate solutions to electronic structure problems, to improve the development of new or enhanced chemical products. Embedding quantum computing into this development cycle may provide a solution to this problem. However, embedding quantum computing is itself a challenge. Therefore, the devices, systems, methods, and computer program products disclosed herein allow for more efficient and effective use of quantum computing to enhance the development of new or enhanced chemical products.

[0007] Since quantum and / or classical computers generate and provide solutions for the first part of the electronic structure representation, and also generate and provide solutions for the second part of the electronic structure representation, for each part of the electronic structure representation, the most suitable computational system can be utilized. These computational systems include quantum computing systems, classical computing systems, and combinations thereof. This allows the utilized computational system to be specifically adapted to the problem requiring a solution. Furthermore, since the solutions for the first and second parts of the electronic structure representation are computationally combined by generating an interaction representation based on a reference state associated with the superposition of electronic configurations generated based on the solutions for the first and second parts, the correlations between and within the first and second parts of the electronic structure representation can be determined again on the appropriate computational system (particularly, classical and / or quantum computers, depending on the problem) regardless of which computational system was used in the previous step. Therefore, for each part of the solution computation, the most suitable computational system can be selected independently of the computational systems used to compute other parts of the solution. This makes it possible to use computer resources very efficiently to solve complex electronic structure problems. Furthermore, compared to, for example, the commonly used reduced density matrix, the reference states defined above provide more information about the electronic structure of the system. Therefore, the reference states defined above allow for the use of various efficient and effective solution methods, which can only be used with the corresponding information on the system and are independent of the methods used to determine the solutions for the second and first parts. Thus, in the development of chemical products, the relevant electronic structure problems, crucial for determining the properties associated with the chemical product, can be solved with greater efficiency and effectiveness.

[0008] In a first aspect of the invention, an apparatus is provided for generating properties associated with a chemical product, wherein the chemical product comprises one or more molecular structures, wherein the apparatus comprises: i) an electronic structure representation providing unit for providing an electronic structure representation associated with the molecular structure of the chemical product, and the electronic structure representation comprising a) a first portion of the electronic structure representation indicating an active space comprising a portion of the electronic structure associated with the molecular structure, and b) a second portion of the electronic structure representation indicating an inactive space comprising another portion of the electronic structure associated with the molecular structure, wherein the properties associated with the chemical product depend on the active space and the inactive space; ii) a solution determining unit for causing a quantum computer and / or a classical computer to generate and provide a solution for the first portion of the electronic structure representation, and for causing a quantum computer and / or a classical computer to generate and provide a solution for the second portion of the electronic structure representation; and iii) An associative computational unit is configured to generate a solution to the electronic structure representation by combining the solution of the first part and the solution of the second part, wherein the solution of the first part and the solution of the second part are computationally combined to generate properties associated with the chemical product, wherein the computational combination includes generating an interaction representation based on a reference state associated with the superposition of electronic configurations generated based on the solution of the first part and the solution of the second part, and enabling a classical computer and / or a quantum computer to provide a solution to the interaction representation.

[0009] Typically, the device can be implemented in software, hardware, or a combination thereof, where hardware can refer to any known specialized or general-purpose classic computer hardware. For example, the device can be implemented as any known computing device, such as a PC. However, the device can also be implemented as a cloud environment, computing network, etc., so that at least a portion of the device can also be implemented as a network solution, thus allowing it to be distributed across multiple computing devices.

[0010] A chemical product can be any chemical product that includes one or more molecular structures (e.g., is composed of one or more molecular structures). A molecular structure is a structure that at least forms a part of a molecule. For example, in a polymer composed of multiple monomers, the molecular structure can be one of those monomers, but it can also refer to multiple of those monomers or even the entire polymer. Furthermore, a molecular structure can also be one or more atoms in the molecule that forms the chemical product. Typically, a molecular structure includes an electronic structure that can be described by electronic structure representation.

[0011] The apparatus used for generating characteristics should be interpreted as suitable for generating characteristics, and in particular, conducive to generating characteristics. Generating characteristics associated with a chemical product means identifying or deriving and providing the corresponding characteristics. A characteristic can generally be any characteristic of a chemical product associated with a solution represented by its electronic structure, for example, a solution represented by the electronic structure of the molecular structure forming the chemical product, or one that can be derived from that solution. The characteristic can be an electronic characteristic represented by its electronic structure. The characteristic can preferably refer to any characteristic of the chemical product that allows for the assessment of the technical suitability of the corresponding chemical product provided after its production. Preferably, technically applicable characteristics include any of the following: chemical reactivity, spectral and spectroscopic characteristics, molecular characteristics, activation energy and reaction energy of a predetermined chemical reaction. Preferably, technically applicable characteristics include at least one of mechanical characteristics, spectral characteristics, physicochemical characteristics, chemical characteristics, and biological characteristics. Generally, mechanical characteristics can refer to any of the following: adhesion, tensile strength, stiffness, hardness, shrinkage, elongation, crack tearing, tear strength, resilience, compressibility, abrasion, spillage, morphology, tactile characteristics, fracture stress, elongation at break, particle size, and filling density. Spectral properties typically include any of the following: tinting, turbidity, opacity, transparency, reflectance, appearance, absorption, scattering, color strength, hue, color saturation, color intensity, cloud point, extinction, optical density, spectrum, refractive index, IR spectrum, Raman spectrum, NMR spectrum, ESR spectrum, and UV / Vis spectrum. Furthermore, physicochemical properties can refer to any of the following: density, viscosity, K-value, molar mass, dispersibility, molar mass distribution, particle size distribution, solubility, partition coefficient, interfacial properties, surface tension, dispersibility, storage stability, odor, segregation, condensation, electrical conductivity, capacitance, surface area, flow time, vapor pressure, VOC, solids content, hygroscopicity, magnetism, miscibility, thixotropy, phase transition properties, glass transition temperature, corrosion inhibition, solvent separation, aggregation, self-heating capacity, impact sensitivity, loss on drying, response angle, electrostatic charge, minimum film-forming temperature, charge density, electrostatic multipole moment, and thermal conductivity. Chemical properties may include any of the following: reaction thermodynamics, reaction kinetics, chemical resistance, reaction time, demolding time, growth, hard / soft segment content, crystallinity, reaction temperature, reaction pressure, decomposition, thermal decomposition, photodegradation, acidity, pKa, pH, moisture / water content, flammability, combustion rate, auto-ignition, flash point, formation of flammable gases, fire reactivity, deflagration rate, residual monomer count, by-product formation, degree of polymerization, salt content, temperature resistance, oxidation properties, reduction properties, reactivity, ash content, non-volatile matter content, stability, chelating ability, calorific value, and saponification value.Furthermore, biological characteristics may include any of the following: biodegradability, biological resistance, particularly resistance to pathogenic viruses, bacteria, fungi, plants or animals or developmental stages of said pathogens, tolerance to environmental parameters, such as drought tolerance, tolerance to enzyme degradation, such as protease resistance, lipase resistance, amylase resistance, hydrolase resistance, resistance to pest control agents, toxicity, biotransformation, ecotoxicology, sensitization, particularly allergenicity, bacterial count, enzyme activity, substrate specificity, cofactor dependence, product specificity, substrate and / or product inhibition, dissociation constant, Michaelis kinetics, activity / stability under or in different of the following: pH, temperature, pressure, organic solvent concentration, carrier formulation, encapsulated formulation; distribution in the environment, compartmentalization, bioaccumulation, biological exposure LD50, mutagenicity.

[0012] An electronic structure representation providing unit is adapted to provide an electronic structure representation associated with at least one molecular structure of one or more molecular structures of a chemical product. Specifically, the electronic structure representation providing unit may refer to a storage unit on which an electronic structure representation is already stored. However, the electronic structure representation providing unit may also include an input unit, for example, which a user can use to instruct the electronic structure representation providing unit on the electronic structure representation. Generally, the electronic structure representation can be provided in any form that allows for determining the electronic structure problem to be solved and defines the quantities of the electronic structure problem and the interactions between these quantities. Preferably, the electronic structure representation refers to a mathematical description of the electronic structure problem to be solved, for example, a mathematical description of the electronic structure problem using electronic structure Hamiltonians. However, the electronic structure representation may also refer to any other explicit symbolic form of the corresponding electronic structure problem. Generally, the electronic structure representation is associated with the molecular structure of the chemical product. In particular, the molecular structure of the chemical product associated with the electronic structure representation can define the electronic structure problem and the quantities of the electronic structure problem. The electronic structure representation is associated with the characteristics of the technological application. For example, if a chemical product refers to a specific molecule whose technical application characteristics should be determined, then the corresponding molecule and its structure define the quantities and interactions of the quantum mechanical electronic structure problem indicated by the electronic structure representation. Therefore, the solution to the electronic structure representation indicates the characteristics. Thus, providing a solution to the electronic structure representation means providing the corresponding characteristics. In particular, the characteristics can be derived from the solution to the electronic structure problem. Preferably, depending on the specific chemical product and / or the quantum mechanical electronic structure problem, the electronic structure representation includes or indicates atomic positions, basis sets, charges, and spin multiplicity.

[0013] Generally, electronic structure representation refers to the problem associated with determining the electronic structure of atoms, molecules, crystals, or amorphous solids. For example, electronic structure representation can be used to determine the high-energy ground state of atoms and / or molecules. Based on the solution of the electronic structure representation, other properties of atoms, molecules, crystals, or amorphous solids can be derived. Typically, electronic structure representation can be mathematically represented using different classes of underlying electronic structure Hamiltonians. Examples include Born-Oppenheimer Hamiltonians, non-Born-Oppenheimer Hamiltonians, Hamiltonians with additional single-electron potentials representing, for example, electrostatic fields, two-component Hamiltonians including spin-orbit coupling, and fully relativistic four-component Dirac Hamiltonians, etc.

[0014] From the solutions of the electronic structure representation, various properties of the corresponding chemical products can be derived. An example of such an electronic structure representation that can be advantageously solved in this invention is the calculation of the ground-state energy of a molecule or a general electronic system. In particular, this allows for the prediction of the final products of the reaction, the thermodynamic properties of the reaction, and the kinetic properties of the reaction in the context of determining the ground-state energies of all molecular species present in the chemical reaction. This understanding and reaction characteristics can then be used again to optimize chemical production processes, predict the microstructure of polymers, optimize material properties, etc. Furthermore, the electronic structure representation can also refer to the calculation of the multipole moment of the chemical product. Such calculations are relevant to determining properties of the chemical product related to electrical and other technical applications (e.g., the dielectric behavior of the chemical product), and also to determining properties arising from intermolecular interactions that strongly depend on the polarity of the chemical product—the range of which can be from solubility and compatibility with certain media to ionic complexation behavior or effects on spectral properties (e.g., color). Therefore, determining the value of a property based on the result of solving the electronic structure representation is based on the corresponding property that should be determined and further on the information provided by the solution of the electronic structure representation.

[0015] Furthermore, the electronic structure representation comprises a first part and a second part of the problem. The first part of the electronic structure representation indicates the active space, which includes a portion of the electronic structure associated with the molecular structure. The second part of the electronic structure representation indicates the inactive space, which includes another portion of the electronic structure representation associated with the molecular structure. Preferably, the portion of the electronic structure representation associated with the molecular structure included in the second part is the remaining portion of the electronic structure representation without the first part. Preferably, the active and inactive spaces of the electronic structure representation refer to subspaces of the Hilbert space of the electronic structure representation. In particular, the basis of the Hilbert space of the electronic structure representation can be formed by electron orbitals and mathematically represented by the antisymmetric tensor product of electron orbitals, and the inactive and active spaces are defined by the electron orbitals they refer to. However, for example, if the electronic structure representation is expressed in another space, the active and inactive spaces can also be defined by other mathematical representations. The first and second parts are preferably defined based on the corresponding active or inactive spaces, i.e., defined on the corresponding basis of the corresponding spaces, but may also include terms related to orbitals representing the corresponding other spaces, for example, terms related to electrons or electron orbitals that form the basis of the corresponding other spaces. Typically, the first and second parts of the electronic structure representation are determined based on the chemical product and the molecular structure to be described by the electronic structure representation. In particular, since the molecular structure of the chemical product defines the quantities of the electronic structure representation and the interrelationships between these quantities, the molecular structure also defines how these quantities and interrelationships are described with respect to the first and second parts of the electronic structure representation. Specifically, since the chemical product defines the electron orbitals in the electronic structure representation, and particularly which orbitals have the strongest correlations, these correlations should be considered more accurately in order to accurately solve the electronic structure representation of the molecular structure of the chemical product; therefore, the chemical product determines how the first and second parts are defined. For example, a first part of the electronic structure representation is provided such that it allows the use of a quantum computer to calculate with high accuracy the part of the electronic structure of the chemical product most relevant to a particular application. In this case, a first part is provided, such that the first part is based on the electronic orbitals most relevant to a particular application, because these electronic orbitals exhibit the strongest correlation in the molecular structure of the chemical product during the chemical reaction of the chemical product and / or change during the particular application, for example, participating in bond breaking and / or bond formation processes during the chemical reaction of the molecular structure of the chemical product.

[0016] The properties associated with a chemical product depend on the active and inactive spaces. Specifically, these properties depend on the electronic structure represented by the first and second parts, and therefore on the solutions of the first and second parts of the electronic structure representation. Typically, the electronic structure representation can directly provide the first and second parts. However, the electronic structure representation can also be provided such that it only indicates how the first and second parts are defined, for example, by indicating the active and inactive spaces, or by indicating which electron orbitals of the electronic structure problem indicated by the electronic structure representation should respectively be part of the active space and the inactive space. The first and second parts of the electronic structure representation can then be derived from the information provided by the electronic structure representation (e.g., by utilizing known mathematical rules and methods). Preferably, the electronic structure representation includes or indicates the number and identification of electron orbitals in the active space, the number of electrons to be considered in the first part, and / or the coefficient matrix of the initial electron orbitals.

[0017] Optionally, the apparatus may further include or utilize a conversion unit configured to convert the electronic structure representation into a representative operational description indicating a sequence of operations to be applied to the quantum elements of the quantum computer. Typically, the conversion unit may be part of the apparatus, but can be omitted from the apparatus, and may be part of the quantum computer, particularly the part of the quantum computer's control unit that automatically converts the provided electronic structure representation into the corresponding operational description. The conversion unit is configured to determine, in particular, the sequence of operations that enables the execution of a first and / or second part of the quantum mechanical computation on the quantum computer. Thus, the conversion unit may be configured to convert only the first part or only the second part into the corresponding operational description, depending on which part is to be computed on the quantum computer. Typically, operations are performed by the quantum computer by manipulating the states of the quantum elements of the quantum computer, where quantum elements can refer to all elements of the quantum computer used to simulate the electronic structure representation, e.g., the quantum elements that form the qubits of the quantum computer, and also the boson field representing the boson mode during the computation of the problem. Methods for determining such operations for a problem to be computed on the quantum computer are generally known and can be used by the conversion unit to determine the operational descriptions of the first or second part of the electronic structure representation, respectively. For example, quantum phase estimation (QPE) or variational algorithms (such as variational Hamiltonian simulation (VHA) or variational quantum eigenvalue solver (VQE) with unitary coupled cluster (UCC) simulation) combined with Jordan-Wigner or Bravyi-Kitaev transformation and CZ algorithm or similar algorithms, and FSIM network algorithm using low-rank decomposition for unitary evolution, can be used to transform and prepare computations on the first or second part of the problem description on a quantum computer, respectively. Examples of this transformation can be found in, for example, the following articles: “Quantum Computational Chemistry”, S. McArdle et al., Rev. Mod. Phys. 92, (2020); “Quantum Algorithms for Quantum Chemistry and Quantum Materials Science”, B. Bauer et al., Chem. Rev. (2020); and “Quantum Chemistry in the Age of Quantum Computing”, Y. Cao et al., Chem. Rev. (2019).

[0018] The solution determination unit can be adapted to enable a quantum computer to generate and provide a quantum computation solution for a first portion of the electronic structure representation. In an example, the solution determination unit is configured to enable the quantum computer to perform a quantum mechanical calculation based on the first portion, such that the result of the quantum mechanical calculation indicates the solution for the first portion, and then generate the solution based on the result of the quantum mechanical calculation. If the device includes an optional conversion unit that has already provided a conversion from the first portion of the electronic structure representation to a representative operational description, the solution determination unit can be adapted to provide the representative operational description to the quantum computer so that the quantum computer performs a quantum mechanical calculation based on the determined representative operational description. However, if the device does not include a conversion unit, the solution determination unit can be adapted to provide the quantum computer with a first or second portion provided or indicated by the electronic structure representation, wherein a portion of the quantum computer system (e.g., a control unit of the quantum computer system) can thus be configured to provide a conversion from the first or second portion to a corresponding operational description that provides operations that can be executed on the quantum computer to compute the solution for the first or second portion. In particular, the solution determination unit can be communicatively coupled to the quantum computer or the control unit of the quantum computer to enable the quantum computer to perform a quantum mechanical calculation and obtain a result indicating the solution for the first or second portion. However, communication coupling can also be indirect coupling, for example via a storage unit such as a cloud storage unit, so that the corresponding control signals for the quantum computer to perform quantum mechanical calculations are stored on the storage unit and then sent to the quantum computer.

[0019] Alternatively, the solution-determining unit can also enable a classical computer to generate and provide a solution for the first part of the electronic structure representation. Depending on the corresponding electronic structure representation, using a classical computer to solve for the first part of the electronic structure representation can be more efficient and effective. For example, for an electronic structure representation with a first part that represents only a small portion of the electronic structure (e.g., only less than a predetermined number of orbitals and electrons), using a classical computer may be more resource-efficient. In this case, methods such as full configuration interactions, density matrix renormalization group theory, Møller-Plesset perturbation theory, or coupled clustering theory can be used.

[0020] Further, the solution determination unit can be configured to enable a classical computer to generate and provide a solution for the second part of the electronic structure representation. For example, the solution for the second part can be a representation of the electronic configuration of the inactive space of the corresponding molecule. Specifically, the solution determination unit can be configured to enable a classical computer to generate and provide a classical computational solution for the second part of the electronic structure representation. Specifically, the solution determination unit can be configured to prepare and control the classical computer using known methods for enabling the classical computer to solve the corresponding second part. The solution for the second part can be any kind of contribution of the second part to the solution of the electronic structure problem. For example, the solution can refer to any contribution of the inactive space considered for the interaction representation. For example, the solution determination unit can be configured to determine the solution for the second part based on a corresponding known algorithm (such as Hartree-Fock or density functional theory (DFT)). In a preferred embodiment, the solution for the second part is determined based on the solution for the first part. Therefore, in this step, the influence of the first part on the second part, i.e., the influence of the active space on the inactive space, can be considered. In a preferred embodiment, the SCF solution for the second part is determined. Therefore, the solution for the second part is a better approximation of the overall solution, and thus the interaction representation is based on a solution that is already quite accurate. In particular, preferably, an electronic structure representation has been provided, which allows the solution to the second part to be computed on a classical computing device using the corresponding known computational methods.

[0021] Alternatively, the solution determination unit can be configured to cause the quantum computer to generate and provide a quantum computing solution for the second part. The same method described above regarding computing the first part on a quantum computer can also be applied to computing the second part on a quantum computer. The solution determination unit can, for example, be configured to cause the quantum computer to generate and provide a solution for at least one of the first and second parts of the electronic structure representation. In an embodiment, the solution determination unit is configured to cause the quantum computer to generate and provide a solution for at least one of the first and second parts.

[0022] The correlation computation unit is configured to generate a solution representing the electronic structure by combining the solutions from the first part and the second part. Specifically, the computational solutions from the first part and the second part are computationally combined to generate properties associated with the chemical product. If the solutions from the first part and / or the second part are generated using a quantum computer, the correlation computation unit can be configured to determine the corresponding solution using measurement results provided by the quantum computer. However, the corresponding control unit of the quantum computer can also be configured to determine the corresponding solution using measurement results.

[0023] Computational combination involves generating interaction representations associated with combinations of active and inactive spaces. These interaction representations are based on reference states associated with superpositions of electronic configurations and are generated based on solutions from both the first and second parts. A reference state is a representation of a superposition of electronic configurations used as the basis for determining associations between electronic structures in the active and inactive spaces, and optionally within one or both of these spaces. Thus, the reference state, based on solutions from both the first and second parts, represents the electronic configuration in such a way that it forms the basis for solutions used to further compute the interaction representations. For example, to generate the reference state, the solutions from both the first and second parts generated on a quantum computer refer to directly measured electronic configurations, which are then directly constructed on the corresponding classical and / or quantum computers used to solve the interaction representations. Therefore, the solutions from both the first and / or second parts prepared on the quantum computer are not measured by measuring, for example, characteristic quantities of the corresponding states (e.g., energy, reduced density matrix, or any other observable), but directly refer to the states measured for the quantum elements representing the corresponding states of electrons in the electronic structure. Therefore, the reference state can be regarded as a mathematical representation of the electronic configuration of the molecular structure of a chemical product after solving the first and second parts of the electronic structure representation.

[0024] A reference state can be generated as a superposition of electronic configurations that are parts of the solutions for the first and second parts, where each electronic configuration is associated with a weight used to weight the contribution of the electronic configuration to the overall solution of the electronic structure problem. Determining the weights refers to determining the overall solution. For example, if the reference state is represented using configuration interaction basis states, the weights are configuration interaction coefficients associated with the corresponding configuration interaction basis states. The electronic configurations used can include parts representing the active space and parts representing the inactive space. For example, an electronic configuration can include electronic orbitals as part of the first part (i.e., the active space) and electronic orbitals as part of the second part (i.e., the inactive space). Depending on the problem, the corresponding parts of the electronic configurations used with the superposition under the reference state can be treated differently. For example, the part of the electronic configuration representing the active space can be more numerous than the part of the electronic configuration representing the inactive space. In particular, the parts of the electronic configuration representing the inactive space can be the same, while the parts of the electronic configuration representing the active space can be different. Therefore, the reference state can refer to a superposition of electronic configurations, wherein different active parts of the electronic configurations are combined (e.g., linearly combined), and the inactive parts are identical. Based on this reference state, the interaction representation can also allow the generation of different inactive parts resulting from the correlation between the active and inactive parts during the corresponding computation. The interaction representation generated based on the reference state then typically represents the correlation between the part represented by the first part and the part represented by the second part of the electronic structure representation, and further represents the correlation within one or both parts, particularly within the second part. The interaction representation can include correlations between electronic orbitals in which at least one electronic orbital belongs to the inactive space. The correlation computation unit is configured to enable a classical computer and / or a quantum computer to provide a solution to the interaction representation. The classical computer and / or quantum computer used can be the same as or different from the classical computer and / or quantum computer used by the solution determination unit. Although it is preferred to use a quantum computer to compute the interaction representation, in embodiments, a classical computer or a combination of both a quantum computer and a classical computer can also be used. The solution computed on the classical computer and / or quantum computer can then be provided. Providing can refer to providing a solution to the device, and also to providing the solution to other computer hardware separate from the device, which is then configured to determine characteristics based on the solution.

[0025] Preferably, the interaction representation includes a) correlations within the inactive space and / or b) correlations between the active and inactive spaces. When the solution of the first part is determined, the correlations occurring within the active space are determined. Typically, correlations between spaces are defined as correlations between quantities defined in those spaces. Therefore, these quantities refer to those defined in the first and second parts of the electronic structure representation. Thus, the preferred embodiment described above can also be stated as follows: the interaction representation includes a) correlations within the second part of the electronic structure representation and / or b) correlations between the first and second parts of the electronic structure representation.

[0026] The solution of the electronic structure representation indicates the properties of the chemical product. These properties can be derived from the solution of the electronic structure representation of the chemical product. Therefore, the method can further include generating and providing properties of the chemical product based on the electronic structure representation. Specifically, the generated properties can be properties of the electronic configuration of the chemical product, for example, the electronic properties of the electronic structure of the chemical product. For example, the properties can be the ground state and / or excited state energies of the chemical product. Based on the corresponding properties, other properties can be derived. For example, based on the determined ground state energies of all molecular species appearing in a chemical reaction, reaction rates, thermodynamic properties of the reaction, and kinetic properties of the reaction can be generated as technical application properties. This understanding and reaction properties can then be used again to optimize chemical production processes, determine the microstructure of polymers, optimize material properties, etc. Furthermore, the properties can also refer to the multipole moments of the chemical product. Such calculations can be related to determining the technical application properties of a chemical product that are relevant to its electrical and other technical applications (e.g., the dielectric behavior of the chemical product), as well as to determining the properties arising from intermolecular interactions that are strongly dependent on the polarity of the chemical product—the range of which can be from solubility and compatibility with certain media to the complexation behavior of ions or the effect on spectral properties (e.g., color).

[0027] Preferably, the method includes providing the characteristic to monitor and / or control a technical application including the chemical product, preferably including a chemical reaction and / or synthesis of the chemical product. Therefore, the provision of the characteristic is configured to be directly usable for the corresponding control and / or monitoring of the application. For example, the provision may include implementing the characteristic into a corresponding control / monitoring system for the application. The provision may include providing the characteristic in a corresponding data format, and providing information on how to use the characteristic to control and / or monitor the application. The method may include providing control signals based on the characteristic to monitor and / or control a technical application including the chemical product. The technical application can be any application within a technical context that includes the chemical product. The technical application can be a chemical reaction including the chemical product (e.g., a catalyst). The technical application can be a synthetic process for synthesizing a chemical product. The technical application can be a product design screening process that includes a screening process for determining one or more characteristics of the chemical product.

[0028] In embodiments, the electronic structure representation is further associated with predefined electronic orbitals, wherein a first part and a second part of the electronic structure representation are defined by electronic orbitals as part of an active space and electronic orbitals as part of an inactive space, respectively. Specifically, the molecular structure is defined by the corresponding electronic orbitals of the molecule, such that the electronic structure representation of the molecular structure includes these electronic orbitals. The electronic orbitals as part of the active space and the electronic orbitals as part of the inactive space form the basis of the respective spaces. Since electrons associated with electronic orbitals in the inactive space can also influence electrons in electronic orbitals in the active space, this influence can also be taken into account as part of the first part of the problem, and vice versa. Generally, an electronic orbital can refer to an atomic orbital or an electronic orbital, depending on the corresponding application, for example, depending on the molecular structure of the chemical product for which an electronic structure representation should be solved. Furthermore, an electronic orbital is generally a mathematical function indicating the probability of finding an electron in a specific region within an atom or molecule.

[0029] In a preferred embodiment, the electron orbitals can be adapted according to the quantities of a first and / or second portion of the electronic structure representation, wherein the device further includes an iterative control unit adapted to control the iteration to minimize or maximize the quantities of the electronic structure representation relative to the electron orbitals, wherein the iteration includes: providing initial electron orbitals and generating solutions for the first and / or second portions, respectively; modifying the initial electron orbitals based on the generated solutions and generating further solutions for the modified electron orbitals; and repeating the electron orbital modification and solution generation until the quantities of the first and / or second portions of the electronic structure representation are maximized or minimized relative to a given criterion. Such solutions for the first and / or second portions can then be used to generate interaction representations, particularly reference states. For example, solutions for the first portion can be iteratively generated as described above and then used to generate reference states. The quantity can refer to any quantity affected by the electron orbitals (i.e., affected by the local probability density of the corresponding electrons in the atoms, molecules, crystals, or amorphous solids associated with the chemical product). Furthermore, more than one quantity of the first and / or second part of the electronic structure representation can be optimized during the aforementioned iterations, for example, using known methods and algorithms for multi-objective optimization (e.g., Pareto optimization techniques, etc.). Additionally, the quantities of the first and / or second part of the electronic structure representation can typically refer to quantities representing the solutions of the first and / or second part of the electronic structure representation, respectively. For example, preferably, the quantity to be optimized refers to the energy of the electronic structure defined by the first and / or second part of the electronic structure representation, wherein, particularly preferably, it is to find the minimum energy of the electronic structure of the atoms, molecules, crystals, or amorphous solids associated with the chemical product.

[0030] Typically, calculating solutions for the first and / or second parts of an electronic structure representation during iteration involves computational steps as described above regarding the solution of the first and / or second parts of the electronic structure representation. Specifically, calculating solutions for the first and / or second parts of an electronic structure representation during iteration involves the following steps: providing the first and / or second parts of the electronic structure representation, which include or indicate the corresponding electronic orbitals for the current iteration step; enabling a quantum computer and / or a classical computer to perform the quantum mechanical and / or classical computations as described above; and calculating the solutions for the first and / or second parts of the electronic structure representation as described above. The initial electronic orbitals for the first iteration step are typically predetermined, for example, based on user experience, known approximate solutions to the electronic structure representation (e.g., calculated using Hartley-Fock calculations), or based on theoretical considerations (e.g., based on corresponding physical assumptions or approximate solutions to similar electronic structure representations). During iterations of each iteration step, the electronic orbitals can be adapted based on predetermined rules (e.g., based on corresponding physical relations or insights that can be expressed and implemented as corresponding rules), or can even be arbitrarily modified by modifying one or more parameters affecting the corresponding electronic orbitals. Furthermore, during the iterative steps, only one electron orbital may be modified, or multiple electron orbitals may be modified simultaneously. Preferably, quasi-Newton methods, gradient descent methods, or gradient-free methods (such as the Nelder-Mead method) are used to modify the corresponding electron orbitals based on the results of the corresponding iterative steps. Typically, optimization is performed against a given criterion, which may depend on the corresponding quantity to be optimized and also on the corresponding characteristics or application for which the electronic structure representation should be solved. For example, if the quantity refers to the energy of the electronic structure defined by the electronic structure representation, the criterion may refer to the minimization of that energy and may be based on, for example, the following determination: if the deviation between the energies determined between subsequent iterative steps is less than a predetermined threshold, then the minimum energy has been reached. In particular, it is preferred that the criterion refers to the iteration converging to the minimum energy. Furthermore, the criterion may also include a termination criterion indicating that the iteration will be terminated if the termination criterion is met. For example, the termination criterion may refer to a predetermined number of iteration steps, where if the predetermined number of iteration steps is exceeded, it can be considered that an efficient solution to the electronic structure problem cannot be found during the iteration, and the iteration will be terminated.

[0031] Preferably, as described above, the quantity refers to the energy of the electronic structure defined by the first and / or second parts of the electronic structure representation, respectively, wherein iteration refers to minimizing the energy of the electronic structure to solve for the electronic structure representation. Typically, the electronic structure (i.e., the electrons and their interactions provided in the different electron orbitals of an atom, molecule, crystal, or amorphous solid) defines the electronic structure representation. Thus, energy refers to the total energy of the electronic structure and includes the kinetic energy of the electrons, the energy of the Coulomb interactions between electrons, and the energy of the Coulomb interactions between electrons and the atomic nucleus. In particular, the total energy can be mathematically defined as the expected value of the corresponding Hamiltonian used.

[0032] In embodiments, the electronic structure representation providing unit is adapted to determine, based on the electronic structure of the chemical product, the division of the electronic structure representation into a first part and a second part. Preferably, the electronic structure representation providing unit is adapted to determine the division of the electronic structure representation into a first part and a second part before providing the electronic structure representation. In particular, this determination can be performed fully or partially automatically. For example, predetermined rules can be automatically applied to the electronic structure representation to determine the first and second parts. Furthermore, the determination may also include a human-computer interaction process. For example, the electronic structure representation providing unit can use a first predetermined rule to determine the first and / or second parts, and then present the determined first and / or second parts to a user. The user can then provide further information as input, which can then be taken into account during the division, and / or the user can modify the determined first and second parts based on his / her experience. Typically, the electronic structure representation providing unit can be adapted to determine the division not only based on the electronic structure representation itself but also based on, for example, further information provided by the user.

[0033] Typically, the electronic structure representation of a chemical product provides information about the electronic structure of the corresponding chemical product. Based on the available information about the chemical product, particularly based on electronic structure information, active space selection processes can be used to determine whether the problem is divided into first and second parts. These active space selection processes utilize information on electron orbital entanglement and single orbital entropy, which is calculated by, for example, density matrix renormalization group (DMRG) methods or other correlation methods (including exact and approximate full configuration interaction schemes). Furthermore, localization processes, population analysis, valence active space (AVAS) processes, and / or natural orbital occupancy can also be used to determine whether the problem is divided into first and second parts. Typically, the electronic structure representation provides information about the correlations between electron orbitals, or at least about hypothetical correlations between electron orbitals, which can then be used to determine whether the electronic structure representation is divided into first and second parts. Therefore, it is preferable that the division of the electronic structure representation is based on chemical product information indicating the correlations between electrons occupying different electron orbitals, particularly information indicating electron orbital entanglement and electron orbital entropy. Additionally or alternatively, the electronic structure representation providing unit is adapted to determine the division of the problem into a first part and a second part of the electronic structure representation based on the number of quantum elements in the quantum computer. In the context of this invention, a quantum element can refer to a physical quantum element implemented and manipulated in the physical implementation of a quantum computer, but can also refer to a logical qubit representing a logical representation of one or more physical quantum elements. For example, a logical qubit can include more than one physical quantum element, wherein some of the physical quantum elements of the logical qubit are used for, for example, error correction. Preferably, the division of the problem is determined based on the number of available quantum elements. The number of available quantum elements takes into account that, according to the corresponding quantum algorithm used to perform quantum mechanical computations, at least some of the physical quantum elements, as well as the logical qubit, must be used for other purposes, such as error correction, boson field representation, etc. In some cases, some quantum elements are idle in quantum mechanical computations because, for a particular algorithm, increasing the number of quantum elements used would lead to unacceptable error rates, etc. Furthermore, the partitioning of the electronic structure representation preferably also takes into account information about the physical characteristics of the quantum computer hardware, such as the type of quantum computer used, the general error rate of the corresponding quantum computer, the error rate of quantum operations, the mass of the quantum elements of the quantum computer, or the general topology of the quantum computer. Preferably, the number of quantum elements of the quantum computer, particularly the number of available quantum elements to be used for the quantum mechanical calculations in the first and / or second parts, determines the maximum number of variables that are considered to belong to the first and / or second parts of the electronic structure representation during the partitioning.In particular, if the variable refers to electron orbitals, the number of quantum elements, especially the number of usable quantum elements, preferably determines the maximum number of electron orbitals considered as part of, for example, a first part of the active space. This allows for a partition of the electronic structure representation that optimally utilizes the advantages of the quantum computers available for computation, while mitigating the disadvantages of current and near-term quantum computer computations, such as high error rates or a correspondingly limited number of qubits, which may necessitate dividing the electronic structure representation into its own feasible subproblems.

[0034] In an embodiment, the reference state is represented by configuration interaction basis states and coefficients associated with these basis states, which are given by a fixed distribution of electrons among electron orbitals. The configuration interaction basis states and coefficients can be used to generate a superposition of electron configurations that mathematically represent the solutions for the first part and the solutions for the second part. For example, the reference state can be represented by a wavefunction described by a linear combination of Slater determinants representing the configuration interaction basis states, where the weights of the Slater determinants represent the configuration interaction coefficients. In this case, the configuration interaction basis states can be constructed from a set of orthogonal spin orbitals. In the example, the first part of the problem can be solved, for example, using a corresponding configuration interaction method that directly provides a wavefunction as a solution based on the configuration interaction basis states and the corresponding coefficients. The second part can then be integrated into this configuration interaction solution of the first part to provide the corresponding reference state.

[0035] In one embodiment, determining the reference state based on the solution of the first part and the solution of the second part includes controlling a quantum computer to generate a representation of the solution of the first part on the quantum computer, wherein the reference state is determined based on the representation of the solution of the first part on the quantum computer. In this embodiment, the state generated on the quantum computer to solve the first part can be considered equivalent to the state in the active space of the reference state of the corresponding described molecule. Therefore, the quantum computer solution directly provides a representation of the active space portion of the reference state on the quantum computer. This control may include, for example, using a phase estimation algorithm or a noisy isoscale quantum (NISQ) algorithm (such as a variable quantum eigenvalue solver (VQE)) to generate the solution of the first part, which can be used to prepare the representation of the active space of the reference state.

[0036] In an embodiment, determining the reference state includes determining the overlap between the solution prepared on the quantum computer and the corresponding configuration interaction ground states to determine the coefficients. The overlap between the solution prepared on the quantum computer and the corresponding configuration interaction ground states can refer to projecting the solution prepared on the first part onto the corresponding configuration interaction ground states. For this purpose, a corresponding projection operation can be used. Based on the projection, the absolute values ​​of the configuration interaction coefficients can be determined, for example, in the form of absolute squares. Furthermore, the phase can also be determined, for example, determining the sign of the coefficients. This allows the representation of the corresponding reference state to be reconstructed on any suitable computer hardware to be used to solve the interaction representation.

[0037] Preferably, determining the overlap includes: measuring a representation of the solution of the first portion on the quantum computer, the representation corresponding to the distribution of these electrons in the active space among these electron orbitals; determining the corresponding coefficients associated with these configuration interaction ground states based on the measurement results; repeating the process until predetermined conditions are met to generate a histogram of the coefficients of the measured configuration interaction ground states; and determining the reference state based on the histogram. For example, the process can be repeated until the generated histogram converges with a predetermined accuracy for the corresponding coefficients of the histogram. However, other conditions can also be used to determine the number of repetitions, for example, a predetermined fixed number of repetitions can be used to limit the computational resources used. Since the reference state representation on the quantum computer refers to quantum states, it is based on a superposition of multiple possible quantum states corresponding to configuration interaction ground states. If sufficient repetitions are performed, the superposition can be determined by utilizing a histogram that reflects the contribution of the weights of the different quantum states, mathematically represented as contributing to the superposition. The weights are mathematically the squares of the absolute values ​​of the configuration interaction coefficients and can be determined based on the histogram. The absolute value of the configuration interaction coefficient can then be determined based on the square of the determined absolute value.

[0038] Preferably, the reference state is determined based on the representation of the solution in the first part on the quantum computer by applying a projection operator to the representation of the solution in the first part, projecting the representation of the solution in the first part onto the corresponding representation of the configuration interaction ground states, and measuring these resulting states on the quantum computer based on the histogram. The measurement of the resulting states refers to measuring the projection operator on the corresponding state as an observable, which means measuring the square of the absolute value of the configuration interaction coefficients. For example, the histogram is determined as described above, and based on the histogram, it is determined which configuration interaction ground states are determined most frequently, i.e., above a predetermined threshold or cutoff value. Then, the projection measurement as described above is performed on the determined configuration interaction ground states to determine the coefficients.

[0039] In an embodiment, the reference state can be mathematically represented by the following equation.

[0040]

[0041] in, It is the base state of configuration interactions, and These are the configuration interaction coefficients, where the index... Iterate through all possible electron distributions between electron orbitals in the active space.

[0042] Preferably, the correlation computation unit is configured to enable a quantum computer to prepare a representation of the reference state on the quantum computer, and to entangle quantum elements representing the correlation between the active space and the inactive space to provide a solution to the interaction representation. Thus, the correlation within the active space and / or inactive space and / or between the active space and the inactive space is determined by entanglement of quantum elements representing corresponding correlated electron orbitals on the quantum computer. The entangled quantum elements can be part of the same quantum computer or part of different quantum computers—for example, when the solutions for the first part and the second part are prepared as reference states on different quantum computers. In an embodiment, a solution to the interaction representation is provided by preparing a representation of the first part of the solution on a first quantum computer and a representation of the second part of the solution on a second quantum computer, and by performing quantum computation on the interaction representation, wherein quantum elements of the first quantum computer and quantum elements of the second quantum computer are entangled to represent the correlation between the active space and the inactive space. Preferably, a unitary correlation simulation, more preferably a unitary coupled cluster simulation, is combined with a variable quantum eigenvalue solver to provide a solution to the interaction representation. The variable quantum eigenvalue solver changes the parameters of the specific assumptions used to minimize the energy of the state produced by applying operators representing the assumptions used to the corresponding reference state, where the solution represented by the interaction is the corresponding state with the minimum energy.

[0043] In an embodiment, the interaction representation includes correlations between electron orbitals, at least one of which belongs to the inactive space, by projecting the reference state onto one or more predetermined configuration interaction basis states and generating the solution based on the result of the projection. Typically, the solutions for the first and second parts refer to superpositions of electron configurations. The correlation can be approximated by considering one or more of these configurations (i.e., only one or more predetermined states) and determining the correlation based on the corresponding configuration. Preferably, a customized coupling cluster method is used to generate the solution of the interaction representation. For example, the customized coupling cluster method can be used to incorporate dynamic correlations within the inactive space and / or between the active and inactive spaces into the interaction representation. The advantage of this method is that it can be executed on a classical computer and still provides reasonably accurate results.

[0044] In the embodiment, the correlation between electron orbitals is incorporated into the interaction representation using the random strong contraction second-order n-electron valence state perturbation theory method, where at least one of these electron orbitals belongs to the inactive space.

[0045] In an embodiment, the solution determination unit and the associated computation unit are configured to enable the quantum computing system to compute solutions to the first part, the second part, and / or the interaction representation, wherein the quantum computing system includes at least two quantum computers with different fidelities, and wherein the solution determination unit and the associated computation unit are configured to assign the computation of solutions to the first part, the second part, and / or the interaction representation to the at least two quantum computers based on the fidelity of the respective at least two quantum computers.

[0046] Quantum computer fidelity is a measure of the quality at which a quantum computer performs a corresponding quantum computation (e.g., the operations of an algorithm executed during a quantum computation, such as a quantum gate). Quantum computer fidelity can be based on quantum gate fidelity and / or decoherence time. A quantum gate is a fundamental quantum operation typically generated by applying one or more control pulses to a corresponding small number of qubits. Multiple quantum gates construct quantum circuits and can therefore be considered analogous to classical logic gates used to construct conventional digital circuits. Any multi-qubit operation can be generated from a series of single-qubit and two-qubit operations. In this context, fidelity measures the degree of similarity between a quantum gate implemented on quantum computer hardware and the theoretical quantum gate that should be implemented in the quantum computer. Thus, quantum gate fidelity measures the difference between a real operation performed by real hardware and a perfect theoretical operation. Decoherence time describes how long quantum information can be stored on the quantum computer before dissipating into the environment. Therefore, the decoherence time also affects the determined quantum gate fidelity, which is determined, for example, by all the small defects in the construction, calibration, and control of the quantum computer, and also based on the specific decoherence time of the quantum computer. Typically, the fidelity of a quantum computer can be determined using known methods and measurements, such as cross-entropy benchmarks, random benchmarks, or full quantum state tomography. More details on possible methods for determining fidelity can be found, for example, in the following literature: “Quantum supremacy using a programmable superconductance processor”, Arute, F., Arya, K., Babbush, R. et al., Nature 574, 505–510 (2019). In most cases, the fidelity will be provided as general information by the quantum computer provider.

[0047] For example, to enable a quantum computer to compute solutions for the first part, the second part, and / or the interaction representation, corresponding control signals can be generated and provided to the quantum computing system. Specifically, control signals can be generated such that fidelity determines on which of at least two quantum computers the solutions for the first part, the second part, and / or the interaction representation are computed. Therefore, the control signals are generated based on the fidelity of the corresponding at least two quantum computers. For example, the solution determining device can be configured to compute the solution for the first part on a quantum computer with high fidelity (e.g., fidelity above a predetermined threshold), and the associated computing unit can be configured to compute the solution for the interaction representation on a quantum computer with lower fidelity (e.g., fidelity lower than that of the quantum computer used to compute the interaction representation). Therefore, control signals can be generated such that the solutions for the first part, the second part, and / or the interaction representation are computed on the quantum computer with the most suitable fidelity among the available fidelities. Typically, where the control signals relate to controlling the quantum computing system, the control signals can be configured to, for example, control the manipulation portion of a quantum computer configured to manipulate the states of quantum elements according to a corresponding manipulation sequence. However, if the quantum computer itself already provides a control unit adapted to control the manipulation parts to manipulate the states of quantum elements, then the control signals can be adapted to control the quantum computer's control unit. In this case, for example, the control signals could simply refer to a representation of a series of manipulations that can be interpreted by the quantum computer's control unit to provide corresponding control signals to control the various parts of the quantum computer accordingly. However, in this case, the control signals could also refer to well-known and interpretable control signals that are converted by the quantum computer's control unit into corresponding dedicated control signals for controlling the specific hardware of the quantum computer.

[0048] In an embodiment, at least two quantum computers in the quantum computer are configured to be mutually entangled, and control signals can be generated to further control the entanglement between the at least two quantum computers in the quantum computing system during parallel quantum computing of the solutions represented in the first, second, and interaction parts. The entanglement between the two quantum computers is defined as at least one quantum element of each quantum computer being mutually entangled. Entanglement between the two quantum computers can be achieved, for example, by configuring the quantum computers such that at least one quantum element of one quantum computer can interact with at least one quantum element of the other quantum computer. To achieve this, a photonic link or a corresponding entanglement bus or another qubit can be utilized. The details of the implementation depend heavily on the properties of the respective quantum computer (e.g., a superconducting quantum computer, a trapped ion quantum computer, a photonic quantum computer, etc.). The quantum states of the entangled quantum elements are interdependent, such that these quantum elements can only be described together as if they were a single object. This state dependency of the entangled quantum elements enables the distribution and sharing of information between at least two quantum computers during quantum computing, during which the states of the quantum elements used in the quantum computing are changed, for example, due to corresponding quantum operations performed during the quantum computing. Therefore, an operation performed on one quantum element in an entangled quantum element will also affect the state of the other quantum element in the entangled quantum element, thus affecting the computation on another quantum computer. In this way, the basic operations, intermediate results, and final results of a quantum computation performed on a first quantum computer can directly (i.e., without needing to be read and processed by a classical computer and then prepared on another quantum computer) affect the quantum computation on another quantum computer. This enables truly parallel computation of solutions to interdependent first, second, and interaction representations. Furthermore, entanglement allows solutions to the first and / or second parts to be directly transferred to another quantum computer (e.g., without utilizing a classical computer in between) to generate a reference state as the starting point for computing solutions to the interaction representation. To achieve entanglement, different hardware solutions can be utilized depending on the corresponding type of quantum computer. For example, for superconducting-based quantum computers, waveguides and transmission lines can be utilized, as described, for example, in the following article: "Quantum computer with superconducting circuits in the ultrastrong coupling regime", Stassi, R., Cirio, M. & Nori, F., Scalable, npj Quantum Inf [npj Quantum Information] 6, 67 (2020), which is incorporated herein by reference.Furthermore, photonic links as described in the following article: “Modular entanglement of atomic qubits using photons and phonons”, Hucul, D., Inlek, I., Vittorini, G. et al., Nature Phys. 11, 37–42 (2015), which is incorporated herein by reference. For ion trap-based quantum computing architectures, ions can be transported between corresponding quantum computers, as disclosed in the following article: “A high-fidelity quantummatter-link between ion-trap microchip modules”, Akhtar, M., Bonus, F., Lebrun-Gallagher, FR et al., NatCommun [Nature Communications] 14, 531 (2023); or electron shuttle can be used, as described in the following article: “Conveyor-mode single-electron shuttling in Si / SiGe for a scalable quantumcomputing architecture”, Seidler, I., Struck, T., Xue, R. et al., npj Quantum Inf [npj Quantum Information] 8, 100 (2022); both articles are incorporated herein by reference.

[0049] In this embodiment, solutions to the first part, the second part, and / or the interaction representation can be generated based on the fidelity of the quantum computing system. For example, if a higher-fidelity quantum computer is available, the first part can be extended to encompass more electron orbitals that can be computed on the higher-fidelity quantum computer. Higher fidelity can be considered relative to: a) the fidelity of at least one of the at least two quantum computers, b) the fidelity of all other quantum computers among the at least two quantum computers, and / or c) a predetermined fidelity threshold. Lower fidelity can be considered relative to: a) the fidelity of at least one of the at least two quantum computers, b) the fidelity of all other quantum computers among the at least two quantum computers, and / or c) a predetermined fidelity threshold. In this example, the first part requires higher solution accuracy because it is more critical to solving the problem. Further, the control signals can be generated based on the computational algorithm to be used to solve the first part, the second part, and / or the interaction representation, wherein the computational algorithm to be used determines the fidelity threshold of the quantum computer on which the computational algorithm can be executed. For example, computational algorithms typically executed on high-fidelity quantum computers (because they are associated with a higher fidelity threshold) can refer to quantum Fourier transforms, quantum phase estimation, Grover-type search algorithms, Shor-type decomposition algorithms, and Harrow-Hassidim-Lloyd-type algorithms. Examples of relevant computational algorithms for lower-fidelity quantum computers (because they are associated with a lower fidelity threshold compared to the algorithms mentioned above) are variational algorithms, such as variational quantum eigenvalue solvers and quantum approximation optimization algorithms. Furthermore, the distribution of solutions to the first, second, and / or interaction representations can also be based on the number of logical quantum elements provided by at least two corresponding quantum computers. Logical quantum elements are quantum elements that can be manipulated during quantum computing. For example, depending on the quantum algorithm used, some quantum elements are used as auxiliary quantum elements and therefore cannot be used to represent the quantities and aspects of the corresponding subproblems. Additionally, considering the number of logical quantum elements on the corresponding quantum computers when deriving subproblems allows for a specific adaptation of the subproblems to the corresponding quantum computers on which they are to be computed, thereby allowing for the computation of subproblems on the corresponding quantum computers using more efficient and effective quantum algorithms.

[0050] In one embodiment, the quantum computing system includes at least one fault-tolerant quantum computer and a noisy intermediate-scale quantum computer, wherein the fault-tolerant quantum computer has higher fidelity than the noisy intermediate-scale quantum computer. Noisy intermediate-scale quantum computers are typically sensitive to their environment and prone to quantum decoherence, meaning they can only apply a limited number of gates or operations before accumulating too many errors (causing too much information to be lost due to noise and rendering computation meaningless). This limits the number of operations and, therefore, also limits the size and complexity of subproblems that can be computed on such a quantum computer. Fault-tolerant quantum computers perform quantum computations with a physical error rate below a predetermined threshold defined by the quantum threshold theorem, such that the logical error rate can be suppressed to arbitrarily low levels by applying quantum error correction. This allows for arbitrarily long quantum computations, i.e., allows for the application of an arbitrary number of gates and operations, resulting in higher computational precision and accuracy and allowing for the computation of more complex subproblems with more variables. Fault-tolerant quantum computers can be implemented by applying quantum error-correcting codes that utilize at least three physical quantum elements to represent a logical qubit. An example is the surface code described in the following article: “Google Quantum AI. Suppressing quantum errors by scaling asurface code logical qubit”, Nature 614, 676–681 (2023). However, other codes that utilize this principle also exist. Many of these error-correcting codes are only applicable to quantum computers with a correspondingly high number of qubits. However, there are also codes that use only three physical quantum elements to represent a logical qubit, such as Steane codes. These codes may not enable fully fault-tolerant quantum computers in all cases, but they significantly improve fidelity and therefore allow for the realization of quantum computers with even higher fidelity.

[0051] In another aspect of the invention, an apparatus for generating properties associated with a chemical product, wherein the chemical product comprises one or more molecular structures, wherein the apparatus comprises: i) an electronic structure representation providing unit for providing an electronic structure representation associated with the molecular structure of the chemical product, the electronic structure representation comprising a) a first portion of the electronic structure representation indicating an active space comprising a portion of the electronic structure associated with the molecular structure, and b) a second portion of the electronic structure representation indicating an inactive space comprising another portion of the electronic structure associated with the molecular structure, wherein the properties associated with the chemical product depend on the active space and the inactive space; ii) a solution determining unit for causing a quantum computer or a classical computer to generate and provide a solution for the first portion of the electronic structure representation, and causing a quantum computer or a classical computer to generate and provide a solution for the second portion of the electronic structure representation; and iii) An associative computational unit is configured to generate a solution to the electronic structure representation by combining the solution of the first part and the solution of the second part, wherein the solution of the first part and the solution of the second part are computationally combined to generate properties associated with the chemical product, wherein the computational combination includes generating an interaction representation based on a reference state associated with the superposition of electronic configurations generated based on the solution of the first part and the solution of the second part, and enabling a classical computer and / or a quantum computer to provide a solution to the interaction representation.

[0052] In another aspect of the invention, an apparatus for generating properties associated with a chemical product, wherein the chemical product comprises one or more molecular structures, wherein the apparatus comprises: i) an electronic structure representation providing unit for providing an electronic structure representation associated with the molecular structure of the chemical product, the electronic structure representation comprising a) a first portion of the electronic structure representation indicating an active space comprising a portion of the electronic structure associated with the molecular structure, and b) a second portion of the electronic structure representation indicating an inactive space comprising another portion of the electronic structure associated with the molecular structure, wherein the properties associated with the chemical product depend on the active space and the inactive space; ii) a solution determining unit for enabling a quantum computer to generate and provide a solution for the first portion of the electronic structure representation, and for enabling a classical computer to generate and provide a solution for the second portion of the electronic structure representation; and iii) An associative computational unit is configured to generate a solution to the electronic structure representation by combining the solution of the first part and the solution of the second part, wherein the solution of the first part and the solution of the second part are computationally combined to generate properties associated with the chemical product, wherein the computational combination includes generating an interaction representation based on a reference state associated with the superposition of electronic configurations generated based on the solution of the first part and the solution of the second part, and enabling a classical computer and / or a quantum computer to provide a solution to the interaction representation.

[0053] In another aspect of the invention, a system for generating properties associated with chemical products is proposed, wherein the system comprises: a) a quantum computer adapted to perform quantum mechanical calculations, and b) the apparatus as described above, wherein the apparatus is adapted to enable the quantum computer to perform quantum mechanical calculations.

[0054] In another aspect of the invention, a computer-implemented method is provided for generating properties associated with a chemical product, wherein the chemical product comprises one or more molecular structures, wherein the method comprises: i) providing an electronic structure representation associated with the molecular structure of the chemical product, and comprising a) a first portion of the electronic structure representation indicating an active space comprising a portion of the electronic structure associated with the molecular structure, and b) a second portion of the electronic structure representation indicating an inactive space comprising another portion of the electronic structure associated with the molecular structure, wherein the properties associated with the chemical product depend on the active space and the inactive space, ii) causing a quantum computer and / or a classical computer to generate and provide a solution for the first portion of the electronic structure representation, and causing a quantum computer and / or a classical computer to generate and provide a solution for the second portion of the electronic structure representation, and iii) The solution to the electronic structure representation is generated by combining the solution of the first part and the solution of the second part, wherein the solution of the first part and the solution of the second part are computationally combined to generate properties associated with the chemical product, wherein the computational combination includes generating an interaction representation based on a reference state associated with the superposition of electronic configurations generated based on the solution of the first part and the solution of the second part, and enabling a classical computer and / or a quantum computer to provide a solution to the interaction representation.

[0055] In another aspect of the invention, a computer program product for generating properties associated with a chemical product is provided, wherein the computer program product includes program code means for causing the apparatus described above to perform the method described above.

[0056] In another aspect of the invention, the apparatus described above is proposed for use in generating at least one of the following: chemical reactivity, spectra and spectral properties, and molecular properties that can be calculated and deduced from the electronic structure of a chemical product.

[0057] In another aspect of the invention, the apparatus described above is proposed for use in generating organometallic compounds containing transition metals (including lanthanides and actinides), chelating agents that interact with metals, catalysts, biomolecules with active centers, macromolecular systems, and transition metal compounds in solution or embedded in the environment.

[0058] In another aspect of the invention, the use of the apparatus described above for determining the activation energy and / or reaction energy of a predetermined chemical reaction is proposed. Preferably, the apparatus described above is used to generate the activation energy and / or reaction energy of a predetermined chemical reaction as a characteristic. Generally, activation energy refers to the energy difference between the transition state and the reactant. Reaction energy refers to the energy difference between the product and the reactant. The chemical reaction may be part of a complex reaction network, such as part of a catalytic cycle. The use of the apparatus described above is particularly advantageous when at least one chemical substance in the reaction system a) contains one or more transition metal atoms, lanthanide atoms, and / or actinide atoms having unpaired electrons, or b) exhibits an electronic structure with a small energy gap between occupied and unoccupied electron orbitals, i.e., the energy gap is equal to or less than the gap of at least one molecule of ozone, pentane, or p-quinone dimethane calculated using the same electronic structure method (i.e., the same basis set, the same self-consistent field (SCF) method, such as Hartley-Focke et al.), or c) exhibits a multi-reference diagnostic exceeding a predetermined limit, for example, (CCSD) greater than 0.02 and / or (CCSD) greater than 0.05 and / or (MP2) greater than 0.04 and / or (MP2 / CCSD) greater than 0.18 and / or Greater than 0.1 and / or %TAE greater than 10, where, The diagnosis is based on the Frobenius norm of the single-excitation amplitude of the CCSD wavefunction based on the Hartley-Fock reference state, determined by scaling the square root of the number of correlated electrons in the CCSD calculation, and where, The diagnosis is determined based on the matrix 2-norm of the single-excitation amplitude of the CCSD or MP2 wavefunction based on the Hartley-Fock reference state, and where, Diagnosis similar to The diagnosis was made, but involved double excitation, and in which, The diagnosis is determined based on orbital entanglement information obtained from approximate correlated wave functions (such as partially convergent but qualitatively correct density matrix renormalization group (DMRG) wave functions), and %TAE diagnosis is determined based on the difference between the total atomization energy obtained by CCSD(T) and CCSD relative to the total atomization energy obtained by CCSD(T).

[0059] In one aspect of the invention, the apparatus described above is proposed for generating properties related to the activation energy of a predetermined catalytic cycle and / or for determining the reaction energy of a predetermined chelating agent.

[0060] In one aspect of the invention, an apparatus for determining the technical application characteristics of a chemical product is provided, wherein the apparatus comprises: a) an input unit configured to receive an electronic structure representation associated with one or more molecular structures of the chemical product; b) the apparatus as described above; and c) a characteristic determination unit configured to generate technical application characteristics based on solutions of interaction representations of one or more molecular structures.

[0061] In another aspect of the invention, a computer-implemented method for determining the technical application characteristics of a chemical product is proposed, wherein the method comprises: a) receiving an electronic structure representation associated with one or more molecular structures of the chemical product; b) providing a solution of the interaction representation using the means described above; and c) generating technical application characteristics based on the solution of the interaction representation of one or more molecular structures.

[0062] In another aspect, a computer program product for determining the technical application characteristics of a chemical product is proposed, wherein the computer program product includes program code means for causing the apparatus described above to perform the method described above.

[0063] In another aspect of the invention, an apparatus for determining a target chemical product including a target technical application characteristic is provided, wherein the apparatus comprises: a) a target characteristic providing unit configured to provide a target technical application characteristic and a potential chemical product; b) a characteristic determining unit configured to determine the technical application characteristic of the potential chemical product using the apparatus and / or the method described above; c) an iteration unit configured to compare the determined technical application characteristic of the potential chemical product with the target technical application characteristic, and based on the comparison: i) determining the potential chemical product as the target chemical product, or ii) providing a new potential chemical product and repeatedly determining the technical application characteristic using the new potential chemical product; and d) a control data generating unit configured to generate control data for producing the determined target chemical product.

[0064] In another aspect of the invention, a computer-implemented method is provided for determining a target chemical product including target technical application characteristics, wherein the method includes: a) providing target technical application characteristics and a potential chemical product; b) determining the technical application characteristics of the potential chemical product using the apparatus and / or the method described above; c) comparing the determined technical application characteristics of the potential chemical product with the target technical application characteristics, and based on the comparison: i) determining the potential chemical product as the target chemical product, or ii) providing a new potential chemical product and repeatedly determining the technical application characteristics using the new potential chemical product; and d) generating control data for producing the determined target chemical product.

[0065] In another aspect, a computer program product for determining a target chemical product including the characteristics of a target technology application is proposed, wherein the computer program product includes program code means for causing the apparatus described above to perform the method described above.

[0066] Examples of properties that can be advantageously generated in this invention include calculating the ground-state energy of molecules or general electronic systems. Specifically, this allows for the prediction of the final products of a reaction, the thermodynamic properties of the reaction, and the kinetic properties of the reaction in the context of determining the ground-state energies of all molecular species present in a chemical reaction. This understanding and reaction characteristics can then be used again to optimize chemical production processes, predict the microstructure of polymers, optimize material properties, and so on. Furthermore, the generated properties can also refer to the multipole moments of chemical products. Such calculations can be relevant to determining properties of chemical products related to electrical and other technical applications (e.g., the dielectric behavior of the chemical product), and also to determining properties arising from intermolecular interactions that strongly depend on the polarity of the chemical product—the range of which can be from solubility and compatibility with certain media to ionic complexation behavior or effects on spectral properties (e.g., color).

[0067] Specifically, providing a target application characteristic can refer to an application, for example, receiving the target application characteristic from user input via a corresponding input unit. Furthermore, this provision can also refer to accessing a storage unit that already stores the target application characteristic and providing that target application characteristic. Further, the provision can also include, for example, receiving the target application characteristic from another source via a network connection, and providing the received target application characteristic. Typically, a target application characteristic can refer to a target value, such as the specific hardness of a chemical product, or it can refer to a range of values ​​that the chemical product should meet. Moreover, a target application characteristic can refer to any kind of objective function, for example, a time series of characteristics under varying environmental conditions, such as hardness under varying temperature conditions. Such more complex target application characteristics can be advantageous when the application of the chemical product involves different environmental conditions (e.g., different temperatures). Then, a target chemical product refers to a chemical product that provides the corresponding target technical application characteristic (i.e., satisfying the target technical application characteristic within predetermined limits) when provided in a corresponding form (e.g., as a pure substance or a mixture). Specifically, when produced according to a corresponding formulation, the target chemical product provides the corresponding target technical application characteristic.

[0068] The potential chemical product can be provided in any digitally representable format, such that the potential chemical product and / or its properties can be processed by the device. Furthermore, providing the potential chemical product may also include providing a corresponding electronic structure representation for determining the technical application characteristics of the potential chemical product. However, the corresponding electronic structure representation can also be automatically selected, for example, by the device based on the potential chemical product and the provided target technical application characteristics. However, for example, a user may also select the corresponding electronic structure representation based on the potential chemical product and / or the target technical application characteristics, preferably based on a selection of multiple possible electronic structure representations presented to the user.

[0069] Comparing the determined technical application characteristics with the target technical application characteristics allows for the determination of whether the determined technical application characteristics meet predetermined criteria, such as whether the determined technical application characteristics conform to the target technical application characteristics within predetermined limits. If such criteria are met, the potential target chemical product is identified as the target chemical product, and the method proceeds to the next step. However, if the comparison indicates that the determined technical application characteristics do not conform to the target technical application characteristics within predetermined limits, a next iterative step utilizing a new potential chemical product must be performed. In particular, for each iterative step, a new potential chemical product is preferably determined based on previous potential chemical products, for example, by modifying one or more characteristics (e.g., one or more components or other properties) of the previous chemical product. However, new potential chemical products can also be generated, for example, by arbitrarily selecting new potential chemical products from a large number of previously generated potential chemical products. Furthermore, more sophisticated methods can be used to select new potential chemical products from multiple previously generated potential chemical products. Based on new potential chemical products, in each iteration step, a quantum computer is again used to determine the technical application characteristics, and these determined technical application characteristics are again compared with the target technical application characteristics. This comparison can lead to further iteration steps, or, if the corresponding criteria are met, a new potential chemical product can be selected as the target chemical product. Furthermore, additional termination criteria for iteration can be selected; for example, the number of iteration steps before termination can be determined, and the user can be notified that no target chemical product for the corresponding target technical application characteristics can be found. Alternatively, after a predetermined number of iteration steps, the method can further include, for example, modifying the target technical application characteristics by increasing predetermined constraints around them and repeating iterations while utilizing the increased constraints during comparisons. This allows for finding as many target chemical products as possible that conform to the target technical application characteristics, even if it may be impossible to meet the original target. After determining the target chemical product as described above, the target chemical product can be provided to the user, for example, via an output unit. Preferably, control data is generated using the formulation of the target chemical product, which can be used to control the production system for producing the target chemical product.

[0070] It should be understood that the apparatus, method, system and computer program product described above have similar and / or identical preferred embodiments, particularly as defined in the dependent claims.

[0071] It should be understood that the preferred embodiments of the present invention may also be any combination of the dependent claims or the above embodiments and the corresponding independent claims.

[0072] These and other aspects of the invention will become apparent and will be illustrated with reference to the embodiments described below. Attached Figure Description

[0073] In the attached diagram:

[0074] Figure 1 The state representation of qubits used in quantum computing devices is demonstrated.

[0075] Figure 2 A schematic example of a quantum computing device using qubits as the computing unit is shown.

[0076] Figure 3 A schematic example method is shown for generating control signals to perform operations on a quantum computing device and for processing measurement signals from a quantum computing device.

[0077] Figure 4 A schematic example of a hybrid system including classical and quantum computing devices is shown.

[0078] Figure 5 A schematic example of a superconductor-based quantum computing device is shown.

[0079] Figure 6 A schematic example of a quantum computing device based on trapped ions is shown.

[0080] Figure 7 An embodiment of a system for generating properties associated with chemical products is illustrated schematically and exemplary.

[0081] Figure 8 A flowchart illustrating, and exemplarily demonstrating, is provided for a method of generating properties associated with a chemical product.

[0082] Figure 9 Examples of quantum computing systems with quantum computers of varying fidelity are illustrated schematically and exemplaryly.

[0083] Figure 10 , Figure 11 A flowchart illustrating, and demonstrating, an exemplary implementation of a computation method on a quantum computer system is shown.

[0084] Figure 12 An illustration of an electron orbital energy diagram is shown schematically and exemplary.

[0085] Figure 13 A schematic and exemplary quantum circuit diagram of Hadamard overlap measurement is shown.

[0086] Figure 14An overview of different embodiments of methods using quantum computer systems is illustrated schematically and exemplary, and

[0087] Figures 15 to 17 Further applications of the method for determining solutions are illustrated schematically and exemplary. Detailed Implementation

[0088] The following section first briefly introduces the general principles of quantum computers and their computational performance. Furthermore, the general principles can also be found in the following literature: "Quantum Computation and Quantum Information: 10..." th Anniversary Edition [Quantum Computing and Quantum Information: 10th Anniversary Edition]”, MANielsen and IL Chuang (2010).

[0089] Classical computing devices use transistor-based processors. Each transistor has two controllable states, 1 or 0, representing digital binary or bits. To perform operations on a classical computing device, human-readable program code is translated into machine-readable instructions by a compiler. Machine-readable instructions are control signals for each transistor, such as voltage settings. The representation of machine-readable instructions can include binary or hexadecimal representations. Based on these machine-readable instructions, operations are performed on the processor of the classical computing device.

[0090] Quantum computing is a relatively new method of computation that uses quantum effects, such as superposition and entanglement, to perform certain calculations more efficiently than classical digital computers. Unlike digital computers, which represent information in bits (e.g., "1" or "0") as described above, quantum computing devices (i.e., quantum computers) use qubits (quantum bits) to represent information. Quantum computing devices are based on quantum elements that follow quantum mechanics, such as superconductors, ions, atoms, quantum dots, photons, particle spin, bosons, etc. These quantum elements can be manipulated in a controlled manner to perform operations.

[0091] Although qubits and their manipulation can be described according to their mathematical properties, each such qubit can be implemented in any of a variety of different ways in physical quantum elements. Examples of such quantum elements include superconducting materials, trapped ions, photons, optical cavities, single electrons trapped in quantum dots, point defects in solids (e.g., phosphorus donors in silicon or nitrogen-vacancy centers in diamond), molecules (e.g., alanine-vanadium complexes), or any medium exhibiting qubit behavior, which includes quantum states and transitions between them that can be controlled to sense or detect.

[0092] Typically, for any given physical quantum element that implements a qubit, any property of that physical unit can be chosen to implement the qubit. For example, if an electron is chosen to implement a qubit, the x, y, or z components of the electron's spin degree of freedom can be chosen as properties of that electron to represent the state of the qubit. For any particular degree of freedom, the physical quantum element can be controllably placed into a superposition or entangled state, and measurements can then be taken at the chosen degree of freedom to obtain a reading of the qubit value.

[0093] Compared to transistors in classical computing devices, each quantum element in a quantum computing device can not only take the form of a ground state... or Furthermore, arbitrary superposition of these basis states can also be used, such as states. The state of each quantum element is represented by the state of a quantum bit (qubit), such as... Figure 1 This is illustrated by the two-dimensional simplification. To represent such states, Dirac notation is commonly used in quantum mechanics. In Dirac notation, states in an n-dimensional complex vector space (such as Hilbert space) are represented by braket notation, for example, In conventional terminology, the superposition of "0" and "1" states in a quantum computing device can be represented as... The states "0" and "1", or bits, of a classical computing device are analogous to the ground states of a quantum computing device. and Or a quantum bit. Value This indicates that the quantum bit will The probability of being measured in a given state, and the value This indicates that the quantum bit will The probability of being measured in a given state. If there is more than one qubit, two or more qubits may become entangled. Entanglement means that the state of one qubit depends on the state of at least one other qubit, and vice versa. Furthermore, in an entangled state, the individual qubits can no longer be considered as separate qubits. Typically, in quantum computers... A register of qubits can be in a superposition of ground states simultaneously, and A classical bit register can only be in a single ground state at a time. Therefore, compared to classical computing devices on quantum computing devices, it is possible to manipulate and process data simultaneously. This allows for the creation of a base state, thereby achieving exponential intrinsic parallelism.

[0094] To perform operations on a quantum computing device, the computational methods used to solve a given problem can be translated into qubit manipulations, which in turn can be translated into control signals for manipulating the qubits. The representation of machine-readable instructions can include common quantum mechanical representations of operations in Hilbert space. Different representations of qubit states can be chosen depending on the specific implementation of the quantum computer. Any state preparation on a quantum computing device can be represented by manipulations acting on the qubit states. Manipulations can be translated into control signals to control corresponding parts of the quantum computer, depending on the type of quantum computing device used. Thus, based on manipulations acting on qubit states, operations can be performed on the quantum equivalent of a classical processor (as part of the quantum computing device).

[0095] In gate-based quantum computer systems, manipulation of a qubit's state typically involves one or more qubit operations. A qubit operation can change the state of a qubit, for example, changing it to a state similar to... Figure 1 The vectors shown The rotation corresponds to a specific superposition. For example, in a superconducting quantum computer, this can be achieved by microwave pulses, or in a trapped-ion quantum computer by irradiating ions with a laser beam. Multi-qubit operations can generate entanglement between two or more qubits. For example, in a superconducting quantum computer, this can be achieved by connecting qubits via an intermediate electrical coupling circuit, or in a trapped-ion quantum computer by controlling the collective vibration of trapped ions.

[0096] Typically, to prepare manipulations for solving a given problem, the corresponding quantum mechanical representation of the problem is converted into qubit manipulations, which are then performed to prepare a solution to the given problem. After the predetermined solution has been prepared, i.e., after the operations have been applied to the qubits of the quantum computer, a projection measurement is performed on all individual qubits, returning 0 or 1 for each qubit. This projection usually occurs on the qubits... In the characteristic basis, this characteristic basis is also used to define the computational ground states "0" and "1" of a qubit. This means that only one state can be measured simultaneously as "0" and "1". The product of Pauli operators can be directly transformed into operators of such operators. On quantum computing devices, this measurement is achieved by applying a series of hardware-specific readout protocols (including control pulses) that manipulate readouts and monitoring the response to those pulses. For example, a superconducting qubit can be coupled to a hardware resonator. Measuring the shift in the resonator frequency allows the determination of the qubit's state, as this shift depends on the state of the coupled qubit. For example, in the case of trapped ions, optical readout can be used; for instance, if the ions emit light, the qubit's state is 1, and if the ions do not emit light, the qubit's state is 0, and vice versa. In this way, qubits can be used to implement logic circuits or gates, as in classical computing devices.

[0097] exist Figure 2 The image shows a schematic example of a quantum computer. Figure 2 The quantum computing device 100 shown includes: a quantum register 104 configured to perform quantum computation, a manipulation section 106 configured to manipulate the quantum register (particularly the quantum elements forming qubits), and a readout section 108 configured to collect measurement signals from the quantum register 104 to read out the qubits after a quantum mechanical computation. Specifically, the manipulation section 106 provides manipulation signals for manipulating the quantum register, wherein these manipulation signals are generated based on received control signals determined based on corresponding operations to be performed on the qubits. In some embodiments, a feedback loop may be provided between the manipulation section 106 and the measurement section 108. In the case of a gate-based quantum computer, quantum computation, compared to classical computation (where one measurement cycle provides the state of a transistor), involves performing multiple measurement cycles to provide the probability density or probability of qubit states.

[0098] The quantum register 104 can be based on different quantum elements representing qubits. In some embodiments of gate-based quantum computers, qubits can be implemented as quantum elements by photons. Such an optical quantum computing device may include a laser that generates photons provided to a waveguide. A beam splitter may be provided for manipulating photon states based on a manipulation signal, such as mechanical rotation applied to a mirror. In this embodiment, the measurement section 108 may be a photon detector, and the measurement signal may be a photon.

[0099] In other embodiments of gate-based quantum computers, qubits can be implemented using the electronic states of ions trapped in a magnetic field. In this case, the manipulation section 106 can utilize a laser, and the manipulation signal can provide control laser pulses. Furthermore, in this case, the readout section 108 can be a photon detector combined with the readout laser pulse, and the measurement signal 102 can be a photon. Other qubit implementations can be based on superconductors as quantum elements, semiconductor materials with anyons as quantum elements, etc.

[0100] Figure 3 A schematic exemplary method is shown for generating control signals to perform manipulation on a quantum computing device and for processing measurement signals from the quantum computing device. In most embodiments of quantum computing devices known to date, the control signals for the quantum computing device are prepared on a classical computing device, and the measurement signals provided by the quantum computing device are further processed on the classical computing device. However, as quantum computing devices mature, other embodiments are conceivable. In the following examples, a quantum computer refers to a gate-based quantum computer, and manipulation refers to the operation on the quantum elements of the quantum computer.

[0101] To generate control signals for performing operations on the quantum computing device, in step S10, a problem to be solved using the quantum computing device is preferably provided in a mathematical description. For example, such a problem may include a mathematical description based on the electronic structure of a material to determine material properties. Other problems may include optimization problems and associated objective functions. In step S12, based on the problem to be solved, an operational description of the problem or subproblems may be generated, wherein the operational description includes operations to be applied to the qubits of the quantum computer to solve the problem in quantum mechanical calculations. Further, the operational description may include a reference state that allows the generation of a representation of an initial qubit state on the quantum computer, and then further operations are applied to the quantum computer by manipulating the qubit state. Then, in step S14, based on the operational description, control signals can be generated to control the quantum computer, for example, by providing these control signals to a manipulation unit, which can then manipulate the qubit state based on these control signals. In step S16, the manipulation unit then applies manipulation operations to one or more qubits of the quantum computer, wherein the qubits perform quantum mechanical calculations based on these manipulation operations. After this manipulation, in step S18, a measurement signal may be generated to determine the result of the quantum mechanical calculation. This step may include reading out (i.e., measuring) the qubit state after applying manipulation to the initial qubit state. Then, in step S20, the measurement signal may be converted into a measurement quantity on a classical computer, and if in the case of a subproblem, it may be fed back into the problem to be solved. Finally, in step S22, the result of the problem calculation, including quantum mechanical calculations, may be provided on a classical computing device.

[0102] Figure 4 A schematic example of a hybrid system including classical and quantum computing devices is shown. (See reference...) Figure 3 The methods described herein indicate that quantum computing devices are typically used in conjunction with classical computing devices. For example... Figure 4 As shown, the problem preparation system (e.g., a control signal generation device) can be implemented to perform, for example... Figure 3The illustrated method uses a classical computing device 110 for steps S10, S12, S20, and S22. A control unit can then be provided as an interface between the classical computing device 110 and the quantum computer 100, wherein the control unit can also be, for example, a classical computing device performing step S14. The control unit can then be communicatively coupled to a manipulation section 106, which can control the manipulators of the quantum computing device. Furthermore, the manipulation section 106 can be implemented as a classical computing device, for example, classical control hardware for controlling specific hardware components in the quantum computer that perform qubit manipulation. However, the manipulation section 106 is generally considered part of the quantum computer because it directly affects the quantum register. The quantum computing device 100 is adapted to perform quantum operation S16 specifically by manipulating the qubits of the quantum register. The measurement section 108, which is also generally considered part of the quantum computing device, can then perform step S18 using classical hardware. The measurement section 108 can then be communicatively coupled to the preparation system 110 for further processing of the measurement signal.

[0103] Figure 5 A schematic example of a superconductor-based quantum computing device is shown. Superconducting quantum computing devices are one type of solid-state quantum computing technology. Here, the quantum register 104 may include superconducting circuits 520, 522, and 524 based on a Josephson junction. Then, depending on the number of superconducting circuits selected to represent qubits, the qubits may refer to, for example, charge qubits, flux qubits, transport qubits, or phase qubits. Figure 5 This is a simplified illustration of a superconducting quantum computer utilizing charge qubits. For a charge qubit, different states of the qubit are represented by an integer number of Cooper pairs on a superconducting island. In the case of gate-based quantum computing, quantum manipulation can be achieved by manipulating the qubits via microwave pulses. Resonators 512, 514, and 516 can be used to manipulate the state of the qubit by applying microwaves, or to read out the state of the qubit by measuring the corresponding microwaves; typically, different resonators are used for manipulating the state of the qubit and reading out the qubit. Furthermore, resonator 518 can be used to apply microwaves that entangle the qubits. However, besides resonator 518, entanglement can also be achieved through inductive or capacitive coupling of a superconducting circuit, or even by providing another qubit (here, a superconducting circuit) between the qubits to be entangled.

[0104] At the operational level, such systems are maintained at extremely low temperatures, for example, tens of mK. This extreme cooling keeps the superconducting material below its critical temperature and helps avoid unwanted state transitions. To maintain this low temperature, quantum information processing systems can operate within cryostats (such as dilution freezers). In some implementations, control signals are generated in a higher-temperature environment and transmitted to the quantum computer using shielded impedance-controlled GHz transmission lines (such as coaxial cables). In some implementations, dispersion detection schemes are used to measure the state of superconducting qubits. To read out or detect the state of any qubit, a probe signal (e.g., traveling-wave microwave) can be excited along a readout transmission line coupled to the qubit via a corresponding readout resonator. The frequency of the probe signal can be near the resonant frequency of the readout resonator. Depending on the internal quantum mechanical state of the qubit, the intensity or phase of the probe signal transmitted along the readout transmission line can be varied because the reflectivity of the readout resonator coupled to the qubit varies according to the qubit's state. This allows for state detection of qubits, where, during the readout of the qubit state, the qubit's state collapses, i.e., it is projected onto one of the ground states with a corresponding probability. The corresponding probabilities can be determined by performing multiple quantum mechanical calculations and readouts. Further details of the superconducting quantum device are described, for example, in documents EP 3830867 A1, EP 3449427 A1, US 2020272925 A1, CN 212061223 U, and US 2019019099A1.

[0105] Figure 6 A schematic example of a quantum computing device based on ions in an ion trap is shown. Similar to neutral atom traps, ion traps with, for example, positively charged calcium ions can be used to implement quantum computing devices. Here, ions 626 are trapped in an oscillating electromagnetic field 624 within a high or ultra-high vacuum. Ions 626 are cooled by a laser and held in the oscillating electric field 624. For qubit manipulation (such as superposition or entanglement), lasers 628 of different frequencies can be used.

[0106] Typically, based on the aforementioned quantum computer implementation methods, gate-based computations can be performed on quantum computer hardware architectures. Gate-based computations are based on quantum gates. Compared to classical gates, there are countless possible single-qubit quantum gates that can change the state vector of a qubit. A state that changes the state vector of a qubit is often referred to as a single-qubit rotation, and in this paper, it can also be referred to as a state change or a single-qubit quantum gate operation. Rotations, state changes, or single-qubit quantum gate operations can be mathematically represented using a unitary 2 × 2 matrix with complex elements. A rotation corresponds to the rotation of the qubit state within its Hilbert space, which can be conceptualized as a rotation of a vector on a Bloch sphere, where the Bloch sphere is often referred to as the geometric representation of the pure state space of the qubit. Multi-qubit gates change the quantum states of a set of qubits. For example, a two-qubit gate rotates the states of two qubits into rotations of those two qubits in a four-dimensional Hilbert space, where, as is well known, a Hilbert space is an abstract vector space with an inner product structure that allows the measurement of lengths and angles. Furthermore, the Hilbert space is complete, i.e., there exists a sufficient limit in the space to allow the use of calculus techniques.

[0107] In the following text, the term "operation description" refers to a representation of a problem that includes a sequence of quantum operations to be applied during the quantum mechanical computation of the problem. In the context of this invention, the term "quantum operation" can include all types of quantum gates as described above, and more generally includes all manipulations of quantum elements known on any quantum computer hardware. Furthermore, the term can also include operations performed on components (and optionally components representing the boson field itself) in a quantum computer that represent the coupling between the quantum elements forming qubits and the boson field. These operations then involve any kind of change representing the coupling of the components or the state of the boson field, such as switching the coupling on and off, or changes in the field frequency. Further, in some applications, quantum operations can also include measurement operations. This allows the use of measurement feedback to implement algorithms. For example, in such an algorithm, the quantum computer can execute a quantum gate defined by a sequence of quantum operations, then measure only a subset (i.e., less than all) of the qubits or other computational elements (such as boson field states) in the quantum computer, and then determine which further quantum manipulations to perform next based on the results of one or more measurements. In particular, measurement feedback can be used to perform quantum error correction, but is not limited to it.

[0108] Not all quantum computers are gate-based quantum computers. Embodiments of this invention are not limited to utilizing gate-based quantum computers. As an alternative example, embodiments of the invention may also utilize, in whole or in part, quantum computers implemented using the quantum annealing paradigm, an alternative to the gate-based quantum computing paradigm. More specifically, quantum annealing is a metaheuristic method that uses the process of quantum fluctuations to find the global minimum of a given objective function on a given set of candidate solutions (candidate states). In particular, quantum annealing is closely related to adiabatic quantum computing.

[0109] Typically, the quantum annealing process also begins by using a classical computer to provide or generate an initial Hamiltonian and a final Hamiltonian based on the computational problem to be solved, and provides the initial Hamiltonian, the final Hamiltonian, and the annealing schedule as inputs to the quantum computer. In the case of an annealing process for solving an optimization problem, preferably, the final Hamiltonian refers to the Ising Hamiltonian representing the optimization problem, or a good approximation of the ground state representing the Ising Hamiltonian of the optimization problem. Then, for example, by using a corresponding control unit controlling the manipulation part of the quantum computer, the quantum computer is adapted to prepare a relatively easy-to-prepare initial state based on the initial Hamiltonian, such as a quantum mechanical superposition of all possible states (e.g., candidate states) with equal weights. After the initial state is prepared on the quantum computer, the initial state then evolves according to the annealing schedule following the time-dependent Schrödinger equation, which refers to the natural quantum mechanical evolution of the quantum computer physical system. More specifically, the state of the quantum computer undergoes time evolution under the time-dependent Hamiltonian, starting from the initial Hamiltonian and terminating at the final Hamiltonian. If the evolution is slow enough, the system will remain in a ground state close to the instantaneous Hamiltonian. At the end of the time evolution, a set of qubits (i.e., quantum elements) on the quantum annealer are in a final state that is expected to approximate the ground state of the Ising Hamiltonian, corresponding to a solution to the primal problem (e.g., an optimization problem). The final state of the quantum computer can then be measured, producing a result that can be used to solve the primal problem. The measurement operation can be performed, for example, in any of the ways described above. The classical computer can then post-process the measurement result to produce an output representing a solution to the primal computational problem. For example, the quantum annealer described above can be implemented on superconducting quantum computer hardware.

[0110] Furthermore, embodiments of the present invention can also utilize, in whole or in part, quantum computers implemented using a one-way quantum computing architecture (also known as a measurement-based quantum computing architecture). More specifically, a one-way or measurement-based quantum computer refers to a quantum computing method that first prepares an entangled resource state, typically a cluster state or graph state, and then performs a single-qubit measurement on it. It is "one-way" because the resource state is destroyed by the measurement. In such an architecture, the result of each individual measurement is random, but they are correlated in a way that ensures the computation always succeeds. Generally, the basis for subsequent measurements needs to depend on the results of previous measurements, so not all measurements can be performed simultaneously.

[0111] Figure 7 A system for generating properties associated with a chemical product and optionally for producing the chemical product is illustrated schematically and exemplary. Specifically, system 700 includes means 720 for generating properties associated with a chemical product to be produced by production plant 740 (e.g., in production system 741). Specifically, this property allows for the determination of the chemical product to be produced, such as a target chemical product including predetermined target technical application properties. Typically, the properties associated with chemical product 750 can be derived from solutions of electronic structure representations and can therefore be solved based on information related to the electronic structure of chemical product 750. In addition to means 720, system 700 may further include an input unit 710 and / or a quantum computer system 730. Typically, production plant 740, and particularly production system 741, may also be part of the system, but may be omitted or configured only to be communicatively coupled to means 720.

[0112] The device 720 includes an electronic structure representation providing unit 721, a solution determination unit 722, and an association calculation unit 723. Optionally, the device 720 further includes an iteration unit and a control data generation unit. Figure 7 (Not shown in the image). Further, device 720 may optionally include a conversion unit 724. However, conversion unit 724 may also be part of quantum computer system 730, or may be a separate device communicatively coupled to device 720 and quantum computer system 730. Typically, device 720 can be implemented as any known classical computing system. For example, the functions provided by the unit can be executed by one or more processors on one or more classical computing devices. In particular, device 720 can also be implemented as a distributed computing framework, for example, as a cloud or network environment, where more than one computing device or processor is utilized to perform the functions of the device.

[0113] Electronic structure representation providing unit 721 is configured to provide an electronic structure representation associated with the molecular structure of a chemical product. For example, problem providing unit 721 may be coupled to input unit 710 to allow a user to instruct, for example, to select from the corresponding provided options, the electronic structure representation to be solved. However, electronic structure representation providing unit 721 may refer to, or be communicatively coupled to, a storage unit on which the corresponding problem description is already stored. Typically, the electronic structure representation, once solved, allows the derivation of the technical application characteristics of the corresponding chemical product. Furthermore, the electronic structure representation, once solved, may allow the determination of one or more production process parameters, for example, allowing the determination of a specific catalyst suitable for producing the chemical product, the corresponding reaction temperature, the corresponding reaction energy, etc. Typically, the electronic structure representation further indicates a first portion representing the active space and a second portion representing the inactive space. The active and inactive spaces of the problem may refer to subspaces of the Hilbert space of the electronic structure representation and may be determined based on the chemical product and / or its properties (e.g., based on the known approximate electronic structure of the chemical product). Further details regarding the first and second portions (including preferred examples and embodiments) will be provided, for example, regarding... Figure 12 Describe it.

[0114] Typically, the electronic structure representation can be provided in any form that allows device 720 to derive corresponding information from the electronic structure representation to solve the electronic structure representation. In particular, the electronic structure representation is preferably provided in a digital format. Furthermore, it is preferred that the electronic structure representation be provided as a mathematical formula. However, the electronic structure representation can also be provided in any other format, as long as the electronic structure representation providing unit 721, or optionally a conversion unit 724, can derive the corresponding mathematical formula of the electronic structure representation from that format. The electronic structure representation providing unit 721 can then be configured to provide the electronic structure representation to the solution determining unit 722.

[0115] The solution determination unit 722 can be configured to cause the quantum computer 730 to perform quantum mechanical calculations based on a first portion of the electronic structure representation, such that the result of the quantum mechanical calculation indicates the solution of the first portion. Specifically, the solution determination unit 722 can be communicatively coupled to the quantum computer 730, for example, to provide the quantum computer 730 with a corresponding control signal to trigger the quantum mechanical calculations. Optionally, before the solution determination unit 722 causes the quantum computer 730 to perform the quantum mechanical calculations, the electronic structure representation or a first portion of the electronic structure representation can be provided to the conversion unit 724. Typically, for quantum mechanical calculations, the corresponding problem is converted into a corresponding operation description indicating a sequence of operations to be applied to the quantum computer to solve the problem. In this case, the sequence of operations is determined to cause the quantum mechanical calculations of the first portion defined in the active space to be performed on the quantum computer. This conversion of the first part, and therefore the conversion unit 724, can be part of the apparatus 720, for example, as a corresponding unit for converting the electronic structure representation or the first part of the electronic structure representation provided by the electronic structure representation providing unit, wherein the solution determining unit 722 can then directly use the determined representative operational description to enable the quantum computer 730 to perform quantum mechanical calculations on the first part. However, the conversion unit 724 can also be provided as a standalone unit, or as a unit as part of the quantum computer system 730, and receive the corresponding electronic structure representation or the first part of the electronic structure representation from the solution determining unit 722 for conversion.

[0116] Typically, algorithms and methods for converting electronic structure representations into corresponding operations to be performed on a quantum computer system 730 to perform quantum mechanical calculations are known. The corresponding conversions depend heavily on the quantum computer system 730 used to determine the solution to the problem. For example, a superconductor-based quantum computer may require different operations compared to a trapped ion-based quantum computer. Furthermore, the corresponding operation description may also refer to manipulations performed on a quantum annealer to solve for the corresponding electronic structure representation. In particular, in this case, the corresponding operation description will differ from, for example, the operation description used for other quantum computer systems (such as gate-based quantum computing systems). Therefore, in many applications, it is preferred that the conversion unit 724 is part of the quantum computer system 730, thereby enabling the device 720 to utilize different quantum computing systems 730 with greater flexibility, wherein, in their respective cases, the corresponding conversion unit 724 can be specialized and specifically adapted to optimally convert the electronic structure representation into a representative operation description particularly suitable for the corresponding quantum computing system to which the corresponding conversion unit is involved. For preferred examples and embodiments, for example, regarding… Figure 10 and Figure 11 It provides details about the algorithms used to prepare quantum mechanical calculations.

[0117] After the quantum computer 730 has performed quantum mechanical calculations, the corresponding calculation results can be provided to the device 720 again. Typically, this determined calculation result indicates a solution for the first part of the electronic structure representation. Specifically, depending on the specific first part, the corresponding solution for the calculated first part can be determined using appropriate known algorithms and methods based on measurements of the states of the quantum elements of the quantum computer 730. This determination of the solution for the first part can be performed, for example, by the part of the quantum computer system 730 that includes a classical computer before providing the corresponding result (in this case, the solution for the first part) to the device 720, or it can be performed by the device 720 itself (e.g., by the associated computing unit 723).

[0118] Alternatively, the solution determination unit 722 can be configured to cause a classical computer to perform a corresponding calculation based on a first part of the electronic structure representation, such that the result of the classical calculation indicates the solution for the first part. Furthermore, the solution determination unit 722 can be configured to cause a quantum computer 730 to perform a quantum mechanical calculation based on a second part of the electronic structure representation, such that the result of the quantum mechanical calculation indicates the solution for the second part. When the quantum computer calculates the solution for the second part, the same principles and embodiments described above regarding the calculation of the solution for the first part can be applied. Alternatively, the solution determination unit 722 can be configured to cause a classical computer to perform a corresponding calculation based on a second part of the electronic structure representation, such that the result of the classical calculation indicates the solution for the second part. Preferably, at least one of the first and second parts is calculated on the quantum computer.

[0119] The correlation calculation unit 723 is configured to generate a solution for the electronic structure representation by combining the solutions of the first part and the second part, wherein the solutions of the first part and the second part are computationally combined to generate properties associated with the chemical product. Preferably, the computational combination includes generating an interaction representation associated with a combination of the active and inactive spaces. The interaction representation is based on a reference state associated with a superposition of electronic configurations generated based on the solutions of the first part and the second part. Therefore, the interaction representation allows the calculation of a solution for the electronic structure representation by combining i) the solution of the second part in the inactive space and ii) the solution of the first part in the active space.

[0120] Typically, generating the interaction problem to combine the solutions of the first and second parts can depend either on the corresponding electronic structure representation itself or on the method used to solve the electronic structure representation. Some preferred methods and algorithms for generating the interaction representation and combining the solutions of the first and second parts will be described in more detail later. The interaction representation can then be solved using a classical computer and / or a quantum computer. Typically, since the solution to the electronic structure representation is related to the properties of the chemical product 750, this solution can then be used, for example, to generate corresponding control data using a corresponding control data generation unit to control the production system 741 used to produce the chemical product 750. For example, such control data may refer to the formulation or specifications of the corresponding chemical product, the preferred production process parameters used to produce the chemical product, the control margin for controlling the production of the chemical product, etc.

[0121] Preferably, based on the solution of the electronic structure representation related to the characteristics of the chemical product, the device 720 is configured to determine the technical application characteristics of the chemical product. Control data can then be generated, for example, based on the determined technical application characteristics. In a further preferred embodiment, the device 720 further includes an iteration unit ( Figure 7 (Not shown in the diagram), this iterative unit allows for control of iteration based on solutions to the electronic structure representations associated with the chemical product. Specifically, it is preferable to provide the target technical application characteristics to the device 720, for example, using input unit 710, and then compare the technical application characteristics determined based on the solutions to the electronic structure representations with the target technical application characteristics. Based on this comparison, further iterative steps can then be initiated, for example, by modifying one or more characteristics of the chemical product and thus the corresponding electronic structure representation, or it can be determined that the corresponding chemical product satisfies the target technical application characteristics and is therefore the target chemical product that should be produced by the production system 741. In this case, control data can be generated to cause the production system 741 to produce the target chemical product 750.

[0122] The following will refer to Figure 8 Further details are described regarding this and other corresponding embodiments of the method that can be performed by device 720. Figure 8A method for generating properties associated with a chemical product is illustrated schematically and exemplary. A key portion of method 800 includes providing an electronic structure representation associated with the chemical product, which indicates or includes a first portion and a second portion of the electronic structure representation, as described above, for example, with respect to unit 721 providing the electronic structure representation. Further, method 800 includes performing quantum mechanical calculations using a quantum computer system (such as quantum computer system 730), wherein the result of the quantum mechanical calculations indicates solutions for the first and / or second portions. By utilizing a quantum computer system, for example, as described above with respect to unit 722 determining the solution, solutions for the first and / or second portions can be computed. Alternatively, the computation of the first or second portion can be performed by a classical computer. Further, method 800 includes generating and solving an interaction representation to combine the solutions for the first and second portions, for example, as described above with respect to unit 723 relating to the problem.

[0123] Optionally, the method may include additional steps, particularly those related to the production of the chemical product. These optional additional steps 810 are described in detail below. Figure 8 The diagram is presented in dashed and dotted box formats. In a preferred embodiment, the additional step refers to determining the technical application characteristics of the chemical product based on the solution of the determined electronic structure representation. However, the additional step may also refer to determining one or more production process parameters for controlling the production process of the chemical product. For example, such production process parameters may be determined based on calculated technical application characteristics. However, such production process parameters may also refer to, for example, the catalyst or reactant used in the production of the chemical product, and therefore may be determined based on solving the corresponding electronic structure representation that allows for the derivation and prediction of the corresponding reaction parameters of potential catalysts or reactants. Examples of specific preferred applications of methods 800 and 810 will be provided in the following description of some more detailed embodiments.

[0124] Preferably, method 810 may further include providing target technical application characteristics of a chemical product, wherein, in this case, the electronic structure representation is provided based on a potential chemical product whose suitability for the corresponding target technical application characteristics should be determined. The target technical application characteristics can then be compared with the determined technical application characteristics, and it can be determined whether the determined technical application characteristics satisfy the target technical application characteristics. This comparison can be used in an iterative algorithm in which the comparison is performed at each iteration step. If the determined technical application characteristics do not satisfy the target technical application characteristics within predetermined limits, then in the next iteration step, the potential chemical product can be modified, for example, by modifying one or more aspects or characteristics of the corresponding potential chemical product, and a new electronic structure representation can be provided based on the new potential chemical product.

[0125] Then, the following steps can be repeated in each iterative step: solving the first or second part using a quantum computer, combining the solutions of the first and second parts to determine the solution for the electronic structure representation, and determining the technical application characteristics. If, in one iterative step, it is determined during comparison that the determined technical application characteristics satisfy the target technical application characteristics within predetermined constraints, then the corresponding potential chemical product can be determined to be the target chemical product, and corresponding control data for producing the target chemical product can be generated. It should be noted that the corresponding control data can also be generated without iteration, for example, based solely on the determined technical application characteristics. Typically, the control data can then refer to control data that allows control, for example, of the production system 741 used to produce chemical product 750 (e.g., the target chemical product). Therefore, the control data can refer to the formulation or specification of the target chemical product, such as the synthesis specification. However, the control data can also refer to, for example, production process parameters determined based on the determined technical application characteristics.

[0126] Further details and embodiments are described below. Quantum computing is an emerging technology that utilizes quantum mechanical phenomena to perform computational tasks. Quantum computers promise to solve certain computational problems significantly faster than classical computers. They can be used, for example, to simulate quantum mechanical problems, such as electronic structure problems, including but not limited to molecules, crystals, and amorphous solids. In industrial settings, such simulations of electronic structure problems are crucial for discovering new materials and chemicals, improving chemical processes, customizing molecules, solids, and materials to desired properties, and often, for making the development and production of new products more efficient by reducing the number of laboratory and production trials that are typically resource-intensive. Additionally, optimization problems, machine learning, and artificial intelligence are further exemplary application areas of quantum computing. In these areas, quantum computing promises to significantly outperform classical computing in terms of the size of the problems it can handle, the computation time required, energy costs, and / or the accuracy achievable.

[0127] The fundamental processing unit of a quantum computer is a quantum mechanical bit (qubit), which can be represented by one or more quantum elements on the quantum computer hardware. By executing appropriate quantum circuitry via control pulses acting on the qubit, a solution to one of the aforementioned problems or a specific subproblem can be prepared on a qubit register, and the solution can ultimately be measured within a hardware-specific readout protocol. The number of logical qubits formed by one or more physical quantum elements and their quality (e.g., error rate or fidelity) primarily determine the maximum size (e.g., dimensionality) and maximum complexity of the problem that can be solved by the corresponding quantum computer.

[0128] Currently, the number and fidelity of qubits are subject to considerable limitations, leading to the development of so-called noisy, medium-scale quantum (NISQ) computers. Typically, these NISQ computers are combined with classical computers, such as classical high-performance computers (HPCs). In this so-called hybrid quantum-classical framework, the components of the algorithm operate on a computational architecture that best solves specific components of the problem. In this context, variational methods are often used, where the quantum computer is controlled by the classical computer. For example, after preprocessing and preparing the problem on the classical computer, in the second step, parameterized quantum states are prepared on the NISQ computer; in the third step, the objective function is measured on the NISQ computer; and in the fourth step, the parameters are optimized on the classical computer to minimize or maximize the objective function. This process is repeated with updated parameters until the value of the objective function converges and thus becomes either a minimum or a maximum, respectively. In the final step, post-processing can be performed on the classical computer.

[0129] The number of qubits and the fidelity are expected to continue to increase. Once a certain threshold is reached, hundreds or thousands of these so-called physical qubits (the exact number depends on the specific error-correcting code, two examples being "surface codes" and "color codes" used for error correction) can be entangled to form a single error-free so-called logical qubit. Logical qubits can be formed from one or more physical quantum elements of the corresponding quantum computer hardware. A quantum device consisting of several of these logical qubits is called a fault-tolerant (FT) quantum computer. It should be noted that the FT quantum computers mentioned in the following examples are not limited to full FT quantum computers, but also include FT quantum computers that still have sufficiently small errors. The error rate of such FT quantum computers depends on the error-correcting code and the number of physical qubits used. Empirically, the more physical qubits of a certain quality used, the more errors are suppressed.

[0130] Such FT quantum computers can accommodate deep quantum circuits, which allow for highly accurate or precise solutions to many highly relevant computational problems that cannot be solved on classical computers in a reasonable time or at a reasonable energy cost. However, due to the enormous overhead of the physical qubits required to construct a single logical qubit, some FT quantum computers still face considerable limitations in terms of the number of logical qubits and therefore the size (e.g., dimensionality) of the computational problems that can be solved. Thus, for many practically relevant computational problems, the problem dimension will exceed the dimension of the Hilbert space spanned by the quantum computer. In such cases, the computational problem cannot be solved directly on the FT quantum computer. Further, more specific examples of problems in the field of electronic structure problems that can be solved using the inventions described herein are described below.

[0131] While fault-tolerant quantum computers (e.g., fault-tolerant quantum processing units (FT-QPUs)) outperform noisy intermediate-scale quantum computers (e.g., noisy intermediate-scale quantum processing units (NISQ-QPUs)) in terms of accuracy because they can accommodate deeper quantum circuits (i.e., more gate operations), in many cases, NISQ-QPUs can accommodate a wider range of quantum circuits—that is, utilizing more qubits but fewer gate operations compared to FT-QPUs—to provide approximate but still accurate solutions to many problems. Furthermore, even without FT-QPUs, NISQ-QPUs exist with a wide range of fidelities, allowing computations to be performed with varying accuracies or running quantum circuits of varying depths.

[0132] For example, regarding Figure 7 and Figure 8 The method described above for solving electronic structure problems can be executed on multiple different hardware combinations. For example, the method can be executed on only one or more classical computers. In a more advantageous embodiment, at least one of the first part, the second part, and the interaction representation is computed on one or more quantum computers. Furthermore, it is particularly advantageous to utilize a quantum computing system comprising at least two quantum computers and one classical computer, wherein the at least two quantum computers include different fidelities. For example, the quantum computing system can be a triple hybrid quantum computing system combining an FT-QPU, a NISQ-QPU, and a classical central processing unit (CPU) or other conventional computing devices, wherein computational operations are performed where they are most advantageous for solving the problem. However, the quantum computing system can also combine different NISQ-QPUs with different fidelities and CPUs or other conventional hardware without using an FT-QPU.

[0133] exist Figure 9The text illustrates two examples of corresponding quantum computing systems that can be advantageously utilized. These examples are shown with respect to quantum computing systems including FT-QPUs and NISQ-QPUs. However, in addition to or as an alternative to FT-QPUs, NISQ-QPUs with higher fidelity can also be used, based on the same principles as those exemplified below. In the following text, the term "higher fidelity NISQ-QPU" is used to mean that a higher fidelity NISQ-QPU can have a higher fidelity than: a) all other NISQ-QPUs in the quantum computing system, b) a higher fidelity than at least one other NISQ-QPU in the quantum computing system, and / or c) a higher fidelity than a predetermined threshold. In particular, any combination of these three criteria can define the NISQ-QPUs that can be used to compute the subproblems described below. For example, the threshold can be based on prior considerations, experience with the corresponding problem type, the algorithm to be utilized, the specific problem type, the desired solution accuracy, etc. However, in most cases, a higher fidelity NISQ-QPU refers only to the NISQ-QPU with the highest fidelity among the NISQ-QPUs of quantum computing systems, where, in this case, the corresponding subproblem is derived such that the subproblem can be computed by the higher fidelity NISQ-QPU.

[0134] In the following examples, the mentioned multiple FT-QPUs are optional and can also be replaced by multiple higher-fidelity NISQ-QPUs, or used together with multiple higher-fidelity NISQ-QPUs. One example involves controlling multiple FT-QPUs and / or multiple higher-fidelity NISQ-QPUs and multiple NISQ-QPUs, and exchanging data via multiple CPUs. Another example includes a quantum computing system in which, additionally, multiple FT-CPUs and / or multiple higher-fidelity NISQ-QPUs and NISQ-QPUs are entangled in such a way that quantum information is distributed and shared among the multiple entangled QPUs, and can also be transferred directly between the respective multiple QPUs. In this case, it is preferred that the multiple FT-CPUs or multiple higher-fidelity NISQ-QPUs and multiple NISQ-QPUs are located on the same chip to facilitate entanglement. However, spatially separated QPUs can also be entangled by using quantum buses (such as optical fibers and photons). Figure 9 The two settings described herein, in principle, allow for the solution of practically relevant computational problems whose problem size (e.g., dimension) exceeds the dimension of the Hilbert space of the FT-QPU or the higher-fidelity NISQ-QPU by optimally distributing computational tasks.

[0135] exist Figure 10The document illustrates a detailed exemplary method for solving the above problem using a non-entangled quantum computing system, and... Figure 11The document illustrates an exemplary detailed method for solving the aforementioned problem using an entangled quantum computing system. However, the principles of the described method can also be implemented using a hybrid computing system, typically known to include both quantum and classical computers, rather than a quantum computing system comprising quantum computers with varying fidelities. In the first step, an electronic structure representation can be defined on a classical computing system, for example, by a user using a user interface. A typical electronic structure representation refers to the electronic structure of molecules, solids, and materials. In the second step, the electronic structure representation may include subproblems or can be divided into subproblems on the classical computing system, for example, a first part of the electronic structure representation and a second part of the electronic structure representation, the first part indicating an active space comprising a portion of the electronic structure associated with the molecular structure, and the second part indicating an inactive space comprising another portion of the electronic structure associated with the molecular structure. Preferably, in defining the first and second parts, the fidelity of the quantum computing system on which the subproblems are to be solved is considered. FT-QPUs or (multiple) higher-fidelity NISQ-QPUs are best suited for solving smaller computational subproblems that require exact or high-accuracy solutions that are inefficiently obtainable on low-fidelity NISQ-QPUs or CPUs. Subproblems requiring deeper quantum algorithms beyond the capabilities of (multiple) lower-fidelity NISQ-QPUs and CPUs can also be derived for solving on (multiple) higher-fidelity NISQ-QPUs or (multiple) FT-QPUs. For example, the dimension of the subproblems in the first part can be chosen to be less than or equal to the dimension of the Hilbert space spanned by the qubits of (multiple) FT-QPUs or (multiple) higher-fidelity NISQ-QPUs. Lower-fidelity NISQ-QPUs are best suited for solving larger computational subproblems that require exact solutions that are inefficiently obtainable on classical computers (e.g., (multiple) CPUs), or solutions that require broad rather than deep quantum algorithms (utilizing a larger number of qubits), as is the case for the second part. The CPU is used for all remaining tasks and for controlling the entangled or non-entangled quantum computer. In the third step, control signals are provided that enable the fabrication and operation of corresponding quantum circuits on the quantum computing system to compute and solve the corresponding subproblems. Optionally, the quantum circuits may contain parameters, which are typically used in the context of a variational process. In this case, a set of initial parameters is provided in the first iterative step.In the next step, the subproblem is encoded into qubits, the quantum circuit is compiled, and control signals are provided simultaneously, for example, to (multiple) FT-QPUs, (multiple) higher-fidelity NISQ-QPUs, or (multiple) NISQ-QPUs, or to a system of (multiple) entangled FT-QPUs, (multiple) higher-fidelity NISQ-QPUs, and (multiple) NISQ-QPUs. This operation is also performed in all subsequent iterative steps using a suitably updated set of parameters.

[0136] In the fourth step, all quantum circuits from the current iteration are executed simultaneously on (multiple) FT-QPUs, (multiple) higher-fidelity NISQ-QPUs, or (multiple) NISQ-QPUs, or on (multiple) entangled FT-QPUs, (multiple) higher-fidelity NISQ-QPUs, and (multiple) NISQ-QPUs, to prepare solutions to the corresponding subproblems. Examples of relevant algorithms for (multiple) FT-QPUs include quantum Fourier transform, quantum phase estimation (QPE), Grover-type search algorithms, Shor-type factorization algorithms, and Harrow-Hassidim-Lloyd-type algorithms. Examples of relevant algorithms that can also be used on (multiple) higher-fidelity NISQ-QPUs or (multiple) NISQ-QPUs include variational quantum eigenvalue solvers (VQE) and quantum approximation optimization algorithms (QAOA). The corresponding quantum gate operations are performed on qubit registers. In the case of entangled FT-QPU or higher fidelity NISQ-QPU and NISQ-QPU systems, solutions to subproblems can be directly transferred between these two types of QPUs.

[0137] In the fifth step, relevant observables of the subproblem can be measured simultaneously on (multiple) FT-QPUs, (multiple) high-fidelity NISQ-QPUs, or (multiple) NISQ-QPUs, or on entangled FT-QPUs or high-fidelity NISQ-QPU and NISQ-QPU systems, and provided to (multiple) CPUs. Examples of measurable observables are qubit occupancy, reduced density matrix, and energy. In the sixth step, the objective function and / or quantity, along with its derivative or other relevant quantities (if needed), can be evaluated on (multiple) CPUs based on the measured observables. Examples of objective functions and / or quantities are the total energy and classical loss function of the electronic structure problem. Then, feedback calculations (such as self-consistency conditions) of the iterative steps of the connection algorithm can be invoked, or, in the case of a variational process, optimization methods such as quasi-Newton methods can be invoked to obtain a new set of parameters, thereby minimizing or maximizing the objective function and / or quantity. Finally, the iteration can return to the second or third step, or if one or more stopping criteria are met (e.g., the objective function and / or quantity has converged), the iteration can terminate the feedback loop and continue to the next step. In the next step after convergence has been achieved, optional post-processing steps can be performed on (multiple) CPUs, for example by associated computational units, to improve overall accuracy or to further process the results (e.g., error mitigation or correction). If necessary, other observables can be measured on (multiple) QPUs. Depending on the interactions between the results of the subproblems, the results of the subproblems can be further combined in this post-processing or during the iteration. Finally, the final result is provided to the user as the solution to the processed problem.

[0138] The following describes examples of methods utilizing a hybrid quantum-classical approach. The exemplary method described below involves solving a “living space” preferably on a quantum computing system, wherein the results are then used to adjust electronic orbitals in both a preferred “inactive space” and a “living space” on a classical or quantum computer. However, other distributions are possible depending on the problem and the “living space” and “inactive space” determined as subproblems. For example, the “inactive space” or the effect of the “living space” on the “inactive space” can also be solved on a quantum computing system. This process is repeated iteratively until the molecular orbitals and total energy converge. This approach can be referred to as the “Completely Active Space Self-Consistent Field” (CASSCF) method. A related approach is the “Completely Active Space Configuration Interaction” (CASCI), which can be considered a special case of CASSCF that ignores the adjustment of electronic orbitals based on the solution of the “living space.” Both methods are referred to as the “CAS method” below. The solutions obtained from such calculations can then be used to generate interaction representations and solve the corresponding electronic structure problems more accurately.

[0139] By describing the partitioning into “active space” and “inactive space,” this method allows for solving electronic structure problems whose scale (e.g., dimensionality) would otherwise exceed the dimensions of a quantum computer (e.g., in terms of the available qubits to which electronic orbitals are mapped and / or in terms of the gate operations required to prepare a solution), because only the electronic orbitals that include the “active space” are explicitly processed on the quantum computer. This method is particularly advantageous for simulating so-called statically correlated molecular systems, such as transition metal compounds associated with the improvement and design of novel catalysts and chelators, which are typically very challenging in terms of computational workload and accuracy using traditional methods utilizing CPUs.

[0140] Typically, the process for solving the "active space" and "inactive space" (i.e., the first and second parts, respectively) conforms to the above description. Figure 10 The general process described herein, in which the type of quantum computer utilized can be determined prior to the quantum computation based on the fidelity of the corresponding available quantum computers and can remain fixed throughout the iterations, is detailed below for the specific case of the hybrid quantum-classical CAS method. Figure 10 The steps in the process are as follows. In the first step, the specific electronic structure problem to be solved is presented on the CPU as a molecular system specified by atomic positions, basis sets, charges, and spins. This is similar to... Figure 10 The first step in the general process. Further, for example, a set of initial electron orbitals is specified according to Hartley-Fock calculations on the CPU. Along with these electron orbitals, a fixed "active space" is defined, for example, by the electron orbitals and electrons constituting the "active space," wherein the active space defines the first part. These steps are executed on the CPU, similar to... Figure 10 The second step in the general process. In the next step, the matrix elements of the effective Hamiltonian of the "active space" in the electron orbital basis are established on the CPU, thereby further defining the first part. This is similar to Figure 10 The third step in the general process. Furthermore, the effective “active space” Hamiltonian operator (which is essentially a fermion / electron operator) is encoded (i.e., transformed) in the qubit operator, for example, via Jordan-Wigner or Bravi-Kitayev transformations. A quantum circuit for solving the “active space” portion is then compiled on the CPU, making the quantum circuit executable on a quantum computer. The “active space” portion is then prepared and solved on the quantum computer (e.g., a high-fidelity NISQ-QPU or FT-QPU), for example, via a so-called quantum phase estimation algorithm (QPE). Thus, an exact or near-exact solution to the “active space” subproblem (e.g., the “active space” Hamiltonian), such as an exact or near-exact eigenfunction, is prepared on the quantum computer. This is analogous to... Figure 10 The fourth step in the general process. The reduced density matrices for single and two particles can then be measured on a quantum computer as a solution to the first problem. This is similar to... Figure 10 The fifth step in the general process. Alternatively, and also according to... Figure 10 In step four of the above steps, the "active space" portion can be solved on the NISQ-QPU, for example, using a so-called variational quantum eigenvalue solver (VQE). Depending on the chosen hypothesis, an approximate but accurate solution can typically be prepared on the NISQ-QPU, for example, as a characteristic function of the "active space" portion. According to step five, the single-particle and two-particle reduced density matrices are then measured on the NISQ-QPU from the above steps. The energy can then be calculated on the CPU based on the single-particle and two-particle reduced density matrices. Furthermore, the gradient with respect to the electron orbital variation can be calculated on the CPU, where this step is performed only in the case of CASSCF, not for CASCI. This is similar to... Figure 10 Step six in the general process. Similar to... Figure 10 In step seven, if the energy and gradient converge, you can proceed to the final step. If they have not yet converged, you can proceed to step seven. Figure 10 Step eight describes updating the electron orbitals on the CPU to minimize energy until the iterative process converges. In the case of CASCI, step seven can be omitted and the self-consistent loop does not exist, thus allowing direct progress to the next step. The following describes the further steps performed to determine the solution to the problem.

[0141] While such CAS methods are well-suited for capturing static correlations in the “active space,” for real-world applications, even exact solutions to the “active space” on an FT-QPU are often insufficiently accurate. This is because the “inactive space” is treated only at a very fundamental level, typically equivalent to the Hartley-Fock level, completely ignoring correlations in the electronic orbitals within the “inactive space” and between the electronic orbitals in the “active space” and the “inactive space.” The problem is addressed below by employing multi-reference dynamic correlation methods, which consider the dynamic correlations in the “inactive space” and between the “active space” and the “inactive space” more systematically than, for example, multi-configuration pair density functional theory (MC-PDFT) and more efficient than, for example, second-order n-electron valence perturbation theory (NEVPT2). Furthermore, these methods are particularly well-suited for use with the aforementioned methods and quantum computing systems, thus taking into account the fidelity of the quantum computer when solving subproblems.

[0142] In all the methods discussed below, as mentioned above, the first step is to determine the solutions for the first and second parts. The result can then be expressed, for example, as a CAS wavefunction. This wavefunction can be used as a reference state for an interaction representation that allows for the combination of the results from the first and second parts. Below, we describe how to begin with this reference state involving the CAS wavefunction. First, we describe how the CAS wavefunction can be read out from a quantum computer to reconstruct it on different hardware devices. Then, we explain how to add dynamic correlations, such as “active space” and “inactive space”, to generate the interaction representation from the CAS wavefunction. For an overview, see also [link to overview]. Figure 14 .

[0143] For all multi-reference dynamic correlation methods (which utilize non-entangled quantum computing systems) that combine the results of active-space computations with those of inactive-space computations using interaction representations, as discussed below, the relevant specific information of the CAS wavefunction, as determined above, can be read from (multiple) QPUs to reconstruct or approximate the wavefunction on different hardware devices best suited for multi-reference dynamic correlation processing (e.g., (multiple) CPUs or, for example, different (multiple) QPUs with different fidelities). In the case of entangled quantum computing systems, it is not necessary to reconstruct the CAS wavefunction on different hardware devices, and therefore the methods for reading out the CAS wavefunction can be omitted.

[0144] The CAS wavefunction of an exemplary reference state, determined by the solutions of the active space portion (i.e., the first portion) and the second portion (i.e., the second portion) obtained as described above, can be expanded as follows:

[0145] (1)

[0146] in, These are ground states that conform to the definition of "active space," such as Slater determinants. More precisely, these ground states can be so-called configuration interaction (CI) states, given by a fixed distribution of electron orbitals between the "active space" and inactive space portions. The index μ iterates through all possible electron distributions between the electron orbitals in the "active space" and "inactive space" portions. Then, the expansion coefficients... These are the so-called CI coefficients, which are used to reconstruct the CAS wavefunction on different QPUs or CPUs that are best suited for the next computational step (e.g., multi-reference dynamic correlation processing based on interaction representations).

[0147] For example, as described above, the CI coefficients of the CAS wavefunction can be determined based on the solution of the active space portion prepared on a quantum computer. The CI coefficients associated with the inactive space can be determined, for example, using the mean-field approximation as a solution of the second part, and in most cases, using known methods on classical computers. Therefore, the following focuses on the more complex determination of the CI coefficients of the “active space” portion. In the first step, the absolute values ​​of the CI coefficients can be measured on the corresponding QPU. The absolute values ​​of the CI coefficients can be measured by determining the overlap of the CAS wavefunction with the defined ground state, for example, according to:

[0148] (2)

[0149] in, Normalized. CAS wavefunctions can be prepared on the QPU. The result is from the previous CAS calculations for the active space portion. Therefore, in the previous step, the CAS wavefunction can be prepared on the QPU, and projection measurements can be performed on all qubits. Since a basis rotation of the qubit state is not required, all qubits can be measured simultaneously. The measurement result (1 or 0 for each qubit) directly corresponds to the distribution of electrons among the electron orbitals in the “active space,” where, in the case of the Jordan-Wigner transform, the measurement value is 0 if the electron orbital is unoccupied and 1 if the electron orbital is occupied. The corresponding ground state, such as the Slater determinant, can be easily deduced from this. The count of the corresponding measured ground state (e.g., the Slater determinant) can be incremented by one, and this process is repeated until a histogram of the frequencies at which the ground state (e.g., the Slater determinant) is measured can be recorded. According to equation (2), the probability of measuring the ground state (e.g., the Slater determinant) is given by... The values ​​are given, and the histogram is directly converted to these absolute values. A significant advantage of running the CAS method and using the measurement results with a quantum computer is that it directly provides the most important ground states (e.g., Slater determinants) to span the relevant parts of the Hilbert space. This information will be used in the following steps. On a CPU, the CAS method would need to search for the relevant ground states (e.g., Slater determinants) that are previously unknown.

[0150] Alternatively, if it is necessary to determine the absolute value of the selected important CI coefficients with an accuracy only higher than that achievable by the above steps, the absolute value can be additionally measured directly in the second step, in which the CAS wavefunction is projected onto the ground state, for example, via a projection operator. superior:

[0151] (3)

[0152] in, It is a unitary operator that excites certain qubits to state 1, according to From vacuum state (That is, each qubit is in state 0) Prepare the base state This allows the distribution of electron orbitals in the "active space" to be reflected in the qubit register, where, in the case of the Jordan-Wigner transform, the qubit in state 0 indicates an empty electron orbital in the "active space," and the qubit in state 1 indicates an electron orbital occupied by one electron in the "active space." Furthermore, in equation (3), unitary basic operator and It is directly converted into unitary basic operations that act on qubits.

[0153] In a further step for reconstructing the CAS wavefunction, the phase of the CI coefficients can be determined in a post-processing step on the CPU. The above steps only determine the complex-valued CI coefficients. absolute value However, the phase is not determined, which may be crucial for reconstructing the CAS wavefunction according to equation (1). To determine the phase of the CI coefficients, the following steps can be performed. Since the absolute values ​​can be measured on (multiple) QPUs... Therefore, it is possible to determine which ground states have the largest CI coefficients, and this is therefore crucial for reconstructing the CAS wavefunction. These ground states can then be selected. The number of CI coefficients determined can be predetermined, for example, such that these measurements produce a manageable number of ground states and also a sufficient representation of a sufficiently large portion of the CAS wavefunction. Truncate the summation in equation (1) to a predetermined number of ground states, thus achieving a more efficient computation of the problem. In the next step, the Hamiltonian, for example, defining the simulated molecule, is reconstructed in the smaller subspace spanned by the most important ground states selected in the previous step. The representation of the Hamiltonian is given. Compared to the full Hamiltonian, the size of the Hamiltonian in this sufficiently small subspace is reduced, and therefore it can be efficiently diagonalized, for example, by exponential iteration or by the Davidson method. Thus, the CI coefficients within this subspace can be obtained. The absolute value and phase. Optionally, to improve accuracy, if necessary, additional CI coefficients not included in the previous step can be obtained in a self-consistent manner using the result of the previous step as input via the following formula:

[0154] (4)

[0155] Alternatively, due to absolute value As already known from previous CAS calculations performed on (multiple) QPUs and the aforementioned measurements of the CI coefficients, therefore, in the real number CI coefficients... In this case, a variant of equation (4) may include a fixed absolute value. Instead, only its sign is modified, for example within the framework of a Monte Carlo-like process that randomly flips the sign: Defined as a vector of values ​​on the left side of equation (4), these values ​​are obtained by utilizing a given set of CI coefficients. This is obtained by evaluating the right-hand side of equation (4). One possible goal of the sign lookup process is, for example, to obtain the sign by evaluating the right-hand side of equation (4). minimize To minimize the vector and The deviation between them. Another possible goal of the symbol search process is to minimize the energy expectation of the Hamiltonian regarding the symbol.

[0156] Instead of the above process, for example, such as Figure 13 The Hadamard overlap measurement shown is used to directly measure the CI coefficients, which have both absolute values ​​and phases. The Hadamard test requires controlled application of the entire quantum state preparation on a QPU. Therefore, this algorithm is not feasible on an NISQ-QPU device but can be performed on an FT-QPU (if it is part of a quantum computer system). This expensive measurement can be combined with the prior determination of the important determinant as described above. Alternatively, other complex measurement schemes exist that can be used to measure the absolute values ​​and phases of the CI coefficients, such as shadow tomography.

[0157] After determining a sufficient number of CI coefficients that adequately represent the CAS wavefunction according to equation (1), the CAS wavefunction can be reconstructed as a reference state on different computing devices (i.e., different QPUs or CPUs) best suited for subsequent multi-reference dynamic correlation processing. To determine how many of the most important CI coefficients are sufficient to adequately represent the CAS wavefunction, the following rules can be implemented. For example, how the energy (i.e., the expectation of the Hamiltonian operator) converges with the included CI coefficients, and thus with the number of base states, can be monitored. For example, if the energy change caused by the additional CI coefficients is below a predetermined threshold, it can be determined that sufficient CI coefficients have been included. Additionally or alternatively, the stability of the probability distribution can be obtained as described below, and thus... The stability of the CI coefficients. During the measurement of the CI coefficients, it can be determined whether the CI coefficients change with the increase of the number of measurements and / or whether the ratio of the important CI coefficients changes with the increase of the number of measurements. Based on the results, it can be determined which CI coefficients to include. Additionally or alternatively, it can be determined how much the absolute value of the CI coefficients determined after reconstructing the Hamiltonian in the reduced subspace as described above differs from the absolute value of the CI coefficients obtained during the original measurement. Additionally or alternatively, if the absolute value remains fixed in equation (4), the value produced by evaluating the right side of equation (4) can be determined. AND value How much do they differ? Based on the results, it can be determined whether the relevant CI coefficients are included in the reconstructed CAS wavefunction.

[0158] Alternatively, for the quantum computing approach described above, the CAS wavefunction of the problem can also be determined by conventional CAS, RAS (“restricted active space,” such as RASSCF or RASCI), or GAS (“generalized active space,” such as GASSCF or GASCI) computations running entirely on (multiple) CPUs without any quantum computing component. Thus, in this case, the first part is computed on a classical computer. The quantum computer can then be used in further computational steps to dynamically correlate the “inactive space” part (i.e., the second part). However, using conventional CAS, RAS, or GAS methods utilizing (multiple) CPUs may be computationally more expensive than using the quantum computing approach combined with the described process to determine the CI coefficients.

[0159] The following describes a multi-reference dynamic correlation process in which the CAS wavefunction is used as the reference state and therefore as a fixed starting point. The CAS wavefunction is used as a reference state that no longer changes. The following method considers the dynamic correlation of the "inactive space" and the dynamic correlation between the "active space" and the "inactive space" in further computational steps. Four exemplary embodiments are presented below. The first embodiment utilizes an NISQ-QPU that is not entangled with the FT-QPU or the higher-fidelity NISQ-QPU used for CAS wavefunction computation, and therefore this is related to... Figure 9 The described non-entangled quantum computing system is compatible. Another embodiment utilizes a NISQ-QPU entangled with an FT-QPU or a higher-fidelity NISQ-QPU used for CAS wavefunction computation, thus relating to... Figure 9 The described entangled quantum computing system is compatible. The other two embodiments focus on post-processing on the CPU. Figure 14 An overview of four embodiments, which will be discussed below, is shown.

[0160] The following sections view the CAS method as a division between two aspects: on the one hand, the dominant static correlations within the “active space”; and on the other hand, the dynamic correlations between electrons in all electronic orbitals (active and inactive). However, the methods described below can also be applied in an embedded context. For example, the CASCI method can be used to calculate both static and dynamic correlations of electrons in electronic orbitals located on fragments of a molecular system or material, and dynamic correlation methods can be used to calculate the interactions between CASCI fragments and surrounding electronic orbitals. A fragment is a spatially connected portion of a molecular system that includes the corresponding electronic orbitals associated with that portion of the molecular system and is independent of the active and inactive space subproblems. For example, a fragment can be associated with spatially connected atoms in a molecular system and includes the electronic orbitals of those atoms. The division between the electronic orbitals inside and outside a CASCI fragment can be achieved through orbital localization methods, which can be aided by other techniques such as natural orbitals, natural orbitals of orbital pairs or subsets, orbital-specific virtual orbitals, and projected atomic orbital domains or other functions. A molecule or material can also contain multiple fragments that are treated at the CASCI level using approximate interactions between fragments (e.g., at the mean-field level). The dynamic association method described below is then used to compute the interactions of the associations.

[0161] The following describes a method involving the use of NISQ unitary dynamic correlation (NISQ-UDC) in non-entangled quantum computing systems. For relevant molecules (such as transition metal compounds), the number of electron orbitals assigned to the “active space” portion defining the “active space” is typically significantly smaller than the number of electron orbitals retained in the “inactive space” portion defining the “inactive space”. As discussed above, multiple FT-QPUs with only a small number of usable qubits and / or multiple high-fidelity NISQ-QPUs can be used in conjunction with multiple larger NISQ-QPUs (i.e., multiple NISQ-QPUs with a large number of qubits but low fidelity). This hardware setup is ideally suited for combining CAS computations (where the “active space” portion is solved with high accuracy using an FT-QPU or a higher-fidelity NISQ-QPU) with an approximate dynamic correlation method for the “inactive space” portion and for approximating the dynamic correlations within and between “active space” and “inactive space” subproblems using the NISQ-QPU. Based on the aforementioned CAS computations that define the CAS wavefunction as a reference state as described above, in further computational steps, interaction representations can be generated and solved by applying unitary dynamic correlation (UDC) fitting combined with a variational quantum eigenvalue solver (VQE) or variational Hamiltonian fitting (VHA) to approximate the dynamic correlations using the NISQ-QPU. The “inactive space” portion can be further solved using known methods. In many cases, the solution to the “inactive space” portion may be insignificant. Furthermore, this solution can also be generated with the "active space" portion already taken into account, for example, by adjusting the electron orbitals in the "inactive space" portion based on the solution in the "active space" portion. Then, this solution in the "inactive space" portion can be integrated into the CAS wavefunction as part of the interaction representation.

[0162] More specifically, this method can be derived from parameterized unitary operators. This indicates that the unitary operator acts on both the "inactive space" and "active space" portions of the previously determined CAS wavefunction, resulting in an example of the interaction representation shown below:

[0163] (5)

[0164] in, It is a set of parameters optimized within a variational process (e.g., VQE or VHA). A concrete example is: This is a unitary coupled cluster (UCC) operator. This method can be referred to as the "internal contraction multireference unitary coupled cluster method" (ic-MR-UCC). For an introductory overview of the MR-CC method, see the article "Perspective: Multireference coupled cluster theories of dynamical electron correlation," FA Evangelista, The Journal of Chemical Physics, Vol. 149, No. 3, which is incorporated herein by reference.

[0165] Cluster Operators Excitations from arbitrary electron orbitals p, r to arbitrary electron orbitals q, s are described to account for dynamic correlations. Typically, this expansion includes only single and double terms as explicitly shown above, resulting in the UCCSD operator and thus the ic-MR-UCCSD method. However, this method can also be systematically extended to higher-order excitations, such as triplet and quartet excitations, leading to variants such as ic-MR-UCCSDT and ic-MR-UCCSDTQ. and These are the electron production operator and the annihilation operator, respectively. Restrictions can be imposed on the index pq in a single term, the index pqrs in a double term, or the corresponding index in a higher-order term. Examples of possible restrictions on the indexes include the following: Whenever When the two indices p and q refer to inactive electron orbitals, this item can be restricted to include only those contributing to the study. , where the occupied inactive electron orbitals are i and the unoccupied inactive electron orbitals are a. Whenever When all indices p, q, r, and s refer to inactive electron orbitals, this item can be restricted to include only contributions. The occupied inactive electron orbitals are i and j, and the unoccupied inactive electron orbitals are a and b. It cannot include all indices t, u, v, and j that specifically refer to active electron orbitals. item or Items containing at least one creation operator and at least one annihilation operator in occupied inactive space can be excluded. Items containing at least one creation operator and at least one annihilation operator in unoccupied inactive space can also be excluded. Examples of such excluded items include... and , where i and j are occupied inactive electron orbitals, a and b are unoccupied inactive electron orbitals, and p and q are arbitrary orbitals.

[0166] The method can then be performed as described below. In the first step, the CAS method and process described above using an FT-QPU or a higher-fidelity NISQ-QPU, along with the quantum phase estimation (QPE) algorithm, are applied to determine an exact or near-exact solution for the “active space” portion as a reference state in the form of a CAS wavefunction. In an embodiment, only the “active space” portion is solved on the FT-QPU or a higher-fidelity NISQ-QPU, meaning that typically as many logical qubits as the electron orbitals present in the “active space” can be used to represent the solution for the “active space” portion. Depending on the algorithm, additional qubits may be required to implement the algorithm; for example, auxiliary qubits are needed for the QPE algorithm. Alternatively, the “active space” portion can be solved using a NISQ-QPU (and, for example, a variational quantum eigenvalue solver, VQE) in this step. Alternatively, the CAS method (or alternatively, RAS or GAS) can be run entirely on the CPU, and the process continues to the steps described below, such as dynamic correlation processing on the NISQ-QPU.

[0167] In the second step, the CI coefficients can be determined as described above. The readout CAS wavefunction or the most relevant CI coefficients can be stored on the CPU and kept fixed as part of the reference state in all subsequent steps. In the third step, by executing again... Figure 10 Several parts of the process described herein can be considered using the NISQ-QPU to account for the dynamic correlations of the “inactive space” and the dynamic correlations between the “active space” and the “inactive space”, as described below. First, a representation of the CAS wavefunction is prepared on a quantum computer with appropriate fidelity (e.g., NISQ-QPU). For example, the entire CAS wavefunction, not just the “active space” solution, can be reconstructed according to equation (1), for example, on the NISQ-QPU using the most relevant CI coefficients as described above:

[0168] (6)

[0169] The summation over μ is limited to the n most important ground states (e.g., the Slater determinant as described above), for example, A ground state greater than a predetermined threshold. This typically requires as many qubits as the number of electronic orbitals present in the molecule, for example, the electronic orbitals in the "active space" plus those in the "inactive space". Depending on the algorithm used to prepare the CAS wavefunction on the corresponding quantum computer, the preparation step may require additional qubits (e.g., auxiliary qubits) to prepare the state superposition. In the next step, the UDC operator can be applied. The trial state is generated as an interaction representation according to equation (5), where Θ is a set of variational parameters that will be adjusted on the CPU later in the VQE or VHA process. An example of such a unitary operator is the unitary coupled cluster (UCC) operator described above, where, and These are the variational parameters. In the first iteration, the parameters can be chosen randomly, or they can be selected using other computationally inexpensive conventional methods (e.g., perturbation theory-based methods) that are pre-run on the CPU. Next, the electron creation and annihilation operators can be encoded into qubit operators (i.e., Pauli operators) for example, via Jordan-Wigner or Bravi-Kitayev transforms. Then the encoded UDC operators... The quantum gates are converted and applied to the previously reconstructed CAS wavefunction on a quantum computer to prepare parameterized trial states as interaction representations according to equation (5). Strategies such as the FSIM network algorithm using low-rank decomposition or the CZ algorithm can be used. The single-particle and two-particle reduced density matrices can then be measured on a quantum computer. The measured quantities allow for the parameterization of the trial states on a classical computer (e.g., a CPU) according to the following equation. Relative to the molecular Hamiltonian The energy is evaluated:

[0170] (7)

[0171] If the energy and variational parameters have not yet converged, the iteration continues by updating this set of variational parameters during the variational process on a classical computer, minimizing the energy E. If the energy and variational parameters converge, the iteration continues to the final step. The final energy and other properties of the solution can then be provided to the user. Furthermore, further post-processing can be performed on a classical computer (e.g., a CPU), including applications to real-world problems related to chemical products such as molecules, solids, materials, etc.

[0172] As mentioned above, multi-reference dynamic correlation methods have advantages over CAS methods because they simultaneously consider the dynamic correlation between the "active space" and the "inactive space." In particular, compared to MC-PDFT, the ic-MR-UCC method provides a more systematic approach to compute observables because it does not rely on the choice of density functional as MC-PDFT does. Furthermore, accuracy can be systematically improved by progressing from ic-MR-UCCSD to ic-MR-UCCSDT to ic-MR-UCCSDTQ, and so on. Traditional internally contracted multi-reference methods for CPUs (such as second-order fully active space perturbation theory (CASPT2), NEVPT2, ic-MRCI, or ic-MRCC) require the computation of three-particle, four-particle, or even higher-order reduced density matrices. The need to compute these reduced density matrices on the CPU or measure them on the QPU makes this approach extremely expensive or completely infeasible when used with large "active spaces." Since the ic-MR-UCC method does not require determining higher-order reduced density matrices, it allows for the simulation of larger electronic structure problems, such as larger molecules, with higher accuracy than previously possible. Another specific advantage of ic-MR-UCC over perturbation methods (such as CASPT2 and NEVPT2) is its improved accuracy, similar to the documented advantages of CCSD and UCCSD over second-order Møller-Plesset perturbation theory (MP2), and similar to the advantages of conventional multi-reference coupled clusters over perturbation multi-reference methods. Unlike MRCI, where the accuracy of results decreases with increasing atomic number due to a lack of scale consistency and scalability, the quality of ic-MR-UCC results is maintained.

[0173] The following describes an FT-NISQ unitary dynamic correlation (FT-NISQ-UDC) method utilizing an entangled quantum computing system, where the FT-QPU can also be replaced by a higher-fidelity NISQ-QPU. As an alternative to the above exemplary method, an entangled quantum computing system can also be used to consider dynamic correlations. As a result of a successful convergence of CAS computation using the corresponding quantum computing system described above, a highly accurate solution to the "active space" portion (e.g., the "active space" Hamiltonian operator) can be obtained on the corresponding quantum computer (preferably an FT-QPU or a higher-fidelity NISQ-QPU), for example, a highly accurate eigenfunction. Furthermore, all the obtained electron orbitals can be stored on a classical computer (e.g., a CPU). These obtained electron orbitals can then be used on a NISQ-QPU with appropriate fidelity to fabricate states that can be readily prepared on the NISQ-QPU. The term "inactive space" is used to denote the electronic orbitals that define the "inactive space" portion, for example, by initializing the qubit to state 1 if the inactive electronic orbital is occupied, and to state 0 if the inactive electronic orbital is not occupied, according to the Jordan-Wigner transform. It should be noted that, preferably, the FT-QPU, the higher-fidelity NISQ-QPU, and / or the NISQ-QPU are located on the same chip to facilitate entanglement in later steps. However, spatially separated QPUs can also be entangled using quantum buses (such as optical fibers and photons).

[0174] In order to approximate the dynamic correlations within the "inactive space" region and between the "active space" and "inactive space" regions using entangled quantum computing systems, parameterized unitary dynamic correlation (UDC) operators that enable entanglement between quantum computers with different fidelities can be applied. Thus, we obtain the interaction expression according to the following formula:

[0175] (8)

[0176] Here, Θ is a set of variational parameters within the variational process (e.g., within a variational quantum eigenvalue solver (VQE) or a variational Hamiltonian fit (VHA). A concrete example is: This is a unitary coupled cluster (UCC) operator. This choice will also yield the ic-MR-UCC method, where, unlike the similar methods described above regarding non-entangled quantum computing systems, an entangled quantum computing system is used here. Further details regarding the operator, possible truncation, and possible restrictions on the index have been described above, and these details can also be applied to this embodiment. The coupled cluster operator describes the electronic excitations / transitions between electronic orbitals. Dynamic correlations are considered. Electron excitations / transitions involving at least one active electron orbital and at least one inactive electron orbital will generate entanglement between the corresponding quantum computers, for example, term (Where p refers to the active electronic orbital mapped to the FT-QPU or the higher fidelity NISQ-QPU, and q, r, and s refer to the occupied or unoccupied inactive electronic orbitals mapped to the NISQ-QPU) Entanglement will be generated between qubits located on two different QPUs.

[0177] This method may include the following steps. In the first step, the CAS method and process described above are performed using, for example, an FT-QPU or a higher-fidelity NISQ-QPU and, for example, a quantum phase estimation algorithm (QPE), to determine an exact or near-exact solution for the “active space” portion. Note that only the “active space” portion is solved on the FT-QPU or the higher-fidelity NISQ-QPU, meaning that typically the same number of logical qubits as the number of electron orbitals present in the “active space” portion can be used to represent the solution. Depending on the algorithm, additional qubits may be required to implement the algorithm; for example, for the QPE algorithm, auxiliary qubits are needed. After the CAS process is complete, the electron orbitals can be stored on the CPU as part of a reference state. In the next step, an entangled quantum computing system is used in conjunction with a method similar to... Figure 11 The variational method for the general process exemplified in the example considers the dynamic correlations of the "inactive space" and the dynamic correlations between the "active space" and the "inactive space". For example, solutions to the "active space" portion can be prepared on a high-fidelity NISQ-QPU or FT-QPU to obtain... For example, this can be achieved by applying a quantum phase estimation (QPE) algorithm that uses electron orbitals stored on the CPU. If CASSCF has already been used, since the optimized electron orbitals have been stored, it is not necessary to run the entire iterative CASSCF process again; instead, it is sufficient to prepare the solution for the "active space" portion, i.e., a single CASCI calculation using the optimized and stored electron orbitals. Simultaneously, the electron orbitals stored on the CPU can be used to prepare the wavefunction describing the "inactive space" portion on the NISQ-QPU, thereby obtaining... As part of the reference state, this might require as many qubits on the NISQ-QPU as the electron orbitals present in the "inactive space". In summary, the entire CAS wavefunction is prepared as the reference state on the QPU of the quantum computing system. The UDC operator is then applied to entangle the corresponding quantum computer on which the subproblems (here, the wavefunctions of the "active space" and the "inactive space") are prepared. The trial state is generated according to equation (8) as the interaction representation, where Θ is a set of variational parameters tuned on the CPU, for example, in a VQE process. An example of such a UDC operator is the unitary coupled cluster (UCC) operator described above. In the first iteration step, the parameters can be randomly selected, or they can be selected by other computationally inexpensive conventional methods (e.g., perturbation theory-based methods) that are pre-run on the CPU. The single-particle and two-particle reduced density matrices can then be measured on the QPU as the result of the computation, and similar to equation (7), the trial state can be tuned on the CPU. The energy relative to the molecular Hamiltonian is evaluated. If the energy and variational parameters have not yet converged, the method updates the set of variational parameters on the CPU such that, for example, the corresponding iteration of the above steps is performed after minimizing the energy during the variational process. If the energy and variational parameters converge, the method can continue to the final step. Preferably, the electronic orbitals stored on the CPU as the result of the CAS calculation remain fixed during this process; that is, the CAS wavefunction used as a reference for dynamic correlation processing no longer changes. However, the electronic orbitals can also be adjusted within an optional self-consistent field (SCF) step. The final energy and additional properties of the solution can then be provided to the user. Furthermore, further post-processing can be performed on the CPU, including applications to real-world problems related to chemical products (such as molecules, solids, materials, etc.).

[0178] Compared to other methods, the multi-reference dynamic correlation method described above exhibits advantages very similar to those described for the NISQ-UDC method. Furthermore, the FT-NISQ-UDC method offers additional advantages compared to the NISQ-UDC method utilizing non-entangled quantum computing systems. Unlike the NISQ-UDC method, the FT-NISQ-UDC method does not rely on the measurement of CI coefficients or on approximate reconstruction of the CAS wavefunction on different hardware devices. This allows for the application of a unitary operator considering dynamic correlations to the exact CAS wavefunction rather than an approximate reconstruction. This approach helps eliminate problems that may arise from the approximate reconstruction of the CAS wavefunction, such as intrusive states. Moreover, while in the case of non-entangled quantum computing systems, the entire CAS wavefunction, encompassing both the "active space" and the "inactive space," is represented on the NISQ-QPU in the above method, it is sufficient to represent only the wavefunction of the "inactive space" on the NISQ-QPU, thus reducing the requirement for the number of qubits on the NISQ-QPU.

[0179] The Customized Coupled Cluster (TCC) method is described below. The TCC method aims to utilize the CAS wavefunction as a reference state to consider the dynamic correlations within the "inactive space" and between the "active space" and the "inactive space," allowing for post-processing on the CPU after CAS computation. The True Multi-Reference Coupled Cluster (CC) method applies the coupled cluster exponent operator to a CAS-like multi-reference wavefunction. For example, see equation (5). On the other hand, TCC is a modification of the widely used single-reference CC method to directly incorporate the effects of static correlation into the coupled cluster exponent operator, which is then applied to the single-reference wavefunction. To generate interaction representations in the following form:

[0180] (9)

[0181] As mentioned above, It is a single ground state, such as a ground state constructed from the natural or canonical orbit of the CAS wavefunction, rather than a linear combination of multiple ground states as in equation (1). Other choices besides canonical or natural orbits are also possible. It can be divided into the sum of two commutative operators. . It is a coupled cluster operator, similar in form to the operator already discussed with respect to equation (5). Here, it is directly determined from previous CAS calculations on the QPU via the aforementioned CI coefficients, for example, the CI coefficients of the single-excited ground state and the double-excited ground state in the case of the TCCSD method. and Associated with the coupled cluster operator via the following relation

[0182] (10)

[0183] therefore, It focuses on static correlations and is restricted to electron orbitals acting within the "active space." Once determined by the preceding CAS calculations, It remains fixed throughout the entire TCC process on the CPU. All other possible excitations, including at least one electron orbital outside the "active space," are coupled cluster operators. As part of this, the coupled cluster operator focuses on the dynamic associations within the "inactive space" and between the "active space" and the "inactive space". The parameters included are determined by solving the coupled cluster equations on the CPU:

[0184] (11)

[0185] The parametric equations for single and double excitations are shown in equation (11), thus yielding the TCCSD method. The extension to higher-order excitations is simple, but computationally more expensive. Indices i and j describe the parameters in a single determinant. The indexes a and b describe the occupied electron orbitals, and the indices a and b describe the unoccupied electron orbitals, but these electron orbitals are not directly in the CAS wavefunction.

[0186] exist After the parameters included converge, the final energy is calculated on the CPU according to the following formula:

[0187] (12)

[0188] The entire process can then be described as follows. In the first step, the CAS method and process described above can be used to solve the "active space" part. In the second step, the CI coefficients can be determined as reference states as described above. In the third step, the dynamic correlations within the "inactive space" and between the "active space" and the "inactive space" can be considered using the TCC method performed entirely on the CPU, while also approximating static correlations. The operator can be determined from the CI coefficients according to equation (10). The parameters are used as part of the interaction representation. If the TCCSD method is applied, only single CI coefficients and double CI coefficients are needed. Furthermore, It can be constructed, for example, from the natural or canonical orbit of the CAS wavefunction. Two quantities. and This can be kept constant throughout all the following steps. Then, the modified coupled cluster equations (Equation (11)) as part of the interaction representation are iteratively solved on the CPU to determine... The parameters included are considered to account for the dynamic correlations between all electron orbitals. After the parameters converge, the final energy can be evaluated on the CPU according to equation (12). Optionally, other properties can be calculated. The final result can be provided to the user. Further post-processing and application to real-world problems related to chemical products (such as molecules, solids, materials, etc.) are possible.

[0189] Overall, compared to true multi-reference (MR) methods that directly construct the CAS wavefunction, and traditional MR methods for CPUs that aim to include dynamic correlations on top of statically correlated reference wavefunctions and therefore typically require computation of higher-order reduced density matrices as described above, the TCC method is simpler and less computationally expensive. After preparing the CAS wavefunction on the QPU and measuring all the necessary quantities, the computational workload of TCC on the CPU is comparable to that of well-known traditional coupled-cluster methods.

[0190] The stochastic strongly contracting NEVPT2 (s-sc-NEVPT2) method is described below. Similar to TCC, the s-sc-NEVPT2 method aims to utilize the CAS wavefunction as a reference state to consider the dynamic relationships within the "inactive space" and between the "active space" and the "inactive space," allowing for post-processing on the CPU after CAS computation. In this case, the s-sc-NEVPT2 energy correction (which is a second-order perturbation energy correction to the CAS energy) can be used as the interaction representation, and its expression is:

[0191] (13)

[0192] in, It represents a subspace The so-called strongly contracting perturbation function. It is to the subspace The projection operator is denoted by k, which is the number of electrons added to or removed from the "active space". l denotes the occupied electron orbitals and virtual electron orbitals in the "inactive space" from which electrons are removed or added, respectively. Typically, dynamic correlations are considered through these electron excitations / transitions within the "inactive space" or between the "active space" and the "inactive space". It is the unperturbed reference wavefunction obtained by CAS calculation in the previous step, which serves as the reference state. It is the energy of the perturbation state:

[0193] (14)

[0194] This energy is calculated as the so-called Dyall Hamiltonian. The expected value. The denominator and numerator in equation (14) are:

[0195] (15)

[0196] (16)

[0197] in, Represents the CI state defined in equation (1), and The corresponding CI coefficients are calculated by overlapping the CAS wavefunction with the CI state, see equation (2) and below. The previous CAS process on the QPU naturally provides the CI state by repeatedly measuring all qubits. A random sample, whose probability distribution is: This result can then be substituted into equations (15) and (16), which can be evaluated on the CPU as part of the interaction representation. Furthermore, the CI coefficients... They can be obtained as described above, and can also be input into equations (15) and (16). The CI coefficients are also used to reconstruct the CAS wavefunction. Accuracy depends on the CI coefficient used. and associated ground state The number of elements. Furthermore, the matrix elements in equations (15) and (16) They can be computed efficiently on a CPU because they are simply matrix elements between base states (e.g., Slater determinants).

[0198] An exemplary method can then be described as follows. In the first step, the CAS method and process described above are used to solve the “active space” part. In the second step, the CI coefficients can be determined as described above. Then, the absolute values ​​and phases of the most relevant CI coefficients can be stored on the CPU as part of the reference state. In the third step, the dynamic correlation is considered by, for example, evaluating the second-order energy correction as an interaction representation on the CPU according to equation (13). The CAS wavefunction can be reconstructed using the most relevant CI coefficients according to equation (1), as described above. The CAS wavefunction is normalized to In addition, CAS energy Alternatively, it can be substituted into equation (13). The matrix elements in equations (15) and (16) These equations can be computed on a CPU. They can ultimately be calculated using the previously determined most relevant CI coefficients. and its square To calculate the value. The final s-sc-NEVPT2 energy correction (see equation (13)) can then be compared with the CAS energy. The energy is summed to obtain the final total energy of the electronic structure problem provided to the user on the CPU. Further post-processing and application to real-world problems related to chemical products (such as molecules, solids, materials, etc.) are possible. Compared to conventional NEVPT2 and other MR methods on the CPU, as well as potential direct implementations of NEVPT2 using a QPU, s-sc-NEVPT2 circumvents the expensive computation of high-order reduced density matrices, thus allowing the simulation of larger electronic structure problems, such as larger molecules.

[0199] The following sections provide some preferred applications of the above embodiments. As a result of the above methods using quantum computers, the total energy and properties of the electronic structure of chemical products (e.g., molecular materials, and optionally periodic materials) can be calculated and provided to users. Using these calculation results, relevant quantities for real-world applications can be predicted, such as the technical application properties of chemical products (e.g., molecules). From this, recommendations can be made regarding the discovery of new materials and chemicals, the improvement of chemical processes, the customization of molecules, solids, and materials according to desired properties, and making research activities more efficient by reducing the number of expensive laboratory and production trials required.

[0200] A key example of a definite technical application characteristic is chemical reactivity, where the prediction of thermodynamic and kinetic quantities of a chemical reaction depends on the calculation of free enthalpies (e.g., on reaction free enthalpies and activation free enthalpies, respectively). For example, reaction free enthalpies indicate whether a chemical reaction can occur in principle, and activation free enthalpies indicate the rate of the chemical reaction, i.e., the velocity. Among the most important and difficult-to-calculate contributions to the correspondingly required free enthalpies is the energy difference between reactants, products, and the transition state, e.g., the energy peak along the reaction path from reactants to products. For example, the reaction energy, one of the main contributions of chemical thermodynamics, is obtained by subtracting the sum of the total energies of all reactants from the sum of the total energies of all products. Similarly, the activation energy, one of the main contributions of chemical kinetics, is obtained by subtracting the sum of the total energies of all precipitates from the total energy of the transition state. The method of the present invention, as described above, can advantageously be used to calculate the total energies of the corresponding products, reactants, and transition state. The calculation of the enthalpy of free energy for all potential reaction pathways (i.e., considering all possible transition states, intermediates, and products) ultimately enables the prediction of the outcome of a molecular reaction by identifying one or more energy-optimal reaction pathways. Highly accurate calculations of all types (i.e., reactants, products, transition states, and intermediates) and their total energies within a chemical reactivity network are essential for reliably predicting thermodynamic and kinetic quantities of chemical reactions (such as reaction enthalpy and activation enthalpy); such highly accurate calculations are required for the computational design of novel chemical products and the improvement of industrial chemical production processes, as well as for other technological applications such as understanding and inhibiting the degradation of chemical products, predicting the microstructure of polymeric chemicals, and thus computationally fine-tuning the technical application properties of chemical products.

[0201] Another example of a definite technological application characteristic is the spectrum and spectral properties of electronically excited states, which involve electronic structure problems. For example, calculating the total energy difference between different electronic states (e.g., between the ground state and one or more electronically excited states, for example, having a specific spin multiplicity or electronic configuration different from the ground state) makes it possible to predict the spectrum and spectral properties of chemical products, which are relevant to understanding the effects of radiation on chemical products (e.g., in photovoltaic and photochemical synthesis and degradation processes). Furthermore, the calculation of electronically excited states is a prerequisite for the computational design of, for example, dyes or photoinitiators, and more complex components such as organic electronic materials.

[0202] Another example of a technology application characteristic that can be determined using the methods described above is molecular properties beyond energy, such as electrostatic multipole moments, hyperfine coupling, electric fields and their gradients associated with Mössbauer spectroscopy, and diamagnetic shielding associated with nuclear magnetic resonance (NMR) spectroscopy. Typically, calculations of physicochemical properties are crucial for elucidating molecular structure and properties.

[0203] Furthermore, the invention described above is particularly advantageous for solving problems in molecular systems exhibiting strong static correlations. However, the invention is not limited to solving statically correlated electronic structure problems, but can be applied to all electronic structure problems. Statically correlated molecular systems typically include parts exhibiting complex electronic structures, making high-accuracy calculations on classical computers often very expensive even for smaller-scale problems. Examples of molecular systems exhibiting strong static correlations typically include organometallic compounds containing transition metals (such as iron, nickel, rhodium, palladium, etc.) or lanthanides and actinides. Therefore, examples of molecular systems exhibiting strong static correlations include statically correlated homonuclear or oligonuclear centers in weakly correlated environments, where the term "nucleus" refers to a single ion or single atom of a transition metal, lanthanide, or actinide element plus optionally a ligand. Such transition metal compounds are of critical importance for the design of novel catalysts, chelating agents, homogeneous catalytic fine chemicals, enzymes, etc. Furthermore, static correlations also occur outside of transition metal chemistry, for example, during chemical reactions of organic molecules in the case of bond breaking and / or formation (e.g., in certain transition states), and also in some common main group element molecules (such as ozone).

[0204] Specific industrially relevant chemical products to which this invention can be applied are, for example, catalysts. Catalysts play a crucial role in achieving or accelerating chemical reactions under mild conditions (e.g., mild temperatures and mild pressures) by interacting with transition states and lowering their energies, thereby reducing activation energies and increasing chemical reaction rates. Currently, catalysts containing 4d or 5d transition metals (such as rhodium and palladium) are frequently used; these catalysts are very expensive, such as rhodium-based Wilkinson catalysts used for hydroformylation. Many technological goals aim to replace those catalysts with those containing, for example, cheaper 3d transition metals, cobalt, or iron. The invention described above can be particularly advantageous in the field of homogeneous catalysis, for example, for calculating oxidation, reduction, hydrogenation, carbonylation, etc., in large-scale chemical production processes (such as polymer production processes) and in the synthesis of basic chemicals using homogeneous catalysis. For example, using the invention described above, the energies of a predetermined catalytic cycle, including undesirable side reactions, can be calculated for a predetermined set of catalysts before their synthesis in the laboratory. As mentioned above, these activation energies facilitate the calculation of chemical kinetics, particularly chemical reaction rates. Specifically, the chemical reaction rate of the identified potential catalyst can be compared with the target chemical reaction rate, and based on this comparison, ii) the corresponding potential catalyst can be identified as the target catalyst, or iii) a new potential catalyst can be provided, and the reaction rate determination according to the invention can be repeated. Therefore, only catalysts with chemical reaction rates greater than a predetermined threshold and no predicted serious undesirable side reactions are ultimately selected for synthesis, for example, by providing control data for the corresponding synthesis of the corresponding catalyst, and for further studies in the laboratory.

[0205] Other specific industrially relevant chemicals to which this invention can be applied are chelating agents. The development of chelating agents tailored for certain metal ions can be enhanced by calculating the complex formation constant. The complex formation constant is a thermodynamic quantity indicating the thermodynamic stability of the resulting complex of the metal ion with the chelating agent. Reliable computational predictions typically require highly accurate calculations of the total energy of the corresponding ion and molecule, which is particularly challenging for transition metal ions. Additionally, reliable predictions of chelating agent selectivity are challenging because both their experimental determination and computational prediction are difficult. Selectivity is a means of describing the degree to which a particular chelating agent is more inclined to bind with a particular metal ion compared to other metal ions, and it can be derived from the corresponding complex formation constant. A well-known example of a chelating agent is ethylenediaminetetraacetic acid (EDTA), which can be used, for example, to solubilize Fe. 3+Ions. Many technical objectives aim to design novel chelating agents with predetermined selectivity that exhibit favorable properties (such as biodegradability) or less harm to aquatic organisms. Chelating agents are used in a wide variety of technical applications, for example, to suppress the undesirable effects of metal ions during washing and cleaning processes. Furthermore, chelating agents are used in mining for the selective extraction of metals. For example, using the invention described above, the reaction energies of predetermined chelating agents can be calculated, which ultimately helps in calculating the complex formation constant and thus facilitates selection relative to different transition metal ions. These calculations are performed, for example, for a predetermined set of chelating agents prior to their synthesis in the laboratory. In particular, the selectivity of identified potential chelating agents can be compared with the target selectivity, and based on this comparison, i) the corresponding potential chelating agent can be identified as the target chelating agent, or ii) new potential chelating agents can be provided, and the determination of selectivity according to the invention can be repeated. Thus, only those chelating agents that satisfy certain predetermined criteria / technical application characteristics (e.g., regarding selectivity) are ultimately selected for synthesis and further laboratory studies, for example, by providing control data that induces the corresponding synthesis of the respective chelating agent.

[0206] Other specific industrial-related chemical products to which this invention can be applied include (biological) macromolecular systems and large biomolecules with active centers, such as enzymes, like peptidases and esterases.

[0207] The following provides more detailed examples of how the above properties can be calculated. One example involves... Figure 15 The image schematically and exemplarily illustrates applications of spectroscopy. Spectroscopy is a non-invasive method for studying systems experimentally, comparing them with other systems or under different environments and / or different physicochemical conditions, to elucidate the molecular structure, properties, and chemical reactivity of a system. Different experimental spectroscopic techniques across different electromagnetic spectral ranges, and combinations thereof, can yield a more comprehensive understanding of the system under study, such as molecules and materials. However, the increasing complexity of these experimental techniques makes interpreting spectroscopic results increasingly difficult without the aid of computational chemistry. For example, experimental results often do not allow for the direct derivation of desired information; in some cases, molecular structures cannot be directly deduced from measured spectra. However, experimental results can be compared with computational results to obtain the desired information; for example, measured spectra can be compared with various calculated spectra assuming different molecular structures to determine the molecular structure that best matches both the measured and calculated spectra.

[0208] The following describes the determination of spectroscopic application properties based on the solutions to the aforementioned electronic structure problem. In UV / Vis spectroscopy, excited-state properties obtained as solutions to the electronic structure problem can be used. Specifically, the energies of the electronic excited states (i.e., the energies of states with predefined spin multiplicity or electronic orbital configurations different from the ground state) and the corresponding energies of the electronic ground states (e.g., both obtained using a gate-based quantum computer) can be used. Additionally and optionally, vibrational contributions (e.g., Frank-Condon curves obtained using, for example, a boson-sampling photonic quantum computer) and other contributions (e.g., linewidths obtained via approximate calculations on a classical computer or as user input) can be used. As output, spectroscopic application properties can be calculated that are directly related to experimentally obtainable properties and thus support the solution of real-world chemical or materials problems. For example, electronic absorption spectra can be calculated that directly refer to, for example, experimentally obtainable UV / Vis spectra.

[0209] UV / Vis spectroscopy uses visible light and adjacent light ranges, where the absorption or reflection of light in the visible range by a chemical product or material directly affects its perceived color. Therefore, the calculated electronic absorption spectrum can support, for example, the design of new dyes. Another example involves photoinitiators, which are molecules that produce reactive species (such as free radicals) when exposed to radiation in the UV or visible range. These reactive species can then initiate, for example, polymerization to produce polymers. In this context, the difference in calculated energy between the lowest-energy electronically excited state and the electronically ground state is directly related to the laser wavelength required to irradiate the photoinitiator to initiate the polymerization process. Further examples of real-world chemistry and materials problems involve photovoltaics and photochemical synthesis.

[0210] Furthermore, electron emission spectra can be calculated, which directly refers to, for example, experimentally obtainable fluorescence spectra. Electron emission spectra are complementary to electron absorption spectra because the former involves the transitions of electrons from excited states to the ground state caused by photon emission, while the latter designs the transitions of electrons from the ground state to excited states caused by photon absorption. For example, as an important characteristic for technological applications, the calculated energy difference between the electronically excited states and the electronically ground state of a molecule or material is directly related to the color of the emitted light. For instance, using this workflow, the color of the emitted light of a potential organic light-emitting diode material can be calculated before the actual synthesis of that material.

[0211] In infrared (IR) spectroscopy, the derivative of the total ground-state energy with respect to the nuclear position, obtained as described above, can be used. Specifically, the second derivative is used, which can be calculated entirely analytically and numerically, or numerically in a subsequent step using the analytically calculated first derivative. The calculated spectrum (also known as the vibrational spectrum within the rigid rotor / harmonic oscillator approximation, as they refer to molecular vibrations) can be directly correlated with experimentally available IR spectra. IR spectroscopy can be used to characterize new chemicals and / or materials or to identify and verify known and unknown samples.

[0212] Furthermore, electronic vibrational spectra can be calculated, taking into account the simultaneous changes in the electronic and vibrational energy levels of chemical products or materials due to the emission of photons with appropriate energy. Electronic vibrational spectroscopy can provide information about the electronically excited states of molecules, such as bond lengths.

[0213] To facilitate comparison of the calculated spectra with the corresponding experimentally determined spectra, these calculated spectra are typically visualized by plotting the calculated transition intensities or related quantities (such as absorbance) against the corresponding calculated transition energies or related quantities (such as transition wavelengths). Further details on general computational spectroscopy predictions are described in the following article: “Computational molecular spectroscopy”, Vincenzo Barone et al., Nature Reviews Methods Primers 1, 38 (2021).

[0214] A preferred example of a identifiable technical application characteristic is chemical reactivity, where the prediction of a single chemical reaction (such as the following chemical reaction) is possible.

[0215]

[0216] The thermodynamic and kinetic quantities depend on the calculation of the reaction free enthalpy and the activation free enthalpy, respectively. For example, the reaction free enthalpy indicates whether a chemical reaction can occur in principle, and the activation free enthalpy indicates the rate of the chemical reaction, i.e., the velocity.

[0217] Reaction free enthalpy It can be determined according to the following formula, by extracting from all products (in the example above). and Subtract all reactants (in the example above) from the sum of their free enthalpies. and Calculated by the sum of the free enthalpies of ).

[0218]

[0219] Among them, the free enthalpy of each individual chemical species in solution Through their corresponding stoichiometric weights Weighted. Similarly, activation free enthalpy. The free enthalpy from the transition state (in the example above) can be determined according to the following formula. The enthalpy of free energy is obtained by subtracting the stoichiometric weighted sum of the free enthalpies of all reactants from the enthalpy of free energy in the reaction. The free enthalpy of free energy in the transition state is the highest point of free enthalpy along the reaction pathway from reactants to products.

[0220]

[0221] Since chemical reactions typically occur in solution (e.g., in water) rather than in the gas phase, it is preferable to account for the effect of the solvent when calculating all free enthalpies. However, for many applications, omitting the solvent effect in the calculation can also be a reasonable approximation. The following examples consider the solvent, but an approximation can also be applied without considering the solvent by accordingly removing the solvent component. Individual chemical species (e.g., reactants) or ,product or transition state Enthalpy of free energy in solution The free enthalpy in the gas phase can be expressed by the following formula. and enthalpy of dissolution The sum is obtained as follows:

[0222]

[0223] It should be noted that the free enthalpy in a solution is sometimes also called the Gibbs free energy in the solution. According to the following formula, at a predetermined temperature... The free enthalpy obtained in the gas phase is as follows:

[0224]

[0225] in, This refers to electron energy. Higher energies can be generated using the methods described above (e.g., using quantum computers). It should be noted that, depending on the electronic state of interest, this energy can refer to both the electronic ground state and the electronic excited state. It is the zero-point energy of vibration, and These are the translational / rotational / vibrational partition functions, respectively. and Both can be calculated from vibrational spectra, which can be generated, for example, using the spectroscopic workflow described above, particularly the IR spectroscopic workflow, and with the aid of a quantum computer as described above. However, these quantities can also be obtained using a combination of classical computers and methods that are generally less accurate, such as density functional theory (DFT). It is Avogadro's gas constant.

[0226] Enthalpy of dissolution of molecules in a predefined solvent This can be achieved using classical computers via a dissolution model, such as the Real Solvent-like Conductor Shielding Model (COSMO-RS). Within the COSMO-RS method, in the first step, the electron density indicating the charge distribution in the molecule, obtained using a quantum computer as described above, can be used to calculate the shielding charge density σ on the molecular surface. In the second step, this information can be used to calculate the chemical potential µ of the molecule in a predetermined liquid solvent or mixture. The resulting chemical potential µ is then used to calculate the enthalpy of dissolution. Further information on the COSMO-RS method can be found in the book: “COSMO-RS: From Quantum Chemistry to Fluid Phase Thermodynamics and Drug Design”, Andreas Klamt, Elsevier (2005). It should be noted that by implicitly including the effects of the solvent on the technical application properties (such as reaction enthalpy and activation enthalpy) via the COSMO-RS method, rather than directly calculating the technical application properties in solution by constructing a supersystem that explicitly includes solvent molecules, computational costs can be significantly reduced.

[0227] Calculating the reaction free enthalpy and activation free enthalpy in solution for all potential reaction pathways (i.e., for multiple chemical reactions taking into account all possible transition states, intermediates, and products) ultimately allows for determining the outcome in a predefined mixture of molecules (i.e., reactants) in a test tube or container by identifying one or more energy-optimal reaction pathways. In particular, highly accurate energy calculations for all types of chemical reactivity networks (i.e., reactants, products, transition states, and intermediates) are essential for reliable determination, and therefore essential for designing new chemical products and materials, improving industrial chemical processes, and for other technological applications, such as understanding the degradation of chemical products and inhibiting it, determining the microstructure of polymeric chemicals, and thus computationally fine-tuning the technical application properties of chemical products.

[0228] Specific industrially relevant chemical products for which chemical reactivity (i.e., reaction rate) workflows can be preferably applied are, for example, catalysts, such as... Figure 16 As shown. Catalysts play a crucial role in achieving or accelerating chemical reactions under mild conditions (e.g., mild temperatures and mild pressures) by interacting with transition states and lowering their energies, thereby reducing the activation enthalpy and increasing the rate of chemical reactions. Currently, catalysts containing 4d or 5d transition metals (such as rhodium and palladium) are frequently used; these catalysts are very expensive, such as rhodium-based Wilkinson catalysts used for hydroformylation. Many technological goals aim to replace those catalysts with those containing, for example, cheaper 3d transition metals such as cobalt or iron. Chemical reactivity workflows can be particularly advantageous in the field of homogeneous catalysis, for example, for calculating oxidation, reduction, hydrogenation, carbonylation, etc., in large-scale chemical production processes (such as polymer chemical production processes) and in the synthesis of fine chemicals using homogeneous catalysis. For example, the activation enthalpy of a predetermined catalytic cycle (including undesirable side reactions) can be calculated using chemical reactivity workflows before synthesizing a predetermined set of catalysts in the laboratory. As mentioned above, those activation enthalpies are helpful in calculating chemical kinetics, particularly chemical reaction rates. Specifically, the chemical reaction rate of the identified potential catalyst can be compared with the target chemical reaction rate, and based on this comparison, ii) the corresponding potential catalyst can be identified as the target catalyst, or iii) a new potential catalyst can be provided, and the reaction rate determination according to the invention can be repeated. Therefore, only catalysts with chemical reaction rates greater than a predetermined threshold and no predicted serious undesirable side reactions are ultimately selected for synthesis, for example, by providing control data for the corresponding synthesis of the corresponding catalyst, and for further studies in the laboratory. Furthermore, the corresponding reaction process can be controlled so that the catalyst is utilized in the reaction; for example, the reactor feed can be controlled accordingly.

[0229] Other specific industry-related chemical products that can be applied to chemically reactive workflows are chelating agents, such as... Figure 17As shown. The development of chelating agents tailored for certain metal ions can be enhanced by calculating the complex formation constant. The complex formation constant is a thermodynamic quantity indicating the thermodynamic stability of the resulting complex of the metal ion with the chelating agent. The complex formation constant can be calculated using the enthalpy of reaction of the chelating agent and the metal ion in solution to form the corresponding chelated complex. Reliable calculations are preferably based on accurate calculations of the enthalpy of reaction, which is particularly challenging for reactions involving transition metal ions. Additionally, reliable determination of the selectivity of the chelating agent is challenging because both its experimental and computational determinations are difficult. However, such accurate solutions have been achieved using a quantum computer as described above. Selectivity is a means of describing the degree to which a particular chelating agent is more inclined to bind with a particular metal ion compared to other metal ions, and it can be derived from the corresponding complex formation constant. A well-known example of a chelating agent is ethylenediaminetetraacetic acid (EDTA), which can be used, for example, to solubilize Fe. 3+ Ions. Many technical objectives aim to design novel chelating agents with predetermined selectivity that exhibit advantageous properties (such as biodegradability) or less harm to aquatic organisms. Chelating agents are used in a wide variety of technical applications, for example, to suppress the undesirable effects of metal ions during washing and cleaning processes. Furthermore, chelating agents are used in mining for the selective extraction of metals. For example, using the chemically reactive workflow described above, the enthalpy of reaction of a predetermined chelating agent can be calculated to obtain the corresponding complex formation constant and thus the selectivity relative to different transition metal ions. These calculations can be performed, for example, for a predetermined set of chelating agents before, for example, the synthesis of such a set in the laboratory. In particular, the selectivity of a identified potential chelating agent can be compared with the target selectivity, and based on this comparison, i) the corresponding potential chelating agent can be identified as the target chelating agent, or ii) a new potential chelating agent can be provided, and the determination of selectivity according to the invention can be repeated. Therefore, only those chelating agents that meet certain predetermined criteria / technical application characteristics (e.g., regarding selectivity) are ultimately selected for synthesis and further laboratory studies, for example, by providing control data that induces the corresponding synthesis of the chelating agent. Furthermore, the corresponding reaction process can be controlled so that the chelating agent is utilized in the reaction; for example, the reactor feed can be controlled accordingly.

[0230] Additionally, a slightly modified workflow based on the COSMO-RS method, as described above, can be used to calculate other technical application characteristics, such as activity coefficients, solubility, partition coefficients, and vapor pressures. For example, equilibrium vapor pressure is also an experimentally available quantity and is defined as the pressure exerted by vapor in thermodynamic equilibrium with its condensed phase (liquid or solid) at a given temperature in a closed environment, and is an indicator of the evaporation rate of the liquid or solid. For example, vapor pressure calculations are important for quantifying the volatility of hazardous or toxic chemicals at a given temperature, either before or in lieu of conducting real-world experiments. Additional safety measures can be established in cases where potentially hazardous or toxic chemicals are volatile (i.e., have high vapor pressures, which would result in high concentrations of the chemicals in the respiration zone). Further information on the overall determination of the above-mentioned technical application characteristics can be found in the following article: "Predicting accurate absolute binding energies in aqueous solution: thermodynamic considerations for electronic structure methods", Jan H. Jensen, Phys. Chem. Chem. Phys. 17, 12441 (2015).

[0231] Another exemplary embodiment relates to quantitative structure-activity relationship (QSAR) or quantitative structure-characteristic relationship (QSPR). QSAR or QSPR models are regression or classification models that, in the case of regression models (partial least squares regression models), correlate a set of predictor variables (also called “descriptors”) with one or more output variables (e.g., the power of the response variable), or, in the case of classification models, correlate a set of predictor variables with categorical values. Furthermore, neural networks can also be used as models.

[0232] In the context of this invention, predictor variables can refer to a set of solutions to an electronic structure problem of an electronic structure system (e.g., a molecule), wherein at least one of the electronic structure properties generated based on the solutions to the electronic structure problem is calculated using a quantum computer. However, predictor variables can also refer to a set of technically applicable properties of a real-world chemical or materials problem obtained as described above by processing electronic structure properties. Furthermore, combinations with predictor variables obtained from other sources (such as cheminformatics processing of structural information or experimental physicochemical properties) are also possible. Predictor variables can be electronic properties, geometric properties, structural properties, or physicochemical properties and / or molecular descriptors, and therefore refer to quantities obtainable by one of the methods described above or similar methods, while output variables refer to technically applicable properties of a real-world chemical or materials problem that cannot be directly obtained by the methods described above or similar methods (e.g., the bioactivity or chemical properties of a molecule).

[0233] The QSAR / QSPR model mathematically summarizes the assumed relationships between a chosen set of predictor variables and the output variables. After model construction, it is carefully validated in terms of robustness, predictive performance, and applicability. Following successful validation, the QSAR / QSPR model can then be used to determine the output variables for new real-world chemical or materials problems, such as technological application characteristics, using a set of predictor variables obtained via quantum computing as described above. Since the quality of the predictions depends significantly on the accuracy of the provided predictor variables, the use of quantum computers is expected to be advantageous. Furthermore, the quality of the predictions also depends on other factors, such as the appropriate selection of predictor variables, the QSAR / QSPR model used, and its validation.

[0234] Specific technical application characteristics that can be calculated using the QSAR / QSPR workflow described above are, for example, the bioactivity of chemical products (such as drugs, poisons, or environmental pollutants) using the corresponding calculated electronic structure characteristics or the aforementioned technical application characteristics as predictive variables. Bioactivity can be quantitatively expressed as the concentration of the chemical product required to give a certain biological response (including desired therapeutic effects and undesirable side effects). For example, the QSAR / QSPR workflow can be used for computational toxicology assessments of novel chemical products.

[0235] By studying the accompanying drawings, this disclosure, and the appended claims, those skilled in the art can understand and implement other variations of the disclosed embodiments when practicing the claimed invention.

[0236] The operations performed in the processes and methods disclosed herein may be implemented in different orders. Furthermore, the operations outlined are provided as examples only, and some of these operations may be optional, may be combined into fewer steps and operations, may be supplemented with more operations, or may be expanded into more operations without departing from the essence of the disclosed embodiments.

[0237] In the claims, the word “comprising” does not exclude other elements or steps, and the indefinite article “a / an” does not exclude multiple / types.

[0238] A single unit or device can perform the functions of several items listed in the claims. The fact that certain measures are listed in different dependent claims does not indicate that combinations of these measures cannot be used advantageously.

[0239] Processes performed by one or more units or devices (such as providing electronic structure representations, enabling quantum computers and / or classical computers to generate and provide solutions, generating solutions to electronic structure representations, etc.) can be performed by any other number of units or devices. These processes can be implemented as program code devices and / or dedicated hardware for computer programs.

[0240] Computer program products can be stored / distributed on suitable media, such as optical or solid-state storage media provided with or as part of other hardware, but can also be distributed in other forms, such as via the Internet or other wired or wireless telecommunications systems.

[0241] Any unit described herein can be a processing unit as part of a classical computing system. Processing units can include general-purpose processors and can also include field-programmable gate arrays (FPGAs), application-specific integrated circuits (ASICs), or any other special-purpose circuitry. Any memory can be physical system memory, which can be volatile, non-volatile, or some combination of both. The term "memory" can include any computer-readable storage medium, such as a non-volatile mass storage device. If the computing system is distributed, the processing and / or storage capabilities can also be distributed. A computing system can include multiple structures as "executable components." The term "executable component" is a structure that is well understood in the computing field to be software, hardware, or a combination thereof. For example, when implemented as software, those skilled in the art will understand that the structure of an executable component can include software objects, routines, methods, etc., that can be executed on the computing system. This can include executable components in the computing system heap or on a computer-readable storage medium. The structure of an executable component can exist on a computer-readable medium such that, when interpreted by one or more processors of the computing system (e.g., by processor threads), it causes the computing system to perform functions. This structure can be directly read by a processor, for example, if the executable is binary, or it can be constructed to be interpretable and / or compileable, for example, whether in a single stage or multiple stages, thereby generating such binary that can be directly interpreted by the processor. In other cases, the structure can be hard-coded or hard-wired logic gates, implemented specifically or almost specifically in hardware, such as within a field-programmable gate array (FPGA), application-specific integrated circuit (ASIC), or any other dedicated circuit. Thus, the term "executable" is a term for a structure well-known to those skilled in the art of computing, whether implemented in software, hardware, or a combination thereof. Any embodiments herein are described with reference to actions performed by one or more processing units of a computing system. If such actions are implemented in software, one or more processors direct the operation of the computing system in response to the execution of computer-executable instructions constituting the executable. The computing system may also include communication channels that allow the computing system to communicate with other computing systems via, for example, a network. A "network" is defined as one or more data links that enable the transfer of electronic data between computing systems and / or modules and / or other electronic devices. When information is transmitted or provided to a computing system via a network or another communication connection (e.g., hardwired, wireless, or a combination of hardwired and wireless), the computing system correctly treats that connection as a transmission medium. The transmission medium may include a network and / or a data link, which may be used to carry desired program code in the form of computer-executable instructions or data structures, and may be accessed by a general-purpose computing system or a special-purpose computing system or a combination thereof.While not all computing systems require a user interface, in some embodiments, the computing system includes a user interface system for interaction with a user. The user interface, for example, acts as an input or output mechanism for the user via a display.

[0242] Those skilled in the art will understand that at least a portion of the present invention can be practiced in network computing environments with a variety of computing system configurations, including personal computers, desktop computers, laptop computers, message processors, handheld devices, multiprocessor systems, microprocessor-based or programmable consumer electronics, network PCs, minicomputers, mainframe computers, mobile phones, PDAs, pagers, routers, switches, data centers, wearable devices (such as glasses), etc. The present invention can also be practiced in distributed system environments, where, for example, local and remote computing systems linked by a network via hardwired data links, wireless data links, or a combination of hardwired and wireless data links jointly perform tasks. In a distributed system environment, program modules can reside on both local and remote memory storage devices.

[0243] Those skilled in the art will also understand that at least a portion of the present invention can be practiced in a cloud computing environment. A cloud computing environment can be distributed, but this is not required. When a cloud computing environment is distributed, it can be spread across multiple countries within an organization and / or have components spanning multiple organizations. In this specification and the appended claims, “cloud computing” is defined as a model for enabling on-demand network access to a shared pool of configurable computing resources, such as networks, servers, storage devices, applications, and services. The definition of “cloud computing” is not limited to any of the many other advantages that can be obtained from such a model when deployed. The computing system of the accompanying drawings includes various components or functional blocks that can implement the various embodiments disclosed herein as explained. These various components or functional blocks can be implemented on a local computing system or on a distributed computing system that includes elements residing in the cloud or aspects implementing cloud computing. These various components or functional blocks can be implemented as software, hardware, or a combination of software and hardware. The computing system shown in the figures may include more or fewer components than those shown in the figures, and some of these components may be combined as needed.

[0244] Any reference numerals in the claims should not be construed as limiting the scope.

[0245] This invention relates to an apparatus for generating properties associated with chemical products. A providing unit provides an electronic structure representation comprising a) a first portion indicating an active space and b) a second portion indicating an inactive space. The properties depend on the active and inactive spaces. A determining unit enables a quantum computer and / or a classical computer to generate solutions for the first portion and solutions for the second portion. A computing unit generates a solution to the electronic structure representation by combining the solutions for the first and second portions to generate the properties. This combination includes generating an interaction representation based on a reference state associated with a superposition of electronic configurations generated from the solutions for the first and second portions.

Claims

1. An apparatus for generating properties associated with a chemical product, wherein, The chemical product comprises one or more molecular structures, wherein the device comprises: An electronic structure representation providing unit is configured to provide an electronic structure representation associated with the molecular structure of the chemical product, and the electronic structure representation includes a) a first portion of the electronic structure representation indicating an active space comprising a portion of the electronic structure associated with the molecular structure, and b) a second portion of the electronic structure representation indicating an inactive space comprising another portion of the electronic structure associated with the molecular structure, wherein the properties associated with the chemical product depend on the active space and the inactive space. A solution determination unit is configured to enable a quantum computer and / or a classical computer to generate and provide a solution for a first portion of the electronic structure representation, and to enable a quantum computer and / or a classical computer to generate and provide a solution for a second portion of the electronic structure representation. An associative computational unit is configured to generate a solution to the electronic structure representation by combining the solution of the first part and the solution of the second part, wherein the solution of the first part and the solution of the second part are computationally combined to generate properties associated with the chemical product, wherein the computational combination includes generating an interaction representation based on a reference state associated with the superposition of electronic configurations generated based on the solution of the first part and the solution of the second part, and enabling a classical computer and / or a quantum computer to provide a solution to the interaction representation.

2. The apparatus according to claim 1, wherein, The reference state is represented by configuration interaction ground states and coefficients associated with these configuration interaction ground states, which are given by a fixed distribution of electrons between electron orbitals.

3. The apparatus according to any one of claims 1 and 2, wherein, Determining the reference state based on the solution of the first part and the solution of the second part includes controlling the quantum computer to generate a representation of the solution of the first part on the quantum computer, wherein the reference state is determined based on the representation of the solution of the first part on the quantum computer.

4. The apparatus according to claim 3, wherein, Determining the reference state involves determining the overlap between the solution prepared on the quantum computer for the first part and the corresponding configuration interaction ground states to determine these coefficients.

5. The apparatus according to claim 4, wherein, Determining the overlap includes: measuring a representation of the solution of the first part on the quantum computer, the representation corresponding to the distribution of these electrons in the active space between these electron orbitals; determining the corresponding coefficients associated with these configuration interaction ground states based on the measurement results; repeating the process until predetermined conditions are met to generate a histogram of the coefficients of these measured configuration interaction ground states; and determining the reference state based on the histogram.

6. The apparatus according to claim 5, wherein, Based on the representation of the solution of the first part on the quantum computer, the reference state is determined by applying a projection operator to the representation of the solution of the first part, projecting the representation of the solution of the first part onto the corresponding configuration interaction basis state representation, and measuring these obtained states on the quantum computer based on the histogram.

7. The apparatus according to any one of the preceding claims, wherein, This interaction represents the association between electron orbitals, at least one of which belongs to the inactive space.

8. The apparatus according to any one of the preceding claims, wherein, The correlated computation unit is configured to enable a quantum computer to prepare a representation of the reference state on the quantum computer, and to entangle quantum elements representing the correlation between the active space and the inactive space to provide a solution to the interaction representation.

9. The apparatus according to any one of the preceding claims, wherein, A solution to the interaction representation is provided by preparing a representation of the solution for the first part on a first quantum computer and a representation of the solution for the second part on a second quantum computer, and by performing quantum computation on the interaction representation, wherein quantum elements of the first quantum computer and quantum elements of the second quantum computer are entangled to represent the association between the active space and the inactive space.

10. The apparatus according to any one of the preceding claims, wherein, The interaction means that the association between electron orbitals is included by projecting the reference state onto one or more predetermined configuration interaction ground states and generating the solution based on the result of the projection, wherein at least one of the electron orbitals belongs to the inactive space.

11. The apparatus according to claim 10, wherein, A solution to this interaction representation is generated using a customized coupling cluster method.

12. The apparatus according to any one of the preceding claims, wherein, The correlation between electron orbitals is incorporated into the interaction representation using the stochastic strongly contracted second-order n-electron valence state perturbation theory method, where at least one of these electron orbitals belongs to the inactive space.

13. A system for generating properties associated with a chemical product, wherein, The system includes: A quantum computer adapted to perform quantum mechanical calculations, and The apparatus according to any one of the preceding claims, wherein the apparatus is adapted to enable the quantum computer to perform quantum mechanical calculations.

14. A computer-implemented method for generating properties associated with a chemical product, wherein, The chemical product comprises one or more molecular structures, wherein the method includes: An electronic structure representation associated with the molecular structure of the chemical product is provided, and the electronic structure representation includes a) a first portion of the electronic structure representation indicating an active space comprising a portion of the electronic structure associated with the molecular structure, and b) a second portion of the electronic structure representation indicating an inactive space comprising another portion of the electronic structure associated with the molecular structure, wherein the properties associated with the chemical product depend on the active space and the inactive space. To enable a quantum computer and / or a classical computer to generate and provide a solution for the first part of the electronic structure representation, and to enable a quantum computer and / or a classical computer to generate and provide a solution for the second part of the electronic structure representation, and The solution to the electronic structure representation is generated by combining the solution of the first part and the solution of the second part, wherein the solution of the first part and the solution of the second part are computationally combined to generate properties associated with the chemical product, wherein the computational combination includes generating an interaction representation based on a reference state associated with the superposition of electronic configurations generated based on the solution of the first part and the solution of the second part, and enabling a classical computer and / or a quantum computer to provide a solution to the interaction representation.

15. A computer program product for generating properties associated with a chemical product, wherein, The computer program product includes program code means for causing the means according to any one of claims 1 to 12 to perform the method according to claim 14.

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