Apparatus for providing control signal for controlling quantum computing system

Abstract

The invention relates to an apparatus (710) for providing a control signal for controlling a quantum computing system. A quantum computing system includes at least two quantum computers having different fidelity. A question providing unit (711) provides a question description indicating a question. A sub-problem derivation unit (712) derives a sub-problem from the provided problem description based on the fidelity of the at least two quantum computers. A control signal generation unit (713) generates control signals for controlling the quantum computing system such that the derived sub-problems are quantum computed on the at least two quantum computers, where the sub-problems are distributed to the respective at least two quantum computers based on the fidelity of the at least two quantum computers.

Description

Technical Field

[0001] This invention relates to an apparatus, method, and computer program product for providing control signals for controlling a quantum computing system. Furthermore, this invention relates to a quantum computing system controllable by control signals, a problem-solving apparatus and method for solving problems using a quantum computer, and a system for calculating solutions to problems. Background Technology

[0002] Quantum computing is an emerging technology that utilizes quantum mechanical phenomena to perform quantum computing tasks. Quantum computers promise to solve certain computational problems significantly faster than classical computers. However, applying quantum computers to real-world problems remains a challenging task. 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, it is extremely important in calculations to capture the complexity of chemical molecules by reflecting the types of atoms, the 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. 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 problems (such as complex electronic structure problems), approximation methods can be used. However, in most systems, properties derived from complex correlations (e.g., electronic correlations) may not be adequately reflected by approximation methods. Therefore, it is necessary to include as much of the complexity of real-world systems (e.g., electronic correlations) as possible to obtain results that are as close as possible to the real-world, technologically applicable properties of the 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. However, solving complex problems with many variables is also a challenging task in other industries and applications (e.g., in cryptography, logistics, etc.).

[0005] Computational calculations of problems associated with chemical products (e.g., 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 results of the calculated electronic structure problems 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. Given the environmental impact of chemical development and the speed at which the chemical industry must adapt 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.

[0006] Embedding quantum computing into this development cycle may offer a solution to such complex problems. 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] Quantum computing can be advantageously embedded in the development of new or enhanced chemical products in a more efficient and effective manner by deriving subproblems from a given problem description based on the fidelity of the quantum computer to be used and inducing quantum computation on the derived subproblems, where fidelity determines which quantum computer performs the computation of the corresponding subproblems. In particular, by distributing subproblems across different quantum computers considering fidelity, the different computational requirements of the subproblems can be taken into account, and corresponding parts of the problem (e.g., involving the molecular substructure of chemical products) can be solved with greater efficiency, thereby improving the overall efficiency of solving the corresponding problem.

[0008] In a first aspect, an apparatus is proposed for providing control signals for controlling a quantum computing system for performing quantum computations on problems, particularly those related to chemical products, wherein the quantum computing system comprises at least two quantum computers with different fidelities, wherein the apparatus comprises a) a problem providing unit for providing a problem description indicating the problem, b) a subproblem derivation unit for deriving subproblems from the provided problem description based on the fidelity of the at least two quantum computers, and c) a control signal generation unit for generating control signals for controlling the quantum computing system such that quantum computations are performed on the at least two quantum computers on the derived subproblems, wherein the subproblems are distributed to the respective at least two quantum computers based on the fidelity of the at least two quantum computers.

[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] Typically, a quantum computer is a computer that uses quantum mechanical phenomena to perform computations. For example, a quantum computer can perform quantum computations using effects such as superposition and entanglement. Quantum computers are based on quantum elements that obey quantum mechanics, such as superconductors, ions, atoms, quantum dots, photons, and particle spin. To perform quantum computations, these quantum elements can be manipulated in a controlled manner according to a predetermined algorithm.

[0011] 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.

[0012] A problem can generally refer to any problem that can be transformed into a problem description that can be computed on a quantum computer. In a preferred embodiment, the problem refers to an electronic structure problem. In an example, the problem relates to a chemical product. For example, the solution to the problem can be used to determine the technical application characteristics of the chemical product, or the solution to the problem can be used to optimize a chemical reaction used to produce the chemical product. In an example, the problem is an electronic structure problem. Generally, an electronic structure problem refers to a problem associated with determining the electronic structure of atoms, molecules, crystals, or amorphous solids. For example, an electronic structure problem can be used to determine the high-energy ground state of atoms and / or molecules. Based on the solution to the electronic structure problem, additional properties of atoms, molecules, crystals, or amorphous solids can be derived. Generally, electronic structure problems can be mathematically represented using different classes of underlying electronic structure Hamiltonians. For example, Born-Oppenheimer Hamiltonians, non-Born-Oppenheimer Hamiltonians, Hamiltonians with an additional single-electron potential representing, for example, an electrostatic field, two-component Hamiltonians including spin-orbit coupling, fully relativistic four-component Dirac Hamiltonians, etc.

[0013] The problem-providing unit is adapted to provide a problem description indicating the problem. The problem-providing unit may refer to a storage unit on which the problem description is already stored. However, the problem-providing unit may also include an input unit, for example, which a user can use to indicate the problem description to the problem-providing unit. Typically, the problem description can refer to any form of problem description that allows for the determination of the quantum mechanical form of the problem and the quantities defining the problem, wherein the quantum mechanical form indicates the interactions between these quantities. Preferably, the problem description refers to a mathematical description of the problem, for example, a mathematical description of an electronic structure problem using electronic structure Hamiltonians, as described above. However, the problem description may also refer to any other explicit symbolic form of the problem. In the example, the problem description is associated with a chemical product. The chemical product associated with the problem description can define the electronic structure problem and the quantities of the electronic structure problem. For example, if the 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 problem description. Depending on the specific chemical product and / or quantum mechanical electronic structure problem, the problem description may include or may indicate atomic positions, basis sets, charges, and spin multiplicity.

[0014] In this embodiment, the problem is an electronic structure problem associated with the molecular structure of a chemical product, wherein the solution of the electronic structure representation indicates the properties associated with the chemical product. The electronic structure problem can be represented by an electronic structure representation, wherein the electronic structure representation indicates that the problem can be handled by appropriate means, such as expressing the electronic structure as a mathematical formula. The chemical product can be any chemical product that includes one or more molecular structures (e.g., composed of one or more molecular structures). A molecular structure is a structure that at least forms a portion of a molecule. For example, in a polymer composed of multiple monomers, the molecular structure can be one of these monomers, but it can also refer to multiple of these monomers or even the entire polymer. Furthermore, the molecular structure can also be the atoms in the molecule that forms the chemical product. Typically, the molecular structure includes the electronic structure that can be described by an electronic structure representation.

[0015] Furthermore, the device includes a subproblem derivation unit configured to derive subproblems from a provided problem description based on the fidelity of a quantum computer. At least some of these subproblems can be dependent subproblems. A subproblem is considered dependent if at least one of it depends on at least one other subproblem. For example, at least two subproblems can be coupled such that the solution to one subproblem depends on the solution to the other. However, subproblems can also interact such that each subproblem depends on the solution to the other. Typically, a subproblem can be defined as one whose solution contributes to solving the problem to be solved. In most cases, depending on the problem, multiple distinct subproblems or combinations of subproblems can be formulated to enable the solution of the overall problem. Subproblems are problems with lower complexity than the original problem and are therefore easier to solve. For example, an overall problem can be divided into smaller problems (e.g., subproblems) in which fewer unknowns exist in the overall problem, and thus into problems that are easier to compute.

[0016] Subproblems are derived based on the fidelity of the quantum computer used to compute the problem. Since fidelity determines the quality and accuracy of the quantum computation performed on the respective quantum computer, subproblems can be determined based on this quality criterion. For example, if a quantum computer with high fidelity and a quantum computer with low fidelity are part of a quantum computing system, subproblems suitable for solving on the quantum computer with high fidelity (e.g., fidelity above a predetermined threshold) can be identified, and subproblems that can be adequately solved on the quantum computer with low fidelity (e.g., fidelity below a predetermined threshold) can be derived. In embodiments, subproblems can be derived based on fidelity and predetermined rules. For example, the rules can determine the size and number of derived subproblems based on available quantum computers and their known fidelity. In embodiments, candidate subproblems can be derived, for example, based on the determined rules, and a fidelity threshold can be determined for each subproblem, where the fidelity threshold indicates the minimum fidelity at which the corresponding subproblem can be computed. Fidelity thresholds can be determined based on expert knowledge, known relationships, and / or general rules. For example, the size and type of subproblems, target accuracy, and expected quantum algorithm can be considered. A rough estimate of the fidelity threshold is usually sufficient. The fidelity of the available quantum computer can then be matched against the fidelity threshold. If all subproblems can be matched with the corresponding quantum computer, candidate subproblems are used as subproblems. If one or more subproblems cannot be matched with a quantum computer, the candidate subproblems can be modified. For example, the size or number of candidate subproblems can be changed, and matching can be determined again for the new candidate subproblems. Furthermore, other criteria can be considered when deriving subproblems. In the example, the problem is represented by an electronic structure representation, and the subproblems are derived from the electronic structure representation. In a preferred example, the problem is represented by an electronic structure representation of a chemical molecule, and the subproblems are either active space problems or inactive space problems, where active space problems are determined to be computed on a higher fidelity quantum computer, and inactive space problems are determined to be computed on a lower fidelity quantum computer, where active space problems represent the portion of the molecule's electronic structure that includes correlations higher than a predetermined correlation threshold, and inactive space problems represent the remaining electronic structure of the molecule. In another preferred example, the problem is an optimization problem that includes multiple degrees of freedom to be optimized, and the sub-problems refer to the correlation problem representing degrees of freedom with correlation above a predetermined threshold and the residual problem representing the remaining degrees of freedom, wherein the correlation problem is determined to be computed by a higher fidelity subcomputer and the residual problem is determined to be computed by a lower fidelity subcomputer.

[0017] A control signal generation unit is adapted to generate control signals for controlling the quantum computing system so that quantum computation of a subproblem is performed on the quantum computers of the quantum computing system. The control signals are generated such that fidelity determines which of the at least two quantum computers the quantum computation of the subproblem is performed on. Therefore, the control signals are generated based on the fidelity of the corresponding at least two quantum computers. For example, a subproblem deduced to be computed on a quantum computer with high fidelity (e.g., fidelity above a predetermined threshold) in the quantum computing system can generate control signals such that the corresponding subproblem is computed on the quantum computer with high fidelity (e.g., fidelity above a predetermined threshold). Thus, the control signals are generated such that the subproblem is computed on the quantum computer with the corresponding fidelity for which the subproblem has already been deduced.

[0018] Generally, when control signals relate to controlling a quantum computing system, the control signal generation unit can be configured to generate control signals for controlling the quantum computer, for example, by controlling the manipulation portion of the quantum computer configured to manipulate the states of quantum elements according to corresponding manipulation sequences. However, if the quantum computer itself already provides a control unit adapted to control the manipulation portion to manipulate the states of quantum elements, the control signal generation unit of the device can be adapted to provide control signals to the control unit of the quantum computer. In this case, for example, the control signal can simply refer to a representation of a series of manipulations that can be interpreted by the control unit of the quantum computer to provide corresponding control signals to control the various parts of the quantum computer accordingly. However, in this case, the control signal can also refer to a well-known and interpretable control signal, which is converted by the control unit of the quantum computer into a corresponding dedicated control signal for controlling the specific hardware of the quantum computer. Therefore, the control by the control signal generation unit of the device can be direct or indirect, depending on the corresponding implementation of the quantum computing system. Thus, the control signal generation unit of the device, alone or together with one or more optional control units of the quantum computer, can be regarded as an interface between the quantum computing system (especially the hardware of the quantum computing system) and the software running on a generally known classical computer for solving the corresponding problem.

[0019] Furthermore, the control signal generation unit can also be adapted to control the readout of the quantum computing system so as to measure at least one observable of the prepared representation of the quantum mechanical state of the solution to one or more subproblems after applying a series of predetermined quantum manipulations (including quantum gates and operations). Specifically, the control signal can be adapted to control the readout portion of the quantum computer so that one or more observables are measured (i.e., read out) after the preparation of the corresponding quantum state for solving the corresponding subproblem is complete. Specifically, the control signal generation unit can be adapted to receive the readout from the readout portion and provide the readout to, for example, another device for further processing, for example, in a classical computing environment. However, as mentioned above, here, the control signal generation unit can also optionally interact with the control unit of the quantum computer to act as an interface between the classical computing environment and the quantum computer.

[0020] Quantum computations performed by a quantum computer on derived subproblems can be executed in parallel, sequentially, or iteratively. For example, control signals can be generated to control the quantum computing system, first enabling quantum computation of a first derived subproblem on a first quantum computer, and then subsequently enabling quantum computation of a second derived subproblem on the same or another quantum computer based on the result of the first subproblem. Thus, for example, if there are more derived subproblems than available quantum computers, different subproblems can also be solved sequentially on the same quantum computer. However, subproblems can also be computed in parallel on quantum computers, sequentially on different quantum computers, or iteratively. For example, dependent subproblems can even be computed in parallel during iterations. In this case, appropriate starting conditions can be used to begin parallel computation of subproblems instead of using the solutions of the subproblems as input for the computation of dependent subproblems, and then the corresponding solutions from previous computations can be utilized in the next iteration. Preferably, subproblems are derived such that each subproblem corresponds to only one available quantum computer, i.e., two subproblems are not computed on the same quantum computer. Therefore, the number of derived subproblems is preferably equal to or less than the number of available quantum computers. This allows for the most efficient use of available quantum computer hardware.

[0021] In an embodiment, at least two quantum computers in a quantum computer are configured to be entangled, and control signals are generated for further controlling the entanglement between the at least two quantum computers in the quantum computing system during parallel quantum computing of a subproblem, in order to distribute and share information between the at least two quantum computers during quantum computing, wherein the entanglement of the two quantum computers is defined by at least one quantum element of each quantum computer being entangled. Entanglement between 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 another 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 allows for truly parallel computation of two subproblems, even if these subproblems are interdependent. To achieve entanglement, different hardware solutions can be utilized depending on the corresponding type of quantum computer. For example, for a superconducting-based quantum computer, waveguides and transmission lines can be utilized, as described, for example, in the following article: “Quantum computer with superconducting circuits in the ultrastrongcoupling 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 can be used 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 quantum matter-link between ion-trap microchip modules”, Akhtar, M., Bonus, F., Lebrun-Gallagher, FR et al., Nat Commun [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 ascalable quantum computing 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.

[0022] In an embodiment, deriving these subproblems from the problem description based on the fidelity of the at least two quantum computers includes identifying subproblems requiring higher solution accuracy compared to another subproblem, wherein these control signals are generated such that these subproblems requiring higher solution accuracy are computed on the quantum computer with higher fidelity, and wherein the other subproblem is computed on the quantum computer with lower fidelity. Higher fidelity can be considered higher than: a) the fidelity of at least one of the at least two quantum computers, b) the fidelity of all other quantum computers in the at least two quantum computers, and / or c) a predetermined fidelity threshold. Lower fidelity can be considered lower than: a) the fidelity of at least one of the at least two quantum computers, b) the fidelity of all other quantum computers in the at least two quantum computers, and / or c) a predetermined fidelity threshold. For example, a subproblem requiring higher solution accuracy could be a subproblem more critical to the solution of the problem. For example, when the problem is an electronic structure problem, the subproblem may involve active spaces, which describe the electrons and electron orbitals that actively participate in the bonding or chemical reactions of the corresponding atoms or molecules. Conversely, subproblems describing inactive spaces of atoms or molecules primarily involve electrons and electron orbitals that remain fully occupied or unoccupied during chemical reactions, and therefore have only a weak effect on the chemical reactions of molecules or atoms. Such subproblems requiring higher solution accuracy can be automatically identified, for example, based on a set of predefined rules that define subproblems with a higher impact on the solution to the problem according to the solution algorithm to be utilized. However, such subproblems can also be identified by the user. For example, derived subproblems can be presented to the user, who can then select the subproblems to be calculated with higher accuracy.

[0023] In an embodiment, subproblems are further derived from the problem description based on a predetermined quantum algorithm class defined for solving the problem. For example, the quantum algorithm class may be predefined by the user, for instance, in a selection step that selects the appropriate quantum algorithm class for the corresponding input problem, or it may be predefined for all problems. However, the quantum algorithm class may also be automatically selected for the corresponding problem based on a predetermined set of rules indicating which quantum algorithm class to use to solve which problem class. The quantum algorithm class may include at least one of variational algorithms, shallow algorithms, annealing algorithms, non-variable algorithms, and deep algorithms.

[0024] In an embodiment, the control signal generation unit is adapted to further generate control signals based on the computational algorithm to be used to solve the corresponding subproblem, wherein the computational algorithm to be utilized determines the fidelity threshold of the quantum computer on which the computational algorithm can be executed, and the control signal generation unit is configured to consider the corresponding threshold when generating the control signal. For example, computational algorithms typically to be executed on higher fidelity quantum computers (because they are associated with higher fidelity thresholds) may 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 lower fidelity thresholds compared to the algorithms described above) are variational algorithms, such as variational quantum eigenvalue solvers and quantum approximation optimization algorithms. Based on the derived subproblem, a set of possible algorithms that can be used to solve the subproblem can be presented to the user. The user can then determine the appropriate algorithm to be used through a corresponding selection, and the control signal generation unit utilizes this selection as described above. However, preset algorithms can also be used for the corresponding derived subproblem.

[0025] In this embodiment, the derivation of the subproblem is further based on the number of logical quantum elements provided by the corresponding at least two 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 may be used as auxiliary quantum elements and therefore cannot be used to represent the quantities and aspects of the corresponding subproblem. Furthermore, considering the number of logical quantum elements on the corresponding quantum computers when deriving the subproblem allows for a specific adaptation of the subproblem to the corresponding quantum computers on which it is to be computed, thereby allowing for the use of more efficient and effective quantum algorithms to compute the subproblem on the corresponding quantum computers.

[0026] In the embodiments, the problem description is an electronic structure representation associated with the molecular structure of a chemical product, and the derived sub-problems refer to: i) a first portion of the electronic structure representation, which indicates an active space including a portion of the electronic structure associated with the molecular structure; ii) a second portion of the electronic structure representation, which indicates an inactive space including another portion of the electronic structure associated with the molecular structure; and iii) an interaction representation associated with a combination of solutions to the first portion and solutions to the second portion. Preferably, the interaction representation is generated based on a reference state associated with a superposition of electronic configurations generated based on solutions to the first portion and solutions to the second portion.

[0027] 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.

[0028] The first and second parts of the problem can be derived from the electronic structure representation. 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. In addition to fidelity, the first and second parts of the electronic structure representation can also be determined based on the chemical product and the molecular structure to be described by the electronic structure representation. Specifically, 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. In particular, since the chemical product defines the electron orbitals in the electronic structure representation, and especially 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 based on the available fidelity of a quantum computer. For example, a first part of the electronic structure representation is provided such that it allows the use of a high-fidelity 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.

[0029] The control signal generation unit can be adapted to generate control signals for inducing quantum computation on the first part based on the corresponding fidelity of the quantum computer. For example, the first part can be derived such that the control signal generation unit controls a higher fidelity quantum computer to perform computation on the first part. Alternatively, the first part can be derived such that the control signal generation unit controls a lower fidelity quantum computer or even a classical computer to perform computation on the first part. Depending on the corresponding electronic structure representation, solving the first part of the electronic structure representation using a lower fidelity quantum computer or a classical computer 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 lower fidelity or classical computer can be 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.

[0030] The control signal generation unit can be adapted to generate control signals for inducing quantum or classical computations on the second part based on the corresponding fidelity of a quantum computer. For example, the second part can be derived such that the control signal generation unit controls a lower-fidelity quantum or classical computer to perform computations on the second part. For example, the solution to the second part can be a representation of the electronic configuration of the inactive space of the corresponding molecule. The solution to 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 to the second part can be determined based on a corresponding known algorithm (such as Hartree-Fock or density functional theory (DFT)). In a preferred embodiment, the solution to the second part is determined based on the solution to 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 of the second part is determined. Therefore, the solution to 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, enabling the solution to the second part to be computed on a classical computing device using corresponding known computational methods. Alternatively, the second part can be derived such that a control signal generation unit controls a high-fidelity quantum computer to perform the computation of the second part.

[0031] 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 further computation of the interaction representation. 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 representation. 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.

[0032] 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, a 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 then, during the corresponding calculations, allow the generation of different inactive parts resulting from the correlations between the active and inactive parts. The interaction representation generated based on the reference state then typically represents the correlation between the parts represented by the first part and the parts represented by the second part of the electronic structure representation, and further represents the correlations 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.

[0033] 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.

[0034] The control signal generation unit can be adapted to generate control signals for inducing quantum computation on the interaction representation. For example, the control signals can control a high-fidelity quantum computer to compute solutions to the interaction representation. However, a low-fidelity quantum computer can also be used. In particular, a fidelity threshold can be determined for the interaction representation, and control signals can be generated to control the quantum computer to perform computations including those with fidelity higher than the determined threshold.

[0035] In one embodiment, the quantum computing system includes at least one fault-tolerant quantum computer and a noisy intermediate quantum computer, wherein the fault-tolerant quantum computer has higher fidelity than the noisy intermediate quantum computer. Noisy intermediate 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 a surface codelogical qubit”, Nature 614, 676–681 (2023). However, other codes also exist that utilize this principle. 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 thus enable quantum computers with higher fidelity.

[0036] In another aspect, a quantum computer system is proposed, comprising a) a control unit for receiving control signals generated by the device as described above, and b) at least two quantum computers with different fidelities, wherein quantum calculations on subproblems, particularly those related to chemical products, are performed on the at least two quantum computers based on the control signals generated based on the different fidelities of the at least two quantum computers.

[0037] In one embodiment, at least two of these quantum computers are configured for entangled quantum computing, wherein the entanglement between the at least two quantum computers is controlled based on these control signals, and wherein the entanglement between the two quantum computers is defined by at least one quantum element of each of the quantum computers being entangled.

[0038] In an embodiment, at least one of the at least two quantum computers is a fault-tolerant quantum computer, and at least one of the at least two quantum computers is a noisy medium-sized quantum computer.

[0039] In another aspect of the invention, a problem-solving apparatus is proposed for solving problems, particularly those related to chemical products, wherein the apparatus comprises: a) a receiving unit for receiving quantum computation results of a pair of subproblems performed by at least two quantum computers of a quantum computing system according to control signals generated by the apparatus as described above; and b) a problem-solving unit configured to determine a solution to the problem based on the quantum computation results of the pair of subproblems.

[0040] In another aspect of the invention, a system for generating solutions to problems, particularly those related to chemical products, is proposed, wherein the system comprises a) the apparatus described above, b) the quantum computer system described above, and c) the problem-solving apparatus described above.

[0041] In another aspect, a computer-implemented method is proposed for providing control signals for controlling a quantum computing system used to perform quantum computations on problems, particularly those related to chemical products. The quantum computing system comprises at least two quantum computers with different fidelities. The method includes a) providing a problem description indicating the problem; a) deriving subproblems from the provided problem description based on the fidelities of the at least two quantum computers; and a) generating control signals for controlling the quantum computing system such that quantum computations are performed on the at least two quantum computers on the derived subproblems, wherein the subproblems are distributed to the respective at least two quantum computers based on their fidelities. Control of the quantum computing system may further include providing quantum computation results such that corresponding solutions can be determined. This provision may refer to providing the results to means configured to determine the corresponding solutions as described above. This means may be the same as or different from the means used to control the quantum computing system.

[0042] In another aspect, a problem-solving method is proposed for solving problems, particularly those related to chemical products, wherein the method comprises: a) receiving the quantum computation results of a subproblem performed by at least two quantum computers of a quantum computing system according to control signals generated by the method described above, and b) determining the solution to the problem based on the quantum computation results of the subproblem.

[0043] In another aspect of the invention, the apparatus described above is proposed for solving problems involving at least one of chemical reactivity, spectra and spectral properties, and molecular properties that can be calculated from the electronic structure of chemical products.

[0044] In another aspect of the invention, the use of the apparatus described above for solving problems involving at least one of the following: 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.

[0045] 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. The apparatus described above can be used to determine the activation energy and / or reaction energy of a predetermined chemical reaction. 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 can 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).

[0046] In one aspect of the invention, the apparatus described above is proposed for determining the activation energy of a predetermined catalytic cycle and / or for determining the reaction energy of a predetermined chelating agent.

[0047] 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) a providing unit for providing a description of a quantum mechanical electronic structure problem related to the chemical product, wherein the solution to the quantum mechanical electronic structure problem indicates technical application characteristics; b) a solution unit for determining a solution to the quantum mechanical electronic structure problem using the apparatus described above; and c) a characteristic determining unit for determining the technical application characteristics of the chemical product based on the solution.

[0048] 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) providing a quantum mechanical electronic structure problem description related to the chemical product, wherein the solution to the quantum mechanical electronic structure problem indicates the technical application characteristics; b) determining the solution to the quantum mechanical electronic structure problem using the apparatus described above; and c) determining the technical application characteristics of the chemical product based on the solution.

[0049] 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.

[0050] 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.

[0051] 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.

[0052] 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.

[0053] Technical application characteristics can generally refer to any characteristic of a chemical product that allows for the assessment of the technical suitability of the corresponding chemical product provided after its production. Generating or determining a characteristic associated with a chemical product means determining or deriving and providing that characteristic. This characteristic can be a characteristic of the chemical product related to a solution to a problem of electronic structure, provided as an electronic structure representation, for example, referring to a solution of the electronic structure representation of the molecular structure forming the chemical product, or one that can be derived from that solution. This characteristic can be an electronic characteristic represented by an electronic structure. This characteristic can refer to a characteristic of a chemical product that allows for the assessment of the technical suitability of the corresponding chemical product provided after its production. Preferably, technical application 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, technical application characteristics include at least one of mechanical characteristics, spectral characteristics, physicochemical characteristics, chemical characteristics, and biological characteristics. Mechanical properties typically refer to any of the following: adhesion, tensile strength, stiffness, hardness, shrinkage, elongation, crack tearing, tear strength, resilience, compressibility, abrasion, spillage, morphology, tactile properties, fracture stress, elongation at break, particle size, and filling density. Spectral properties typically include any of the following: tinting, turbidity, opacity, transparency, reflection, 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. In addition, 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, coagulation, 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.

[0054] In determining the properties of a chemical product, a problem-providing unit is adapted to provide an electronic structure representation associated with at least one of one or more molecular structures of the chemical product. Specifically, the problem-providing unit may refer to a storage unit on which the electronic structure representation is already stored. However, the problem-providing unit may also include an input unit, for example, which a user can use to instruct the problem-providing unit on the electronic structure representation as a problem. Typically, the electronic structure representation can be provided in any form that allows for the determination of 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. Typically, 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. For example, if the chemical product refers to a specific molecule whose technical application properties 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. Preferably, depending on the specific chemical product and / or quantum mechanical electronic structure problem, the electronic structure representation includes or indicates atomic positions, basis sets, charges, and spin multiplicity.

[0055] 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 solutions of the electronic structure representation, additional 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. Various properties of the corresponding chemical products can be derived from the solutions of the electronic structure representation.

[0056] In embodiments, the problem of generating control signals for controlling a quantum computer, as described above, can refer to any problem for which solving it allows the derivation of corresponding technical application characteristics (e.g., one of the aforementioned technical application characteristics) of a chemical product. Specifically, this problem can refer to an electronic structure problem, where, based on a solution to the electronic structure problem, several additional characteristics of the corresponding chemical product can be derived. An example of such a problem that can be advantageously solved in this invention is calculating the ground-state energy of a molecule or a general electronic system. In particular, this allows for the prediction of the final reaction products, 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 problem can also involve calculating the multipole moments of chemical products. Such calculations can be relevant to determining properties of chemical products that relate to their 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—these technical application properties can range from solubility and compatibility with certain media to ionic complexation behavior or effects on spectral properties (e.g., color). Therefore, determining the values ​​of technical application properties based on the results of quantum mechanical calculations is based on the corresponding technical application property to be determined, and further on the information provided by the solution to the problem indicated by the results of the quantum mechanical calculations.

[0057] 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. Furthermore, 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). In particular, when produced according to a corresponding formulation, the target chemical product provides the corresponding target technical application characteristic.

[0058] 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 corresponding questions for determining the technical application characteristics of the potential chemical product. However, the corresponding questions can also be automatically selected by the device, for example, based on the potential chemical product and the provided target technical application characteristics. Alternatively, for example, a user may select the corresponding question based on the potential chemical product and / or the target technical application characteristics, preferably based on selecting from a plurality of possible questions presented to the user.

[0059] 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.

[0060] 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.

[0061] 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.

[0062] These and other aspects of the invention will become apparent and will be illustrated with reference to the embodiments described below. Attached Figure Description

[0063] In the attached diagram:

[0064] Figure 1 The state representation of qubits used in quantum computing devices is demonstrated.

[0065] Figure 2 A schematic example of a quantum computing device using qubits as the computing unit is shown.

[0066] 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.

[0067] Figure 4 A schematic example of a hybrid system including classical and quantum computing devices is shown.

[0068] Figure 5 A schematic example of a superconductor-based quantum computing device is shown.

[0069] Figure 6 A schematic example of a quantum computing device based on trapped ions is shown.

[0070] Figure 7 An embodiment of a system for determining solutions to problems related to chemical products is illustrated schematically and exemplary.

[0071] Figure 8 A flowchart illustrating, and exemplarily demonstrating, is provided for a method of determining solutions to problems related to chemical products.

[0072] Figure 9 Examples of quantum computing systems with quantum computers of varying fidelity are illustrated schematically and exemplaryly.

[0073] Figure 10 , Figure 11 A flowchart illustrating, and demonstrating, an exemplary implementation of a computation method on a quantum computer system is shown.

[0074] Figure 12 An illustration of an electron orbital energy diagram is shown schematically and exemplary.

[0075] Figure 13 A schematic and exemplary quantum circuit diagram of Hadamard overlap measurement is shown.

[0076] Figure 14An overview of different embodiments of methods using quantum computer systems is illustrated schematically and exemplary, and

[0077] Figures 15 to 17 Further applications of the method for determining solutions are illustrated schematically and exemplary. Detailed Implementation

[0078] 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).

[0079] 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.

[0080] 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.

[0081] 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.

[0082] 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.

[0083] 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.

[0084] 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).

[0085] 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.

[0086] 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 is prepared—that is, after operations are applied to the qubits of the quantum computer—a projection measurement is performed on all individual qubits, returning either 0 or 1 for each qubit. This projection typically occurs at the qubit level. 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.

[0087] 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.

[0088] 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.

[0089] 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.

[0090] 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.

[0091] 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.

[0092] 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 registers. The quantum computing device 100 is adapted to perform quantum operation S16 specifically by manipulating the qubits of the quantum registers. 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.

[0093] 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.

[0094] 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.

[0095] 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.

[0096] Generally, 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.

[0097] 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.

[0098] 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.

[0099] Generally, 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 that controls 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.

[0100] 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.

[0101] Figure 7 A system for generating solutions to problems associated with chemical products is illustrated schematically and exemplary. For example, system 700 can be configured to determine the properties of a chemical product, which can then be used to monitor and / or control the production of the chemical product or to perform experiments involving the chemical product. However, in other examples, the problems solved by system 700 may also relate to other applications, such as those in logistics, scheduling, cryptography, engineering, etc.

[0102] System 700 includes a control signal generation device 710, a quantum computer system 720, and a problem-solving device 730, which will be described in detail below. The control signal generation device 710 and the problem-solving device 730 can be implemented in any software and / or hardware form of a classical computing system. Specifically, the functions performed by the units of the respective devices can be performed by one or more computing systems, for example, in distributed computing (such as cloud computing). The control signal generation device 710 is configured to provide control signals for controlling the quantum computer system 720. The quantum computer system 720 includes at least two (three in this example) quantum computers 721, 722, and 723. Further, the quantum computing system 720 may include hardware and / or software for controlling, managing, and monitoring the respective quantum computers. The quantum computers 721, 722, and 723 of the quantum computing system 720 can be independent of each other; for example, they can be located in different locations and can be controlled and managed by different providers. However, at least some of the quantum computers in the quantum computer system 720 may also allow direct interaction between the quantum computers. This direct interaction can refer to exchanging information from quantum computing in different ways. In embodiments, this information can be exchanged in a classical manner, for example, using communication coupling between classical computers that control, monitor, and / or manage the quantum computers. In this case, the results of quantum computing can be exchanged at the classical level of the quantum computers (i.e., using classical computer communication with the classical computer portion associated with the quantum computer) and then prepared or integrated into the quantum computing of another quantum computer. However, in embodiments, at least two quantum computers in a quantum computer can also be directly connected at the quantum level (i.e., without measuring, processing, and deriving information from one quantum computer) to send that information to another quantum computer, where the information must be processed, implemented, and prepared by that other quantum computer. For example, this direct exchange at the quantum level can be achieved by allowing entanglement between at least two quantum computers in a quantum computer, where entanglement of quantum computers is defined as at least one quantum element of each quantum computer being entangled with each other. Because entanglement couples the states of corresponding quantum elements, manipulations performed on one quantum element and one quantum computer can be directly correlated with quantum elements on another quantum computer, thus enabling direct exchange of information at the quantum level. This will be discussed further. Figures 9 to 14 Further details of this embodiment are described below.

[0103] The quantum computers in the quantum computing system 720 are configured such that at least two of the quantum computers (e.g., quantum computer 721 and quantum computer 722) include different fidelities. For example, quantum computer 721 may include a higher fidelity than quantum computer 722. The fidelity of a quantum computer typically depends on its specific construction, such as its hardware and / or control system. Therefore, the fidelity is determined individually for each quantum computer.

[0104] The device 710 includes a problem providing unit 711, a sub-problem derivation unit 712, and a control signal generation unit 713. The problem providing unit 711 can be implemented as, for example, a user interface where a user can input a corresponding problem. However, the problem providing unit 711 can also be implemented as an interface to a storage device on which corresponding problems are already stored. The problem can be any problem that can be converted for quantum computing. In an embodiment, the problem is an electronic structure problem, which allows the derivation of the properties of chemical products based on the solution to the electronic structure problem. Therefore, the problem description provided by the problem providing unit 711 can refer to any form of digital representation of the problem, such as a mathematical representation, an identifier that allows retrieval of the problem from the storage device, a digital code that encodes the corresponding problem, etc.

[0105] The subproblem derivation unit 712 is configured to derive subproblems from the provided problem description based on the fidelity of at least two quantum computers. Solving the subproblems then allows computation of the solution to the provided problem. Furthermore, subproblems are problems that solve only multiple parts of the overall problem; for example, these problems involve fewer quantities or otherwise reduce complexity, making the subproblems easier to solve than the overall problem in most cases. At least some of the derived subproblems are dependent problems in most cases, where the solution to one subproblem depends on the solution to another subproblem. However, in some cases, at least one subproblem can be independent, in a way that allows these subproblems to be solved independently of each other. The subproblems are derived based on the fidelity of the quantum computers in the quantum computing system. For example, rules can be implemented for the corresponding problem category, which can be used by the subproblem derivation unit 712 to identify and derive subproblems of the problem while taking into account the fidelity of the quantum computers. For example, the fidelity of the quantum computers can determine the maximum size of the corresponding subproblem, such as the maximum number of variables in the subproblem. The complexity of a subproblem may also be affected by the fidelity of the available quantum computer; for example, the maximum number of interaction variables can be determined based on fidelity. However, the subproblem-driving unit 712 may also include an interface to a user, whereby the subproblem-deriving unit 712 can provide suggestions to the user for the corresponding subproblem, which the user can then confirm or modify. Furthermore, in addition to the fidelity of the available quantum computer in the quantum computing system 720, other criteria can be considered when deriving the corresponding subproblem. For example, the user can predetermine or select a solution algorithm to be used to solve the problem, and then the subproblem-deriving unit 712 can be configured to further derive the subproblem based on the predetermined solution algorithm. Furthermore, the number of logical quantum elements provided by the quantum computer of the quantum computing system 720 can also be considered when deriving the corresponding subproblem. Regarding... Figures 9 to 14 Further details and examples of the methods used to derive subproblems are provided.

[0106] The control signal generation unit 713 is configured to generate control signals for controlling the quantum computing system, particularly the quantum computer within the quantum computing system 720. The control signals cause one or more quantum computers in the quantum computing system 720 to perform quantum computation on at least one of the derived subproblems. The control signal can refer to any signal that causes one or more quantum computers to perform quantum computation on one or more subproblems. For example, the control signal can be configured to directly control the quantum computer, i.e., the operation performed on the quantum computer. However, the control signal may also include information about the subproblem and which quantum computer should compute the subproblem, wherein further adjustments to the quantum computer hardware (e.g., determining the specific operational algorithm for performing the quantum computation on the subproblem) can be performed by a classical computer acting as the control unit of the quantum computer. Therefore, the generation of the control signal may include transforming the corresponding subproblem into a corresponding operational algorithm, which includes one or more operations for preparing and manipulating quantum states of quantum elements on the quantum computer to perform the quantum computation. However, this step may be omitted if the control of the corresponding quantum computer is configured to perform such a transformation of the provided problem.

[0107] Furthermore, the control signal distributes the subproblem to the corresponding quantum computer of the quantum computing system 720 based on the fidelity of the corresponding quantum computer. Specifically, since fidelity has already been considered when deriving the subproblem, the subproblem can be assigned to the corresponding quantum computer with the appropriate fidelity for the corresponding derived subproblem. For example, if the subproblem is derived to be computed on a quantum computer with high fidelity in the quantum computing system, then the subproblem is assigned to the corresponding quantum computer of the quantum computing system via the control signal. Subproblems derived for lower fidelity can be computed by the corresponding quantum computer with the corresponding lower fidelity, but can also be computed on a quantum computer with higher fidelity if necessary. Generally, higher fidelity can be considered to be higher than: a) the fidelity of at least one of the at least two quantum computers, b) the fidelity of all other quantum computers in the at least two quantum computers, and / or c) a predetermined fidelity threshold. Lower fidelity can be considered to be lower than: a) the fidelity of at least one of the at least two quantum computers, b) the fidelity of all other quantum computers in the at least two quantum computers, and / or c) a predetermined fidelity threshold.

[0108] The control signal can enable the quantum computation of the subproblem to be performed sequentially, in parallel, iteratively, or in a combination thereof. Then, the quantum computer of the quantum computing system 720 provides the result of the quantum computation (e.g., the measurement result of the quantum elements on the quantum computer or the solution to the subproblem determined based on the measurement result of the quantum elements after the quantum computation) to the problem-solving device 730.

[0109] The problem-solving apparatus 730 includes a receiving unit 731 and a problem-solving unit 732. The receiving unit can be implemented as an interface with the quantum computing system 720 to receive the results of quantum computing. The received quantum computing results of sub-problems are then provided to the problem-solving unit 732, which is configured to determine the solution to the problem based on the results of the quantum computing of the sub-problems. Determining the solution to a problem based on the results of sub-problems typically involves a combination of the results of the sub-problems. This combination is determined by the type of sub-problems and how these sub-problems are derived from the problem. Therefore, the solution to a problem based on the results of sub-problems is different for different problems. Appropriate rules for the corresponding sub-problems and the problem can be implemented and utilized separately. The solution can then be used to control, for example, the production of chemical products in a chemical plant 740 or a series of experiments in a laboratory 750. For example, the solution could refer to the chemical product characteristics that can be used to control chemical reactions in the chemical plant 740 or to plan corresponding experiments in the laboratory 750.

[0110] exist Figure 7 In the example shown, the problem is the electronic structure of a chemical product (e.g., a molecule, crystal, or atom), and the solution is the solution to the corresponding electronic structure problem. From the solution to the electronic structure problem, the properties of the corresponding chemical product can be derived based on the corresponding known calculations. These properties can then be used, for example, to control the production of the chemical product or to control laboratory equipment to perform corresponding experiments involving that chemical product.

[0111] Figure 8 A flowchart illustrating, and exemplarily demonstrating, is provided for a method of generating solutions to problems related to chemical products, wherein the method may, for example, be derived from... Figure 7The described system is used to execute the method. The method includes providing a problem description indicating the problem, and deriving subproblems from the provided problem description based on the fidelity of the quantum computer of the quantum computing system. Further, the method includes generating control signals to control the quantum computing system such that quantum computations are performed on the derived subproblems on the quantum computer, wherein these subproblems are distributed to the quantum computer based on the fidelity of the corresponding quantum computer. Further, the method includes performing quantum computations on the corresponding subproblems. In a next step, the results of the quantum computations are received. Optionally, based on the received results, iterations can be performed, wherein control signals are generated again based on these results to recompile the subproblems based on the results of previous quantum computations of the subproblems. Furthermore, subproblems can be computed sequentially, wherein control signals are generated based on the solution to a subproblem to control the computation of the next subproblem based on that solution. For example, previous quantum computation results can now be used as a starting point or input to other subproblems. Based on the results of the quantum computations, optionally after one or more further iterations, a solution to the problem can be determined based on the results of the subproblems. This solution to the problem is generally applicable to the corresponding application of controlling and / or monitoring the problem. For example, in the case of an electronic structure problem, the solution to the electronic structure problem can be used to determine the properties of a chemical product, and then used to control and / or monitor the production of the chemical product based on the determined properties.

[0112] 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 with desired properties, and generally, for improving the efficiency of research activities by reducing the number of required laboratory and production trials, which are often 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.

[0113] The fundamental processing unit of a quantum computer is a quantum mechanical bit (qubit), physically represented by one or more quantum elements of the quantum computer. 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 qubits (e.g., the number of logical quantum elements) and their quality (e.g., error rate or fidelity) primarily determine the maximum size (e.g., dimension) and maximum complexity of the problem that can be solved by the corresponding quantum computer.

[0114] Currently, the number and fidelity of qubits are quite limited, leading to the development of so-called noisy medium-sized 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 best suited to solve a specific part 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.

[0115] Both the number of qubits and the fidelity are expected to continue to increase. Once a certain threshold is reached, hundreds or thousands of 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 logical qubit. 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 computer mentioned in the following examples is not limited to a fully FT quantum computer, but also includes FT quantum computers that still have sufficiently small errors. The error rate of such an FT quantum computer 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.

[0116] 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.

[0117] While fault-tolerant quantum computers (e.g., fault-tolerant quantum processing units (FT-QPUs)) outperform noisy medium-sized quantum computers (e.g., noisy medium-sized 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.

[0118] This invention relates to a quantum computing system having multiple quantum computers with different fidelities. For example, the quantum computing system could 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 most advantageous for solving the problem. However, the quantum computing system could also combine different NISQ-QPUs with different fidelities, along with a CPU or other conventional hardware, without using an FT-QPU.

[0119] exist Figure 9Two examples of corresponding quantum computing systems are shown in the figure. These examples are shown for quantum computing systems including FT-QPU and NISQ-QPU. However, in addition to or as an alternative to FT-QPU, NISQ-QPUs with higher fidelity can also be used, based on the same principles as those described below. In the following text, the term "higher fidelity NISQ-QPU" means that a higher fidelity NISQ-QPU can have a higher fidelity than a combination of: 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.

[0120] 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.

[0121] exist Figure 10The present invention illustrates an exemplary detailed method for solving problems according to the present invention in non-entangled quantum computing systems, and... Figure 11This document illustrates an exemplary detailed method for solving problems according to the invention using entangled quantum computing systems. In a first step, the problem can be defined on a classical computing system, for example, by a user using a user interface. Typical problems include, for example, problems concerning the electronic structure of molecules, solids, and materials, or optimization problems. In a second step, considering the fidelity of the quantum computing system(s) on which the subproblems are to be solved, the problem can be divided into subproblems on the classical computing system. FT-QPUs or (multiple) higher-fidelity NISQ-QPUs are preferably used to solve smaller computational subproblems on which accurate or highly accurate solutions cannot be obtained efficiently on lower-fidelity NISQ-QPUs or CPUs. Subproblems whose solutions require deeper quantum algorithms beyond the capabilities of (multiple) lower-fidelity NISQ-QPUs and CPUs can also be derived to solve these subproblems on (multiple) higher-fidelity NISQ-QPUs or (multiple) FT-QPUs. Accordingly, the dimension of the subproblem 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. (Multiple) lower-fidelity NISQ-QPUs are best suited for solving the following two larger computational subproblems: those for which an exact solution is desired that cannot be efficiently obtained on a classical computer (e.g., (multiple) CPUs), or for which a solution requires a wide quantum algorithm using a larger number of qubits rather than a deep quantum algorithm. 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 preparation and operation of the corresponding quantum circuits on the quantum computing system to compute and solve the corresponding subproblems. Optionally, the quantum circuits may contain parameters that 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 all control signals are simultaneously provided 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 iterations using an appropriately updated set of parameters. In the fourth step, all quantum circuits from the current iteration are simultaneously executed 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 the solutions to the corresponding subproblems.Examples of relevant algorithms for (multiple) FT-QPUs or (multiple) high-fidelity NISQ-QPUs include quantum Fourier transform, quantum phase estimation (QPE), Grover-type search algorithms, Shor-type decomposition algorithms, and Harrow-Hassidim-Lloyd-type algorithms. Examples of relevant algorithms that can also be used on (multiple) high-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-QPUs or high-fidelity NISQ-QPU and NISQ-QPU systems, solutions to subproblems can be directly transferred between these two types of QPUs. 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 quantities have 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, to improve overall accuracy or to further process the results (e.g., error mitigation or error correction). If necessary, other observables can be measured on (multiple) QPUs. The results of subproblems can be further combined in this post-processing or during the iteration, depending on the interactions between the subproblem results. Finally, the final result is provided to the user as the solution to the processed problem.

[0122] The following sections describe in detail how the methods and systems described above can be used to solve electronic structure problems, such as the simulation of quantum systems (e.g., molecules). The following examples are based on a method of dividing electronic structure problems (such as problems describing molecules or solids) into so-called "active spaces" and "inactive spaces" based on their electronic states (e.g., electron orbitals), such as... Figure 12As shown.

[0123] The following describes an example of a method that utilizes a hybrid quantum-classical approach for the aforementioned quantum computer system, along with methods for deriving and distributing subproblems. The exemplary method described below involves solving an “active space” on a quantum computing system, wherein the results are then used to adjust the electron orbitals in both, preferably, the “inactive space” and the “active space”, on a classical computer. However, other distribution methods are possible depending on the problem and the “active space” and “inactive space” determined as subproblems. For example, the effects of the “inactive space” or the “active space” on the “inactive space” can also be solved on the quantum computer system. This process is repeated iteratively until the electron orbitals and total energy converge. This method can be referred to as the “Completely Active Space Self-Consistent Field” (CASSCF) method. A related method is the “Completely Active Space Configuration Interaction” (CASCI), which can be considered a special case of CASSCF that ignores the adjustment of the electron orbitals to the solution in the “active space.” In the following, both methods are referred to as the “CAS method.”

[0124] 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), since only the electronic orbitals that include the “active space” are explicitly processed on a 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.

[0125] 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 10The first step in the general process. Further, for example, a set of initial electron orbitals is specified based on 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," where the active space defines the first subproblem. 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 subproblem. 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 a Jordan-Wigner or Bravyi-Kitaev transformation. A quantum circuit for solving the “active space” subproblem is then compiled on the CPU, making the quantum circuit executable on a quantum computer. The “active space” subproblem 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 solutions to the subproblem. 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" subproblem 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 usually be prepared on the NISQ-QPU, for example, as a characteristic function of the "active space" subproblem. According to step five, the single-particle and two-particle reduced density matrices are then measured on the NISQ-QPU in 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 10Step 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.

[0126] 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, considering the fidelity of quantum computing when solving subproblems, these methods are particularly well-suited for use with the aforementioned methods and quantum computing systems.

[0127] In all the methods discussed below, the first step has already been described above. The result is then the CAS wavefunction. The following describes how the principles of the invention can be utilized, starting with the CAS wavefunction. First, it is described how the CAS wavefunction can be read out to reconstruct it on different hardware devices, for example, where the quantum computing system does not provide the possibility of entanglement between different quantum computers. Then, it is explained how dynamic correlations can be added to the CAS wavefunction using quantum computing systems comprising quantum computers with different fidelities and correspondingly derived subproblems. For an overview, see also [link to overview]. Figure 14 .

[0128] For all the multi-reference dynamic correlation methods using non-entangled quantum computing systems discussed below, the specific information about 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.

[0129] The CAS wavefunction obtained as described above can be expanded as follows:

[0130] (1)

[0131] Among them, | 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 electrons between electron orbitals in "active space." In the "active space" subproblem, the index μ traverses all possible electron distributions between electron orbitals. 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).

[0132] For example, as described above, the CI coefficients of a CAS wavefunction already prepared on a quantum computer can be determined using the following method. 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 between the CAS wavefunction and the defined ground state, for example, according to:

[0133] (2)

[0134] Among them, | Normalized. CAS wavefunctions can be prepared on the QPU. As a result of the previous CAS calculation, the CAS wavefunction can be prepared on the QPU in the previous step, 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 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 frequency 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 equation (2). 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.

[0135] Alternatively, if it is necessary to determine the absolute value of the selected important CI coefficient 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:

[0136] (3)

[0137] in, It is a unitary operator that excites certain qubits to state 1 according to | Prepare the base state | vac> from the vacuum state |vac> (i.e., the state where each qubit is in state 0). This allows the distribution of electron orbitals in the "active space" to be reflected in the qubit register, where, under the Jordan-Wigner transform, the qubit in state 0 represents an empty electron orbital in the "active space," and the qubit in state 1 represents 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.

[0138] 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 thus this is 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 . Compared to the full Hamiltonian, the size of the Hamiltonian in this sufficiently small subspace is reduced, and therefore it can be diagonalized efficiently, 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:

[0139] (4)

[0140] 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.

[0141] 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.

[0142] After determining a sufficient number of CI coefficients to adequately represent the CAS wavefunction according to equation (1), the CAS wavefunction can be reconstructed 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 value of the Hamiltonian operator) converges with the included CI coefficients, and therefore with the number of ground 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 and optionally, the probability distribution can also be obtained as described below, and therefore... 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 measurements on (multiple) QPUs. 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.

[0143] 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 components. In this case, (multiple) QPUs can be used in further computational steps to dynamically correlate the “inactive space.” 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 process described above to determine the CI coefficients.

[0144] The following describes a multi-reference dynamic correlation process using the CAS wavefunction as a fixed starting point. The CAS wavefunction is used as a reference state that no longer changes. The following method considers the "inactive space" and the dynamic correlation between the "active space" and the "inactive space" in the further computational steps of distributing the subproblems to be computed using the principles of the invention. 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 the dynamic correlation between the CAS wavefunction and the subproblems to be computed. 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, and therefore this is consistent with... 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 the embodiments that will be discussed below is shown.

[0145] 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 using orbital localization methods, which can be aided by other techniques such as natural orbitals, natural orbitals for 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.

[0146] 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 electronic orbitals assigned to the “active space” defining the “active space” subproblem is typically significantly smaller than the number of electronic orbitals retained in the “inactive space” defining the “inactive space” subproblem. 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 calculations with an approximate dynamic correlation method utilizing the NISQ-QPU. This involves using an FT-QPU or a higher-fidelity NISQ-QPU to solve the "active space" subproblem with high accuracy. The approximate dynamic correlation method is applied to the "inactive space" subproblem and considers the dynamic correlations within and between the "active space" and "inactive space" subproblems. Based on the aforementioned CAS calculations that determine the CAS wavefunction as described above, in further computational steps, a unitary dynamic correlation (UDC) fitting can be applied using a variational quantum eigenfunction solver (VQE) or variational Hamiltonian fitting (VHA) to approximately interpret 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, the solution can be generated even if the solution to the "active space" portion has already been considered, for example, by adjusting the electron orbitals of the "inactive space" portion based on the solution to the "active space" portion. Then, this solution in the "inactive space" part can be integrated into the CAS wavefunction as part of the interaction representation.

[0147] 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:

[0148] (5)

[0149] 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. The method is known 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: Multireferencecoupled cluster theories of dynamical electron correlation," FA Evangelista, The Journal of Chemical Physics, Vol. 149, No. 3, which is incorporated herein by reference.

[0150] 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 index include the following: Whenever When the two indices p and q refer to inactive electron orbitals, this term can be restricted to include only the contributions of occupied inactive electron orbitals i and unoccupied inactive electron orbitals a. .whenever When all indices p, q, r, and s refer to inactive electron orbitals, this term can be restricted to include only contributions regarding occupied inactive electron orbitals i and j and unoccupied inactive electron orbitals a and b. It cannot include items that specifically refer to all indicators t, u, v, w of active electron orbitals. 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 It has occupied inactive electron orbitals i and j, unoccupied inactive electron orbitals a and b, and arbitrary electron orbitals p and q.

[0151] 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 the exact or near-exact solution to the “active space” subproblem in the form of a CAS wavefunction. In embodiments, only the “active space” subproblem is solved on the FT-QPU or a higher-fidelity NISQ-QPU, meaning that typically as many logical qubits as the number of electron orbitals present in the “active space” are used to represent the solution to the “active space” subproblem. Depending on the algorithm, additional qubits may be required to implement the algorithm; for example, auxiliary qubits are required for the QPE algorithm. Alternatively, the “active space” subproblem can be solved using a NISQ-QPU (and, for example, a variational quantum eigenvalue solver, VQE) in this step. Alternatively, the CAS (or alternatively, RAS or GAS) method can be run entirely on the CPU and proceed to the steps described below, such as dynamic correlation processing on the NISQ-QPU. Thus, in order to calculate the CAS wave function, quantum computing systems, including quantum computers with the same or lower fidelity, can be used.

[0152] 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 constant 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 correlation between the "inactive space" and the "active space" and the "inactive space," as described below. First, a representation of the CAS wavefunction is prepared on a quantum computer (e.g., the NISQ-QPU) with appropriate fidelity. For example, the entire CAS wavefunction, not just the "active space" solution, can be reconstructed from equation (1), for example, on the NISQ-QPU using the most relevant CI coefficients as described above:

[0153] (6)

[0154] 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 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 the parameterized trial state 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 the trial state to be prepared on a classical computer (e.g., a CPU) according to the following equation. Relative to molecular Hamiltonian The energy is evaluated:

[0155] (7)

[0156] If the energy and variational parameters have not yet converged, the iteration continues on a classical computer during the variational process by updating this set of variational parameters to minimize 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.).

[0157] 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.

[0158] The following describes an FT-NISQ unitary dynamic correlation (FT-NISQ-UDC) method utilizing entangled quantum computing systems, where the FT-QPU can also be replaced by a higher-fidelity NISQ-QPU. As an alternative to the exemplary method described above, entangled quantum computing systems can also be used to consider dynamic correlations. A highly accurate solution (e.g., a highly accurate eigenfunction) to the "active space" subproblem (e.g., the "active space" Hamiltonian operator) is obtained as a result of a successfully converged CAS computation using the corresponding quantum computing system described above. The electron orbitals can be obtained on a suitable quantum computer (preferably an FT-QPU or a high-fidelity NISQ-QPU). Furthermore, all the obtained electron orbitals can be stored on a classical computer (e.g., a CPU). The information about the electron orbitals can be used on a NISQ-QPU with the appropriate fidelity, using states that can be easily prepared on the NISQ-QPU. The electronic orbitals defining the "inactive space" subproblem are, for example, initialized 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).

[0159] To approximate the dynamic correlations within the "inactive space" subproblems and between the "active space" and "inactive space" subproblems using entangled quantum computing systems, a parameterized unitary dynamic correlation (UDC) operator that enables entanglement between quantum computers with different fidelities can be applied according to the following formula. :

[0160] (8)

[0161] 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 limitations 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.

[0162] 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 to the “active space” subproblem. Note that only the “active space” subproblem is solved on the FT-QPU or the higher-fidelity NISQ-QPU, which means that typically as many logical qubits as the number of electron orbitals present in the “active space” subproblem are 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 completed, the electron orbitals can be stored on the CPU. In the next step, the CAS method and process are performed using an entangled quantum computing system combined with a similar approach. Figure 11 The variational approach to the general process exemplified in the example considers the "inactive space" and the dynamic relationships between the "active space" and the "inactive space." For example, solutions to the subproblems of the "active space" can be prepared on a higher fidelity NISQ-QPU or FT-QPU, thereby obtaining... 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 to the "active space" subproblem, i.e., to perform 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" subproblem on the NISQ-QPU, thereby obtaining... 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 on the QPU of the quantum computing system. The application of the UDC operator causes entanglement between 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), where Θ is a set of variational parameters adjusted 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 variational 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 a result of the computation, and, similar to equation (7), the trial state can be adjusted 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 energy is minimized during the variational process, and then the corresponding iterations of the above steps are performed. 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 the 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.).

[0163] 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.

[0164] 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.

[0165] 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.

[0166] 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.

[0167] 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.

[0168] 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).

[0169] 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.

[0170] 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.

[0171] 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.

[0172] 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.

[0173] 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.

[0174] 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.

[0175] 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.

[0176] 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.

[0177] 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.

[0178] 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).

[0179] A preferred example of a identifiable technical application characteristic is chemical reactivity, where the thermodynamic and kinetic quantities for predicting a single chemical reaction (such as the following chemical reaction) depend on the calculation of the reaction free enthalpy and the activation free enthalpy, respectively.

[0180]

[0181] For example, the reaction free enthalpy indicates whether a chemical reaction can occur in principle, and the activation free enthalpy indicates the rate of a chemical reaction, i.e., the speed.

[0182] 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 ).

[0183]

[0184] 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.

[0185]

[0186] 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:

[0187]

[0188] 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:

[0189]

[0190] 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 utilizing 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.

[0191] Enthalpy of dissolution of molecules in a predefined solvent This information can be obtained using classical computers via a dissolution model, such as the Real Solvent-like Conductor Shielding Model (COSMO-RS). In 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 molecule's 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 computational costs can be significantly reduced by implicitly including the effects of solvent on technical application properties (such as reaction free enthalpy and activation free enthalpy) via the COSMO-RS method, rather than by directly calculating technical application properties in solution by constructing a supersystem that explicitly includes solvent molecules.

[0192] 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.

[0193] 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 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.

[0194] 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.

[0195] 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).

[0196] 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.

[0197] 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).

[0198] 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.

[0199] 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.

[0200] 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.

[0201] 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.

[0202] In the claims, the word “comprising” does not exclude other elements or steps, and the indefinite article “a / an” does not exclude multiple / types.

[0203] 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.

[0204] Processes such as providing a problem description, deriving subproblems, and generating control signals, which are performed by one or more units or devices, 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.

[0205] 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.

[0206] 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.

[0207] 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.

[0208] 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.

[0209] Any reference numerals in the claims should not be construed as limiting the scope.

[0210] This invention relates to an apparatus for providing control signals for controlling a quantum computing system. The quantum computing system includes at least two quantum computers with different fidelities. A problem providing unit provides a problem description indicating the problem. A subproblem derivation unit derives subproblems from the provided problem description based on the fidelities of the at least two quantum computers. A control signal generation unit generates control signals for controlling the quantum computing system such that quantum computations are performed on the derived subproblems on the at least two quantum computers, wherein the subproblems are distributed to the respective at least two quantum computers based on their fidelities.

Claims

1. An apparatus for providing control signals for controlling a quantum computing system, the quantum computing system being used to perform quantum computations on problems, particularly those related to chemical products, wherein, The quantum computing system comprises at least two quantum computers with different fidelities, wherein the device includes: The problem providing unit is used to provide a problem description that indicates the problem. A subproblem derivation unit, which is used to derive subproblems from the provided problem description based on the fidelity of the at least two quantum computers, and A control signal generation unit is used to generate control signals for controlling the quantum computing system so that quantum computations are performed on the at least two quantum computers for the derived subproblems, wherein the subproblems are distributed to the respective at least two quantum computers based on the fidelity of the at least two quantum computers.

2. The apparatus according to claim 1, wherein, At least two of these quantum computers are configured to be entangled, and wherein control signals are generated to further control the entanglement between the at least two quantum computers in the quantum computing system during parallel quantum computing of these subproblems, so as to distribute and share information between the at least two quantum computers during the quantum computing, wherein the entanglement of the two quantum computers is defined by at least one quantum element of each of these quantum computers being entangled.

3. The apparatus according to any one of claims 1 and 2, wherein, Based on the fidelity of the at least two quantum computers, these subproblems are derived from the problem description, including identifying subproblems that require higher solution accuracy compared to another subproblem, and wherein these control signals are generated such that these subproblems requiring higher solution accuracy are computed on the quantum computer with higher fidelity, and wherein another subproblem is computed on the quantum computer with lower fidelity.

4. The apparatus according to any one of the preceding claims, wherein, The derivation of the subproblem is further based on the number of logical quantum elements provided by at least two corresponding quantum computers.

5. The apparatus according to any one of the preceding claims, wherein, This problem is an electronic structure problem related to the properties of chemical products, and these subproblems are derived such that one subproblem is defined in the active space and another subproblem is defined in the inactive space, wherein the subproblem defined in the active space is derived such that it can be computed on a quantum computer with high fidelity, and the subproblem defined in the inactive space can be computed on a quantum computer with low fidelity, wherein these control signals are generated so that these corresponding subproblems can be computed on these corresponding quantum computers.

6. The apparatus according to any one of the preceding claims, wherein, The quantum computing system includes at least one fault-tolerant quantum computer and a noisy medium-sized quantum computer, wherein the fault-tolerant quantum computer has a higher fidelity than the noisy medium-sized quantum computer.

7. A quantum computer system, comprising: A control unit, configured to receive a control signal generated by the apparatus according to claim 1, and At least two quantum computers with different fidelities, wherein quantum computations on subproblems, particularly those related to chemical products, are performed on the at least two quantum computers based on received control signals generated based on the different fidelities of the at least two quantum computers.

8. The system according to claim 7, wherein, At least two of these quantum computers are configured for entangled quantum computing, wherein the entanglement between the at least two quantum computers is controlled based on these control signals, and wherein the entanglement between the two quantum computers is defined by at least one quantum element of each of the quantum computers being entangled.

9. The system according to any one of claims 7 and 8, wherein, At least one of the at least two quantum computers is a fault-tolerant quantum computer, and at least one of the at least two quantum computers is a noisy medium-sized quantum computer.

10. A problem-solving apparatus for solving problems, particularly those related to chemical products, wherein, The device includes: A receiving unit, configured to receive the quantum computation results of a subproblem performed by at least two quantum computers of a quantum computing system according to control signals generated by the apparatus according to claim 1, and A problem-solving unit is configured to determine the solution to the problem based on the quantum computation results of these subproblems.

11. A system for generating solutions to problems, particularly those related to chemical products, wherein, This system include: The apparatus according to claim 1, The quantum computer system according to claim 7, and The problem-solving apparatus according to claim 10.

12. A computer-implemented method for providing control signals for controlling a quantum computing system used to perform quantum computations on problems, particularly those related to chemical products, wherein, The quantum computing system comprises at least two quantum computers with different fidelities, wherein the method includes: Provide a problem description indicating the issue. Based on the fidelity of these at least two quantum computers, subproblems are derived from the provided problem description, and Control signals are generated to control the quantum computing system so that quantum computations are performed on the at least two quantum computers for the derived subproblems, wherein the subproblems are distributed to the respective at least two quantum computers based on the fidelity of the at least two quantum computers.

13. A problem-solving method for solving problems, particularly those related to chemical products, wherein, The method includes: Receive the quantum computation results of a subproblem performed by at least two quantum computers of the quantum computing system according to control signals generated by the method according to claim 12, and The solution to the problem is determined based on the quantum computation results of these subproblems.

14. A computer program product for providing control signals for controlling a quantum computing system to perform quantum computation of a problem, wherein, The computer program product includes program code means for causing the means according to any one of claims 1 to 6 to perform the method according to claim 12.

15. The apparatus according to any one of claims 1 to 6 is used for determining the technical application characteristics of a chemical product based on a solution to an electronic structure problem generated using a control signal from the apparatus.

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