Apparatus for generating control signals for measuring the state of quantum elements of a quantum computer

Abstract

The present invention relates to an apparatus 810 for generating control signals for measuring states of quantum elements of a quantum computer 830. A providing unit 811 provides a problem description. A transforming unit 812 converts the problem description into a quantum mechanical representation. The transforming includes determining a unitary transformation that rotates operators representing observables to be measured into a basis that results in a pure occupied number representation. A translating unit 813 translates the quantum mechanical representation into a sequence of quantum operations including unitary transformation operations to be applied to the quantum elements. The translation includes determining a unitary transformation operation based on the determined unitary transformation. A generating unit 814 generates signals for controlling the application of the determined sequence of quantum operations to the quantum computer so that a quantum mechanical representation of the problem is prepared and observables indicative of a solution to the problem are measured.

Description

[Technical Field]

[0001] FIELD OF THE INVENTION The present invention relates to an apparatus, method and computer program product for generating control signals for measuring the states of quantum elements of a quantum computer. Further, the present invention relates to a system for performing quantum mechanical calculations on a quantum computer using control signals. Further, the present invention relates to an apparatus, method and computer program product for determining a solution to a problem using the above-mentioned apparatus, method and / or computer program product for generating control signals for measuring the states of quantum elements of a quantum computer. Furthermore, the present invention relates to an apparatus, method and computer program product for determining target technological application properties of chemical products using the above-mentioned method, apparatus and / or computer program product. [Background technology]

[0002] Background of the Invention Quantum computers are generally a completely novel class of computational systems that allow the unique behavior of quantum mechanical systems to be exploited to perform calculations on problems that, under appropriate conditions, conventional computers cannot perform in a reasonable time or with reasonable resources. Furthermore, quantum computers have already been shown to be particularly well-suited for solving problems related to the quantum mechanical world, i.e., problems that can be translated into quantum mechanical descriptions. Such problems relate, for example, to electronic structure problems, molecular problems, condensed matter problems, etc. Solutions of such problems are particularly useful in connection with the optimization and design of chemical products. However, problems other than descriptions of physical quantum mechanical systems, such as encoding and decoding problems, complex analysis problems, optimization problems, etc., can also be translated into quantum mechanical descriptions. Examples of such problem translations can generally be found, for example, in the paper by Montanaro, A., "Quantum algorithms: an overview," npj Quantum Information volume 2, pages 1 to 8 (2016).

[0003] However, a disadvantage of quantum computers is that to determine a solution to a problem, not only must the state of each quantum device be measured by applying a respective hardware-specific readout protocol following each control pulse, but this quantum mechanical measurement is inherently a statistical process, such that measurements of each quantum device must be averaged over multiple repeated state preparations to obtain a meaningful result of the quantum computer computation. Because the number of measurements required typically increases strongly depending on the size of the problem and the required accuracy of the results, the applicability of quantum computer computation to larger problems may be significantly limited by the effort required to perform these measurements. Therefore, it would be advantageous to reduce the effort required to measure the results of a quantum computer computation, i.e., the amount of measurements. Such a possibility would enable the application of quantum computer computation to problems important for chemical applications, and in this regard, would allow problems to be solved not only faster and with fewer computational resources, but also more accurately. Summary of the Invention [Problem to be solved by the invention]

[0004] Summary of the Invention It is an object of the present invention to provide an apparatus, method, system and computer program product that allows for the use of quantum computer computational solutions, in particular quantum computers, to reduce the effort, in particular the number of state preparations, required to provide solutions to problems that can be translated into quantum mechanical descriptions. Furthermore, the apparatus, system, method and computer program product allow for the computation of chemical or solid product related problems of increased complexity and / or problem size, enabling a wider application of quantum computers in the art, which may result in the provision of more accurate, faster and less computationally resource-intensive solutions to the chemical industry. [Means for solving the problem]

[0005] In a first aspect of the present invention, an apparatus is presented for generating control signals for measuring states of quantum elements of a quantum computer, the measured states representing observables indicative of a solution to a problem translatable into a quantum mechanical description, the apparatus comprising: i) a problem providing unit for providing a problem statement indicative of a problem to be solved, the problem statement being translatable into a quantum mechanical description; ii) a transformation unit for transforming the problem statement into a quantum mechanical representation comprising one or more operators representing one or more observables to be measured, indicative of the solution to the problem, the transformation further comprising determining a unitary transformation for rotating the one or more operators representing the one or more observables to be measured into one or more bases, the one or more bases resulting in pure occupation number representations of the one or more operators after application of the unitary transformation; and iii) a translation unit for translating the quantum mechanical representation into a quantum algorithm description comprising a sequence of quantum operations to be applied to quantum elements of the quantum computer, the translation unit comprising: The series of quantum operations includes: a) a preparation portion including quantum operations for preparing a quantum mechanical representation on a quantum computer so that observables indicative of a solution to the problem are measurable; and b) a measurement portion including quantum operations for measuring the observables by measuring the states of quantum elements after the quantum mechanical representation is prepared, wherein the measurement operation includes a unitary transformation operation applied to the quantum elements, and the translation includes determining a unitary transformation operation based on the determined unitary transformation such that the unitary transformation operation initiates a rotation of the states of the quantum elements to respective basis states corresponding to one or more bases that result in pure occupation number representations of one or more operators representing the one or more observables to be measured; and iv) a control signal generation unit for generating a control signal for controlling the application of the determined series of quantum operations to a quantum computer so that a quantum mechanical representation of the problem is prepared and observables indicative of a solution to the problem are measured according to the quantum algorithm description.

[0006] The representation of the problem statement is transformed by a measurement operation, which includes a unitary transformation operation that initiates a rotation of the states of quantum devices into basis states corresponding to one or more bases that result in a pure occupation number representation of the operator representing the observable being measured, so that the states of the quantum devices representing the observables can be measured simultaneously. This significantly reduces the number of state preparations and measurements, especially non-simultaneous measurements, required to determine the result of a quantum computer computation. This allows for larger problems, e.g., larger molecules, more accurate computations, e.g., considering more variables, or for smaller problems to be computed faster and with fewer resources.

[0007] In general, the apparatus may be implemented in the form of software or hardware, or a combination thereof, where hardware may refer to any known dedicated or general-purpose classical computer hardware. For example, the apparatus may be implemented as a known computing device, such as a PC. However, the apparatus may also be implemented in a cloud environment, a computer network, etc., whereby at least parts of the apparatus may also be implemented as a network solution and thus distributed across multiple computing devices. The apparatus is adapted to provide control signals that can be provided to, i.e., interpreted by, any known quantum computer hardware architecture.

[0008] The problem may generally include any problem statement that can be translated into a quantum mechanical description and thus can be calculated on a quantum computer. However, it is preferred that the problem pertain to a chemical or solid product, for example, a solution to which can be used to determine the properties of a chemical product for technological applications or a solution to which can be used to optimize a chemical reaction that produces a chemical product. Examples of such problems that can be advantageously solved with the present invention include the calculation of the ground-state energy of molecules or general electronic systems. This makes it possible to determine the ground-state energy of all molecular species occurring in a chemical reaction, in particular, to predict the end product, thermodynamic properties, and kinetic properties of the reaction. This understanding and properties of the reaction can then be used again to optimize chemical production processes, such as to predict the microstructure of polymers, optimize material properties, etc. Another important problem is determining the ground state of solids, which can predict the magnetocrystalline anisotropy of magnetic materials, which is important, for example, for magnetic materials in electric motors. Furthermore, the problem may also refer to the calculation of multipole moments of a chemical product. Such calculations may be related to characterizing a chemical product with respect to its electrical properties, for example, determining the behavior of a chemical product in an electric field. Furthermore, it is preferred that the problem be translatable into a quantum mechanical description of fermionic systems, in particular electronic structure problems, since the methods performed by the present apparatus are particularly well suited to such problems, allowing for a significant reduction in the number of state preparations and non-simultaneous measurements required.

[0009] The problem providing unit is adapted to provide a problem description indicating a problem that can be translated into a quantum-mechanical description. In particular, the problem providing unit may refer to a storage unit in which the problem description is already stored. However, the problem providing unit may also include an input unit, which can be used, for example, by a user to provide the problem description to the problem providing unit. The problem description may include a description of the problem in any format that allows determining the quantities that describe the problem and the form of interaction between these quantities. Preferably, the problem description refers to a mathematical description of the problem. However, the problem description may also include any other clear notation form of the problem. In a preferred embodiment, the problem description is already provided in the form of a quantum-mechanical description, which represents the problem as quantities that obey quantum-mechanical rules, i.e., includes a representation of the problem in the quantum-mechanical world. However, the problem description may be provided in any other format, in which case the providing unit is preferably adapted to translate the provided problem description into a quantum-mechanical problem description before providing it to the conversion unit. However, this translation may also be omitted, in which case the conversion unit and translation unit are preferably adapted to process the respective form of problem description accordingly or to translate the problem description accordingly, for example by utilizing principles derived from the processing of problem descriptions in quantum mechanical descriptions.

[0010] The conversion unit is configured to convert the problem description into a quantum mechanical representation including one or more operators representing one or more observable quantities to be measured. In particular, a quantum mechanical representation refers to a representation of at least a part of the problem description that can be prepared on a quantum computer and that allows a solution to the problem to be determined based on the measured states of quantum elements of the quantum computer. Generally, depending on the problem, methods are known for converting each problem into a quantum mechanical representation that can be prepared on a quantum computer in order to determine the solution to the problem. Examples of these known methods for some general and specific problems can be found in the papers "Quantum Computational Chemistry", S. McArdle et al., Rev. Mod. Phys. 92, (2020), "Quantum Algorithms for Quantum Chemistry and Quantum Materials Science", B. Bauer et al., Chem. Rev. (2020), and "Quantum Chemistry in the Age of Quantum Computing", Y. Cao et al., Chem. Rev. (2019). In particular, quantum mechanical expressions include one or more operators, i.e., quantum mechanical operators, that represent one or more observables being measured. Generally, an observable refers to a measurable quantity, such as position, momentum, energy, magnetic moment, etc., and in quantum mechanics, the term operator refers to an operator. For example, observable energy is related to a Hamiltonian operator that represents the observable in the Hilbert space in which the quantum mechanical expression is formulated. The transformation not only involves determining a general quantum mechanical expression that can be prepared in a quantum computer, but also determining a unitary transformation that rotates one or more operators that represent one or more observables being measured into one or more bases, resulting in a pure occupied number representation of the one or more operators after application of the one or more bases, the unitary transformation. In general, a unitary transformation refers to a transformation that preserves the dot product of two quantities. In particular, a unitary transformation changes the base of one or more operators but does not change the observables represented by the operators. Therefore, the same value is still measured for the observable after applying the unitary transformation.Providing a transformation of a problem statement that results in a quantum mechanical representation containing operators in pure occupation number representation has the advantage that measurements of observables represented by these operators can be performed simultaneously on a quantum computer. In general, a pure occupation number representation refers to a problem statement containing observables that can be measured simultaneously on a quantum computer. To be simultaneously measurable, the observables must have quantum mechanical representations such that i) the observables are compatible, i.e., have a common basis in the Hilbert space containing the quantum mechanical descriptions, i.e., the operators representing the observables commute, and ii) the Pauli operators representing the observables have a common measurement basis. An example is the electron number operator, which can be expressed in terms of the Pauli Z operator using the Jordan-Wigner transformation, which therefore satisfies both requirements.

[0011] In general, if the problem description is not provided in the form of a quantum mechanical description, the conversion unit is preferably further adapted to appropriately translate the problem description before determining the quantum mechanical representation, e.g., by mapping the problem description to a Hamiltonian of a quantum mechanical system that defines similar relationships between quantities and their effects on the quantities as the problem description, e.g., to map the problem description to a description of a quantum mechanical system that can generally be simulated by the respective selected quantum computer. Thus, for example, an optimization problem in the field of optimizing production parameters for producing a product, such as temperature, pressure, flow rate, etc., can be translated into a quantum mechanical description that represents the problem in the quantum mechanical world of a quantum computer. In such a case, for example, an Ising model can be utilized for the translation. However, if the problem already refers to a quantum mechanical problem, e.g., an electronic structure problem, this particular step of translating the problem into a quantum mechanical description can be omitted. In general, the conversion unit can be adapted to translate the problem description based on predetermined rules or predetermined models for a particular problem category, or to translate the problem description in an interactive process based on user input. In the case of interactive processing, a user interface may be provided to the user, allowing the user to select different problem categories, e.g., optimization problems, electronic structure problems, etc., to determine the category of the provided problem, and further to select a respective set of rules or model to be applied to transform the provided problem. However, other interactions by the user interface for translating the problem may also be facilitated. Furthermore, in order to translate the provided problem, the translation unit may also be adapted to access a storage in which translations for the particular problem are already saved, e.g., for problems that have already been solved previously for different parameters.

[0012] The translation unit is then configured to translate the quantum mechanical representation of the problem into a quantum algorithm description that includes a sequence of quantum operations to be applied to the quantum elements of a quantum computer. The term "quantum element" may refer to the fundamental building block of a quantum computer. In the context of quantum computing, these elements may be commonly known as qubits. Qubits may be the quantum analog of classical bits. Classical bits can represent either 0 or 1, while qubits can exist in a superposition of both states simultaneously due to the principles of quantum mechanics. Qubits may be realized using a variety of physical systems, such as atoms, ions, superconducting circuits, or photons. These physical systems may provide methods for manipulating and measuring the quantum state of qubits.

[0013] In general, operations are performed by a quantum computer by manipulating the states of quantum elements of the quantum computer, which may refer to all elements of the quantum computer used to simulate a problem, such as quantum elements that form the qubits of the quantum computer. The set of quantum operations determined by the translation unit includes a preparation portion and a measurement portion. In general, the preparation portion includes quantum operations for preparing a quantum mechanical representation of the problem on the quantum computer such that observables that indicate a solution to the problem are measurable. General methods for determining such operations for problems that can be translated into quantum mechanical representations are generally known and can be used to determine the preparation portion of the quantum operations by the translation unit. Examples of these known methods for some general and specific problems can be found in the articles "Quantum Computational Chemistry", S. McArdle et al., Rev. Mod. Phys. 92, (2020), "Quantum Algorithms for Quantum Chemistry and Quantum Materials Science", B. Bauer et al., Chem. Rev. (2020) and "Quantum Chemistry in the Age of Quantum Computing", Y. Cao, et al., Chem. Rev. (2019).

[0014] The measurement part of the quantum operations includes quantum operations for measuring the observables of the quantum mechanical representations by measuring the states of the quantum devices after the quantum mechanical representations are prepared. These measurement operations include unitary transformation operations applied to the quantum devices. The unitary transformation operations are determined such that, based on the unitary transformation determined by the transformation unit, the unitary transformation operations initiate a rotation of the states of the quantum devices to respective base states corresponding to one or more bases that result in pure occupation number representations of one or more operators that represent one or more observables to be measured, as determined by the transformation unit. Thus, the unitary transformation determined by the transformation unit is used by the translation unit to determine the unitary transformation operations and to transform the quantum devices in the states represented by the quantum mechanical representations, particularly the states after the application of the preparation part of the series of operations, into states that represent pure occupation number representations of one or more operators that represent one or more observables to be measured. In general, application of the unitary transformation operations changes the states of the quantum devices so that the states represent the observables in the bases that result in pure occupation number representations. However, measuring the states of the quantum devices provides the same result regarding the solution to the problem, i.e., does not change the determined values ​​of the observables. However, by changing the basis, rather than requiring the quantum computer to perform multiple preparations to measure the observables represented by the quantum device states for each observable, it becomes possible to simultaneously read out, i.e., measure, the states of the quantum devices based on the same preparation of the quantum mechanical representation in the quantum computer, which can significantly reduce the number of preparations required for measurements during quantum computer calculations.

[0015] The control signal generation unit is configured to generate control signals for controlling the application of the determined sequence of quantum operations to the quantum computer. In particular, the control signals are generated such that a quantum mechanical representation of the problem is prepared in the quantum computer and observables indicative of a solution to the problem are measured according to the quantum algorithmic description. In particular, the control signals may include signals that directly control the quantum computer, e.g., an operating unit of the quantum computer that operates on the state of a quantum element, but may also include indirect control of the quantum computer, e.g., by providing the control signals to a quantum computer controller, which translates the control signals into respective control actions of the operating parts of the quantum computer. Thus, the control signals may be directly usable for controlling the quantum computer or may be provided in any format that is readable by the quantum computer controller and translatable into respective control actions.

[0016] In one embodiment, the transformation unit is adapted to determine a unitary transformation by i) applying a decomposition to a tensor representation of one or more operators of one or more observables to be measured, and ii) applying diagonalization to the resulting matrix terms of the decomposed tensor representation of the one or more operators. In most applications, at least some of the operators representing the observables can be represented as tensors. Then, using respective matrix decompositions, the tensors can be decomposed into sums of matrix products. Thus, through the decomposition, tensors representing one or more operators are decomposed into products of matrix terms. These matrix terms of the decomposed tensor representations can then be diagonalized to determine a unitary transformation based on the diagonalized matrix terms. In general, known algorithms can be utilized by the transformation unit to perform the decomposition and diagonalization. Preferably, the transformation unit is adapted to determine, for each matrix term of the decomposed tensor representation for diagonalization of the matrix terms in the decomposed tensor representation of the one or more operators, eigenvalues ​​and corresponding eigenvectors, and determine the measured observable as an expression in terms of the corresponding eigenvectors and eigenvalues ​​of the decomposed tensor representation of the operator. Thus, decomposition and diagonalization allow the expression of operators that represent observables in terms of eigenvalues ​​and corresponding eigenvectors. In particular, the basis into which an operator is rotated by a unitary transformation points to the eigenvector states of the decomposed tensor representation of the operator. Thus, a unitary transformation operation can be determined by determining an operation that allows a quantum device to rotate to a state that points to each determined eigenvector state of the decomposed tensor representation.

[0017] In a preferred embodiment, the problem statement can be translated into a relativistic Hamiltonian description of the problem. In this case, the transformation unit is preferably adapted to apply Takagi decomposition to determine the unitary transformation. Alternatively, the transformation unit is preferably adapted to apply pivoted Cholesky decomposition to determine the unitary transformation. In particular, both decomposition methods can be applied by the transformation unit, for example as described above, to decompose tensorial representations of one or more operators. Furthermore, these two decomposition methods are preferably applied in particular to operators that refer to two-fermion operators of the relativistic Hamiltonian, in particular two-electron operators.

[0018] In one embodiment, the transformation unit is adapted to separate operators of a quantum mechanical representation representing an observable to be measured into a first part including a first operator and a second part including a second operator, and the transformation unit is adapted to transform the second operator into a quantum mechanical representation including only pure occupation number representations of operators representing one or more observables to be measured. For example, by using any of the methods described above to separate operators representing one or more observables to be measured into a first part and a second part and transforming only the second operator into a pure occupation number representation, the transformation is performed, for example, only on terms of the quantum mechanical representation, i.e., operators, for which the transformation is most advantageous. In particular, the first part and the second part are determined so that transforming the second part reduces the number of preparations required for the measurement, whereas transforming the first part, for example, does not provide such additional advantage, i.e., would not further reduce the number of preparations required for the measurement. Therefore, by correspondingly determining the first part and the second part, the computational resources required for the transformation and determination of the unitary transformation are reduced. Preferably, the first operator of the first part is translatable into a quantum mechanical representation in terms of a pure occupation number representation of the operator representing the observable to be measured. Therefore, where possible, the first part preferably refers to a part of the operator that is already translatable into a pure occupation number representation without applying the above-mentioned transformations. In this respect, therefore, there is no need to apply a unitary transformation to enable more accurate measurement of the state of the quantum device.

[0019] In a preferred embodiment, the quantum mechanical representation includes a two-electron operator, and the conversion unit is adapted to convert the two-electron operator into a density-density interaction term. In general, the representation converted into a density-density interaction term is an example of an occupation number representation, and the above-mentioned methods can also be used to convert the two-electron operator into a density-density interaction term, in particular the decomposition and diagonalization leading to the determination of eigenvalues ​​and eigenvectors. However, other methods allowing the conversion of the two-electron operator into a density-density interaction term can also be used. Preferably, the conversion unit is adapted to convert the two-electron operator into a density-density interaction term by using the identity decomposition (RI) approximation. This method allows a particularly efficient measurement of the two-electron operator on a quantum computer.

[0020] In one embodiment, the quantum mechanical representation includes an operator that refers to a contracted density matrix of any order, in particular an operator with an expectation value that refers to a contracted density matrix of any order, and a tensor of any order, and the transformation unit is adapted to symmetrize and / or Hermitianize the tensor of any order before determining the unitary transformation. In particular, many problems related to chemical applications include operators defined as described above. Symmetrizing and / or Hermitianizing this tensor then makes it possible to use, for example, the above-mentioned method for determining the unitary transformation. Thus, symmetrizing and / or Hermitianizing each tensor makes it possible to widen the range of problems for which improved measurements can be performed, respectively. Preferably, the transformation unit is adapted to further apply a low-rank decomposition to the symmetrized and / or Hermitianized tensor of any order in order to determine the unitary transformation. The low-rank decomposition may, for example, include the steps of decomposing and diagonalizing and determining eigenvectors and eigenvalues, as already described above.

[0021] In a further aspect of the present invention, a system for performing a quantum mechanical calculation on a quantum computer is presented, the system comprising: i) a quantum computer adapted to perform the quantum mechanical calculation based on provided control signals; and ii) an apparatus according to any one of the preceding claims adapted to provide control signals to the quantum computer in order to control the performance of the quantum mechanical calculation.

[0022] In a further aspect of the present invention, a computer-implemented method for generating control signals for measuring states of quantum elements of a quantum computer is presented, the measured states representing observables indicative of a solution to a problem translatable into a quantum mechanical description, the method comprising the steps of: i) providing a problem statement indicative of the problem to be solved, the problem statement being translatable into a quantum mechanical description; ii) transforming the problem statement into a quantum mechanical representation comprising one or more operators representing one or more observables to be measured that are indicative of the solution to the problem, the transformation further comprising determining a unitary transformation that rotates the one or more operators representing the one or more observables to be measured into one or more bases, the one or more bases resulting in pure occupation number representations of the one or more operators after application of the unitary transformation; and iii) translating the quantum mechanical description into a quantum algorithm description comprising a sequence of quantum operations to be applied to quantum elements of the quantum computer, the one or more bases being indicative of the solution to the problem. The series of quantum operations includes: a) a preparation portion including quantum operations for preparing a quantum mechanical representation on a quantum computer so that observables indicative of a solution to the problem are measurable; and b) a measurement portion including quantum operations for measuring the observables by measuring the states of quantum devices after the quantum mechanical representation is prepared, wherein the measurement operation includes a unitary transformation operation applied to the quantum devices, and the translation includes determining a unitary transformation operation based on the determined unitary transformation such that the unitary transformation operation initiates a rotation of the states of the quantum devices to respective basis states corresponding to one or more bases that result in pure occupation number representations of one or more operators representing the one or more observables to be measured; and iv) a step of providing a control signal for controlling the application of the determined series of quantum operations to the quantum computer so that a quantum mechanical representation of the problem is prepared and observables indicative of a solution to the problem are measured according to the quantum algorithmic description.

[0023] In a further aspect of the present invention, a computer program product for generating control signals for measuring the state of a quantum element of a quantum computer is presented, the computer program product comprising program code means for causing the apparatus or system, respectively, as described above, to perform the method as described above.

[0024] In a further aspect of the present invention, a solving apparatus for determining a solution to a problem translatable into a quantum mechanical description is presented, the apparatus comprising: i) the apparatus described above for generating control signals for controlling a quantum computer; ii) a quantum computer interface unit for interfacing with the quantum computer to provide the control signals to the quantum computer and to receive results of measured observables; and iii) a decision unit configured to determine a solution to the problem based on the received measurement results.

[0025] In general, a solution to a problem based on received measurements may be determined in any known manner, particularly depending on the particular problem, and may be performed in a classical computing system. Furthermore, hybrid computing approaches are also available for determining a solution to a problem, in which calculations are performed in a classical computing system based on measurements of observables in a quantum computing system, the results of these classical calculations are reused as inputs to quantum computer calculations, e.g., by correcting one or more variables of the problem solved by the quantum computer, and the measurements of the observables are reused for further calculations in the classical computing system. Such iterations can be used to improve the accuracy of the solution to the problem while simultaneously optimizing the computing resources required to calculate the problem.

[0026] In a further aspect of the present invention, a computer-implemented solution method for determining a solution to a problem translatable into a quantum mechanical description is presented, the method comprising: i) using any one of the above-mentioned apparatus, methods and computer program products to generate control signals for controlling a quantum computer; ii) providing an interface with the quantum computer to provide the control signals to the quantum computer and to receive measured observable results; and iii) determining a solution to the problem based on the received measurement results.

[0027] In a further aspect of the present invention, a property determination device is provided for determining technological application properties of a chemical product or solid product based on a solution to a problem relating to the chemical product or solid product, the problem being translatable into a quantum mechanical description, the device comprising: i) the device described above for generating control signals for controlling a quantum computer; ii) a quantum computer interface unit for interfacing with the quantum computer to provide the control signals to the quantum computer and receive results of measured observables; and iii) one or more processors configured to determine technological application properties of the chemical product or solid product based on the received measurement results. Generally, the chemical product may include any chemical product, such as a substance or mixture of substances, molecules, proteins, polymers, etc. In particular, the chemical product may be any organic or inorganic chemical product, chemical molecule, and / or biological product. The solid product may be any solid product, such as a metal compound, crystal, etc. In particular, the solid product may be a solid having a periodic lattice structure. Preferably, the solid product is a semiconductor or a superconductor.

[0028] The technical application properties may generally include any properties of a chemical or solid product that allow the evaluation of its technical applicability after production. Preferably, the technical application properties include at least one of mechanical properties, spectroscopic properties, physicochemical properties, chemical properties, and biological properties. In general, the mechanical properties may include any of adhesion, tensile strength, stiffness, hardness, shrinkage, elongation, splitting, tear strength, rebound, compressibility, abrasion, leakage, morphology, tactile properties, break stress, break elongation, particle size distribution, and packing degree. The spectroscopic properties may generally include any of color, turbidity, opacity, gloss, reflectance, appearance, absorption, scattering, color intensity, color tone, color saturation, color saturation, cloud point, matteness, optical density, spectrum, refractive index, IR spectrum, Raman spectrum, NMR spectrum, ESR spectrum, and UV / Vis spectrum. Furthermore, the physicochemical properties may include any of density, viscosity, K value, molar weight, dispersity, molar mass distribution, particle size distribution, solubility, partition coefficient, interfacial properties, surface tension, dispersibility, storage stability, odor, separation, coagulation, electrical conductivity, electrical capacity, 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, impact sensitivity, loss on drying, reaction angle, electrostatic charge, minimum film formation temperature, charge density, electrostatic multipole moment, and thermal conductivity. The chemical properties may include any of chemical resistance, reaction timing, demolding time, growth, hard / soft segment content, crystallinity, reaction temperature, reaction pressure, decomposition, thermal decomposition, photolysis, acidity, pKa, pH, moisture / water content, flammability, burning rate, autoignition, flash point, production of flammable gases, reaction to fire, deflagration rate, residual monomer count, by-product production, degree of polymerization, salt content, temperature resistance, oxidizing properties, reducing properties, reactivity, ash content, non-volatile matter content, stability, chelating ability, calorific value, and saponification value.Further biological properties may include biodegradability, biological resistance, in particular resistance to pathogenic viruses, bacteria, fungi, plants or animals or developmental stages of said pathogens, resistance to environmental parameters, such as desiccation resistance, resistance to enzymatic degradation, such as protease resistance, lipase resistance, amylase resistance, hydrolase resistance, insecticide resistance, toxicity, biotransformation, ecotoxicology, sensitization, in particular allergenicity, bacterial count, enzyme activity, substrate specificity, cofactor dependency, product specificity, substrate and / or product inhibition, dissociation constant, Michaelis-Menten kinetics value, activity / stability at constant or different pH, temperature, pressure, organic solvent concentration, carrier formulation, encapsulated formulation, environmental distribution, compartmentalization, bioaccumulation, biological exposure LD50, mutagenicity.

[0029] In general, in this embodiment, the problem for generating a control signal for the device described above to control the quantum computing system can include any problem whose solution can lead to the derivation of a respective technological application property of a chemical or solid-state product, such as one of the aforementioned technological application properties. In particular, the problem can refer to an electronic structure problem from which multiple additional properties of the respective chemical or solid-state product can be derived based on the solution of the electronic structure problem. An example of such a problem that can be advantageously solved with the present invention is the calculation of the ground state energy of a molecule or a general electronic system. This makes it possible to determine the ground state energy of all molecular species occurring in a chemical reaction, in particular, to predict the end product, thermodynamic properties, and kinetic properties of the reaction. This understanding and properties of the reaction can then be used again to optimize chemical production processes, such as to predict the microstructure of polymers and optimize material properties. Another important problem is determining the ground state of a solid. This allows the prediction of the magnetocrystalline anisotropy of magnetic materials, which is important, for example, for magnetic materials in electric motors. The problem can also refer to the calculation of multipole moments of a chemical product. Such calculations may relate to determining the properties of a chemical product with respect to electrical properties, for example, the behavior of a chemical product in an electric field. Thus, determining the value of a technology application property based on measurements of observables is based on the respective technology application property to be determined and further based on information provided by the solution of the problem addressed by the measurements of the observables.

[0030] In a further aspect of the present invention, a computer-implemented property determination method is presented for determining technological application properties of a chemical or solid product based on a solution of a problem relating to the chemical or solid product, the problem being translatable into a quantum mechanical description, the method comprising: i) using any one of the above-mentioned apparatus, methods and computer program products to generate control signals for controlling a quantum computer; ii) providing an interface with the quantum computer to provide the control signals to the quantum computer and to receive results of measured observables; and iii) determining the technological application properties of the chemical or solid product based on the received measurement results.

[0031] In a further aspect of the present invention, an apparatus for determining a target chemical or solid product having a target technology application characteristic is provided, the apparatus including: i) an input interface configured to provide the target technology application characteristic and a candidate chemical or solid product; ii) the above-mentioned apparatus for generating a control signal for controlling a quantum computer based on the candidate chemical or solid product and the target technology application characteristic; iii) a quantum computer interface unit for interfacing with the quantum computer to provide the control signal to the quantum computer and receive results for the observable quantity to be measured; iii) one or more processors configured to: a) determine the technology application characteristic of the candidate chemical or solid product based on the received measurement results; b) compare the determined technology application characteristic of the candidate chemical or solid product with the target technology application characteristic, and based on the comparison, l) determine the candidate chemical or solid product as the target chemical or solid product, or ll) provide a new candidate chemical or solid product and repeat the determination of the technology application characteristic using the new candidate chemical or solid product; and iv) an output interface configured to provide a control signal for producing the determined target chemical or solid product.

[0032] In particular, in this context, the provisioning performed by the input interface may include receiving target application properties from a user's input, applying each input interface, and providing the target application properties to the quantum computer interface. Furthermore, the provisioning may also include accessing a storage unit in which the target application properties are already stored to provide the target application properties. Furthermore, the provisioning may also include receiving target application properties from another source, for example, via a network connection, and providing the received target application properties. Generally, a target application property may refer to a single target value, such as the inherent hardness of a chemical or solid product, or may include a range of values ​​that the chemical or solid product should satisfy. Furthermore, a target application property may refer to any type of target function, such as a time series of properties under varying environmental conditions, such as hardness under varying temperature conditions. Such more complex target application properties may be advantageous when the application of the chemical or solid product involves different environmental conditions, such as different temperatures. The target chemical or solid product then refers to a chemical or solid product that, when provided in its respective form, for example, as a pure substance or a mixture, satisfies each target technological application property within predetermined limits. In particular, the target chemical or solid product provides the properties of each target technological application when produced according to the corresponding recipe.

[0033] The candidate chemical or solid product may be provided in any digitally representable format so that the candidate chemical or solid product and / or the properties of the candidate chemical or solid product can be processed by the device. Furthermore, providing the candidate chemical or solid product may also include providing a respective problem for determining the technological application properties of the candidate chemical or solid product. However, the respective problem may also be automatically selected by the device, for example, based on the candidate chemical or solid product and the provided target technological application properties. However, the user may also select the respective problem, preferably based on a selection of multiple possible problems presented to the user based on the candidate chemical or solid product and / or the target technological application properties.

[0034] By comparing the determined technology application characteristics with the target technology application characteristics, it can be determined whether the determined technology application characteristics meet a predetermined criterion, for example, whether the determined technology application characteristics meet the target technology application characteristics within a predetermined limit. If such a criterion is met, the candidate target chemical or solid product is determined as the target chemical or solid product, and the method proceeds to the next step. However, if the comparison indicates that the determined technology application characteristics do not meet the target technology application characteristics within a predetermined limit, a next iteration step using a new candidate target chemical or solid product can be performed. In particular, for each iteration step of the iteration, a new candidate chemical or solid product is preferably determined based on the previous candidate chemical or solid product, for example, by correcting one or more characteristics of the previous chemical or solid product, such as one or more components or other properties. However, a new candidate chemical or solid product can also be generated, for example, by arbitrarily selecting a new candidate chemical or solid product from a large number of previously generated candidate chemicals or solid products. Furthermore, more sophisticated methods for selecting a new candidate target chemical or solid product from multiple previously generated candidate target chemicals or solid products can be used. Based on the new candidate target chemical or solid product, in each iteration step, the quantum computer is again used to determine the technology application characteristics, and such determined technology application characteristics are again compared with the target technology application characteristics, so that the comparison can again lead to further iteration steps, or if the respective criteria are met, each new candidate target chemical or solid product can be selected as the target chemical or solid product. Furthermore, it is also possible to select additional stopping criteria for the iteration, such as notifying the user that it is impossible to find a target chemical or solid product for each technology application characteristic, and determining the number of iteration steps before the iteration is stopped. However, alternatively, after a predetermined number of iteration steps, the method may further include a step of modifying the target technology application characteristics, for example, by increasing the predetermined limit for the technology application characteristic and repeating the iteration while using the increased limit during the comparison.This makes it possible to find a target chemical or solid product that satisfies the technical application characteristics as closely as possible, even if it cannot meet the original goal. After the target chemical or solid product has been determined as described above, the target chemical or solid product can be provided to a user, for example, via an output unit. Preferably, a recipe for the target chemical or solid product is used to generate control data that can be used to control a production system that produces the target chemical or solid product.

[0035] In a further aspect of the present invention, a computer-implemented method for determining a target chemical or solid product having target technology application properties is provided, the method comprising: i) providing the target technology application properties and a candidate chemical or solid product; ii) using any one of the above-mentioned apparatuses, methods, and computer program products to generate control signals for controlling a quantum computer based on the candidate chemical or solid product; iii) providing an interface with the quantum computer to provide the control signals to the quantum computer and receive results of the measured observables; iv) determining the technology application properties of the candidate chemical or solid product based on the received measurement results; v) comparing the determined technology application properties of the candidate chemical or solid product with the target technology application properties, and based on the comparison, either a) determining the candidate chemical or solid product as the target chemical or solid product, or b) providing a new candidate chemical or solid product and repeating the determination of the technology application properties using the new candidate chemical or solid product; and vi) providing a control signal to produce the determined target chemical or solid product.

[0036] In a further aspect of the present invention, there is provided the use of the above-described apparatus for solving problems directed to at least one of chemical reactivity, spectral and spectroscopic properties and molecular properties derivable from electronic structure problem calculations of chemical or solid state products.

[0037] A further aspect of the present invention provides the use of the above-described apparatus to solve problems relating to at least one of organometallic compounds containing transition metals, including lanthanides and actinides, chelating agents that interact with metals, catalysts, biomolecules containing active centers, polymeric systems in solution or embedded in an environment, and transition metal compounds.

[0038] In a further aspect of the present invention, the use of the above-described device for determining the activation and / or reaction energy of a given chemical reaction is provided. Generally, activation energy refers to the energy difference between a transition state and a reactant. Reaction energy refers to the energy difference between a product and a reactant. The chemical reaction may be part of a complex reactivity network, for example, a catalytic cycle. The use of the above-described device is particularly advantageous when at least one species in the reaction system a) contains one or more transition metal, lanthanide, and / or actinide atoms with unpaired electrons, or b) exhibits an electronic structure with a small energy gap between occupied and unoccupied electronic orbitals, i.e., an energy gap equal to or less than that of at least one of the molecules ozone, pentacene, or paraquinodimethane calculated using the same electronic structure approach, i.e., the same basis set, the same self-consistent field (SCF) method, e.g., Hartree-Fock, or the like, or c) exhibits multi-reference diagnostics beyond a predetermined limit, e.g., T1(CCSD) > 0.02, and and / or D1(CCSD) is greater than 0.05, and / or D1(MP2) is greater than 0.04, and / or D2(MP2 / CCSD) is greater than 0.18, and / or Zs(1) is greater than 0.1, and / or %TAE is greater than 10, and the T1 diagnostic is determined based on the Frobenius norm of the amplitude of a single excitation of a CCSD wave function based on a Hartree-Fock reference state scaled by the square root of the number of correlated electrons in the CCSD calculation, the D1 diagnostic is determined based on the matrix-2 norm of the amplitude of a single excitation of a CCSD or MP2 wave function based on a Hartree-Fock reference state, and the D2 diagnostic is determined similarly to the D1 diagnostic but with reference to a double excitation, and Z s(1)This is the case when diagnostics are determined based on orbital entanglement information obtained from approximate correlated wave functions such as partially converged but qualitatively correct density matrix renormalized group (DMRG) wave functions, and %TAE diagnostics are determined based on the difference in total atomization energies obtained for CCSD(T) and CCSD relative to the total atomization energy obtained for CCSD(T).

[0039] In a further aspect of the present invention, there is provided the use of the above described device for determining the activation energy of a given catalytic cycle and / or for determining the reaction energy of a given chelating agent.

[0040] In a further aspect, a control signal generated in accordance with any of the above-described apparatus, method, and computer program product is presented.

[0041] It is to be understood that the above-mentioned device, the above-mentioned system and the above-mentioned computer program product have a number of similar and / or identical preferred embodiments, in particular as defined in the dependent claims.

[0042] It is to be understood that a preferred embodiment of the invention can also be any combination of several dependent claims or the above-mentioned embodiments with the respective independent claims.

[0043] These and other aspects of the invention will be apparent from and elucidated with reference to the embodiments described hereinafter. [Brief explanation of the drawings]

[0044] [Figure 1] 1 shows a representation of the state of a qubit used in a quantum computing device. [Figure 2] 1 shows a schematic example of a quantum computing device in which a quantum bit is used as a computing unit. [Figure 3] 1 shows a schematic example of a method for generating control signals for performing operations on a quantum computing device and for processing measurement signals from the quantum computing device. [Figure 4]1 shows a schematic example of a hybrid system including classical and quantum computing devices. [Figure 5] 1 shows a schematic example of a quantum computing device based on superconductors. [Figure 6] 1 shows a schematic example of a trapped ion based quantum computing device. [Figure 7] 1 illustrates, in a schematic and exemplary manner, one embodiment of a system for determining a solution to a problem. [Figure 8] 1 shows, by way of example only, a flow chart of a method for determining a solution to a problem. [Figure 9] 1 shows, by way of example only, a flowchart of further details of a method for determining a solution to a problem for a particular application. [Figure 10] 1 shows, by way of example only, a flowchart of further details of a method for determining a solution to a problem for a particular application. [Figure 11] 1 shows, by way of example only, a flowchart of further details of a method for determining a solution to a problem for a particular application. [Figure 12] 1 shows, by way of example only, a flowchart of further details of a method for determining a solution to a problem for a particular application. DETAILED DESCRIPTION OF THE INVENTION

[0045] Detailed Description of the Drawings In the following, we first briefly introduce the general principles of quantum computers and their computational performance. Further general principles can also be found in "Quantum Computation and Quantum Information: 10th Anniversary Edition," MA Nielsen and IL Chuang (2010).

[0046] Classical computing devices use transistor-based processors. Each transistor has two controllable states: 1 or 0, which represent digital binary, i.e., bits. To perform operations on a classical computing device, human-readable program code is converted into machine-readable instructions via a compiler. The machine-readable instructions are control signals for each transistor, such as voltage settings. The representation of the machine-readable instructions can include binary or hexadecimal representations. Based on these machine-readable instructions, operations are performed by the processor of the classical computing device.

[0047] Quantum computing is a relatively new method of computing that uses quantum effects such as superposition and entanglement to perform certain calculations more efficiently than classical digital computers. In contrast to digital computers, which represent information in the form of bits (e.g., "1" or "0") as described above, quantum computing devices, or quantum computers, represent information using qbits, or quantum bits. Quantum computing devices are based on quantum elements that obey the physical laws of quantum mechanics, such as superconductors, ions, atoms, quantum dots, photons, particle spins, and bosons. These quantum elements can be manipulated in a controlled manner to perform operations.

[0048] Although qubits and their operations can be described in terms of their mathematical properties, each such qubit can be implemented in any of a variety of different ways into a physical quantum device, examples of which include superconducting materials, trapped ions, photons, optical cavities, individual 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 that exhibits qubit behavior, including quantum states and transitions between states that can be induced or detected in a controllable manner.

[0049] In general, for any given physical quantum element that implements a qubit, any of a variety of properties of that physical unit may be selected to implement the qubit. For example, if an electron is selected to implement the qubit, the x, y, or z component of the electron spin degree of freedom may be selected as a property of such electron to represent the state of such qubit. For any particular degree of freedom, the physical quantum element may be controllably superposed or entangled, and then a measurement may be taken at the selected degree of freedom to obtain a readout of the qubit value.

[0050] In contrast to transistors in a classical computing device, each quantum element in a quantum computing device can be in not only a basis state |1> or |0>, but also any superposition of such basis states, e.g., state |X>. The state of each quantum element is represented by the state of a quantum bit, or qbit, as shown in the two-dimensional simplified diagram in Figure 1. 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 bracket notation, e.g., |X>. In conventional terminology, the superposition of "0" and "1" states in a quantum computing device can be represented by α|0>+β|1>. The states "0" and "1" or bits in a classical computing device are analogous to the basis states |0> and |1> or qubits, respectively, in a quantum computing device. The value |α| 2 represents the probability that the qubit is measured in the |0> state, and the value |β| 2 represents the probability that a qubit is measured in the |1> state. If more than one qubit is present, two or more qubits can be 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, each qubit cannot be identified as an individual qubit. In general, a quantum computer's N-qubit register can be in a superposition of basis states at once, whereas N classical bits can only be in one basis state at a time. Thus, in contrast to classical computing devices, a quantum computer can have 2 N Since basis states can be manipulated and processed simultaneously, exponential parallelism is inherently possible.

[0051] To perform an operation on a quantum computing device, a computational method for solving a given problem can be translated into qubit operations, which can be translated into control signals for manipulating the qubits. The representation of the machine-readable instructions can include a general quantum mechanical representation of the operation in Hilbert space. Depending on the specific implementation of the quantum computer, different representations of the qubit states can be selected. Any state preparation in the quantum computing device can be represented by an operation acting on the qubit states. The operations can be translated into control signals for controlling parts of the quantum computer, and these signals depend on the type of quantum computing device used. In this way, operations can be performed on a quantum equivalent of a classical processor as part of the quantum computing device based on the operations acting on the qubit states.

[0052] In gate-based quantum computer systems, operations acting on qubit states can generally be single- or multi-qubit operations. A single-qubit operation can change one qubit state into a particular superposition corresponding to a rotation of the vector |X>, as shown in Figure 1. For example, in a superconducting quantum computer, this can be achieved in a trapped-ion quantum computer by irradiating ions with microwave pulses or laser beams. A multi-qubit operation can create entanglement between two or more qubits. For example, in a superconducting quantum computer, this can be achieved in a trapped-ion quantum computer by connecting the qubits through intermediate electrical coupling circuits or through control of the collective oscillations of the trapped ions.

[0053] In general, to prepare operations for solving a given problem on a quantum computer, each quantum mechanical representation of the problem is translated into qubit operations, which are then executed to prepare a solution to the given problem. After preparing a given solution, i.e., after applying the operations to the qubits of the quantum computer, a projection measurement of the individual qubits is performed, returning either a 0 or a 1 for each qubit. This projection is typically performed using the σ of the qubits. zIt arises in the eigenbasis and is also used to define the computational basis states "0" and "1" of a qubit. This is z This means that only operators that are products of operators or that can be directly converted into such operators can be measured simultaneously. In a quantum computing device, this measurement is achieved by applying a hardware-specific readout protocol, a sequence of readout operations that, in the case of a quantum computing device, includes a control pulse, and monitoring the response to the control pulse. For example, a superconducting qubit can be coupled to a hardware resonator. The measured shift in the resonator frequency can determine the state of the qubit, since this depends on the coupled qubit state. For example, in the case of a trapped ion, an optical readout can be used; e.g., if the ion emits light, the qubit state is 1, or if it does not emit light, it is 0, or vice versa. In this way, qubits can be used, particularly in gate-based quantum computers, to implement logic circuits and gates similar to classical computing devices.

[0054] FIG. 2 shows a schematic example of a quantum computer. The quantum computing device 100 shown in FIG. 2 includes a quantum register 104 configured to perform a quantum computation, an operation unit 106 configured to operate quantum elements forming the quantum register, particularly qubits, and a readout unit 108 configured to collect measurement signals from the quantum register 104 to read out the qubits after a quantum mechanical computation. The operation unit 106 provides operation signals, particularly for operating the quantum register, which are generated based on received control signals determined based on each operation to be performed on the qubits. In some embodiments, a feedback loop may be provided between the operation unit 106 and the measurement unit 108. In contrast to classical computing, in which a transistor state is obtained in a single measurement cycle, quantum computing, in the case of a gate-based quantum computer, involves performing multiple measurement cycles to obtain probability densities or probabilities of qubit states.

[0055] The quantum register 104 may be based on different quantum elements representing qubits. In some embodiments of gate-based quantum computers, qubits may be implemented by photons as quantum elements. Such optical quantum computing devices may include a laser that generates photons that are provided to a waveguide. A beam splitter may be provided to manipulate the photon state based on a manipulation signal, such as a mechanical rotation applied to a mirror. The measurement unit 108 may, in such embodiments, be a photon detector, and the measurement signal may be a photon.

[0056] In other embodiments of gate-based quantum computers, qubits can be implemented by the electronic states of ions confined in a magnetic field. The manipulation unit 106 can then utilize a laser, and the manipulation signal can result in the provision of control laser pulses. Furthermore, in this case, the readout unit 108 can be a photon detector combined with a 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 anions as quantum elements, etc.

[0057] 3 illustrates an exemplary method for generating control signals for performing operations on a quantum computing device and processing measurement signals from a quantum computing device. In most embodiments of quantum computing devices known to date, control signals for the quantum computing device are prepared by a classical computing device, and measurement signals provided by the quantum computing device are further processed by the classical computing device. However, as quantum computing devices mature, other embodiments are possible. In the following examples, quantum computers refer to gate-based quantum computers in which operations refer to operations on quantum elements of the quantum computer.

[0058] In step S10, a problem to be solved using the quantum computing device is preferably provided in a mathematical description to generate control signals for performing operations on the quantum computing device. Such a problem may include, for example, determining material properties based on a mathematical description of the material's electronic structure. Other problems may include optimization problems and associated objective functions. Based on the problem to be solved, a quantum algorithmic description of the problem or subproblem may be generated in step S12, the quantum algorithmic description including operations to be applied to the quantum computer's qubits to solve the problem with quantum mechanical computations. Furthermore, the quantum algorithmic description may include reference states that allow for generating representations of initial qubit states in the quantum computer, and further operations are then applied to the quantum computer by manipulating the qubit states. Based on the quantum algorithmic description, control signals for controlling the quantum computer may be generated in step S14, e.g., by providing control signals to a manipulation unit, which can then manipulate the qubits based on the control signals. In step S16, the manipulation unit then applies manipulation operations to individual or multiple qubits of the quantum computer, causing the qubits to perform quantum mechanical computations based on the manipulation operations. After manipulation, a measurement signal that determines the result of the quantum mechanical computation can be generated in step S18. This step may include reading out, or measuring, the qubit state after applying the manipulation operation to the initial qubit state. The measurement signal is then converted to a measurand in step S20 on a classical computer and, in the case of a subproblem, fed back into the problem being solved. Finally, the result of the computation of the problem, including the quantum mechanical computation, can be provided on the classical computing device in step S22.

[0059] FIG. 4 shows a schematic example of a hybrid system including a classical computing device and a quantum computing device. As described with respect to the method shown in FIG. 3, quantum computing devices are often used in conjunction with classical computing devices. As shown in FIG. 4, the problem preparation system can be implemented as a classical computing device 110, for example, that performs steps S10, S12, S20, and S22 of the method shown in FIG. 3. A control unit can then be provided as an interface between the classical computing device 110 and the quantum computer 100, and the control unit can also be a classical computing device that performs step S14, for example. The control unit can then be communicatively coupled to an operation unit 106 that can control a manipulator of the quantum computing device. The operation unit 106 can also be implemented as classical control hardware that controls specific hardware elements of the classical computing device, for example, a quantum computer that performs operations on qubits. However, the operation unit 106 is generally considered part of the quantum computer because it directly affects the quantum register. The quantum computing device 100 is adapted to perform the quantum operation in step S16, particularly by manipulating the qubits of the quantum register. The measurement unit 108, which is also generally considered to be part of the quantum computing device, can then perform step S18 by utilizing classical hardware. The measurement unit 108 can then be communicatively coupled to a preparation system 110 for further processing of the measurement signal.

[0060] FIG. 5 shows a schematic example of a superconductor-based quantum computing device. Superconducting quantum computing devices are one type of solid-state quantum computing technology. Here, quantum register 104 can include Josephson junction-based superconducting circuits 520, 522, and 524. A qubit can then include, for example, a charge, flux, transmon, or phase qubit, depending on the quantity of superconducting circuitry selected to represent the qubit. FIG. 5 is a simplified diagram of a superconducting quantum computer utilizing charge qubits. For charge qubits, different qubit states can be represented by an integer number of Cooper pairs in superconducting islands. For gate-based quantum computing, quantum operations can be performed by manipulating the qubits via microwave pulses. Resonators 512, 514, and 516 can be used to manipulate the qubit state by applying microwaves or to read out the qubit state by measuring the respective microwaves; typically, different resonators are used for manipulating the qubit state and reading out the qubit. Additionally, resonator 518 can be used to apply microwaves that entangle the qubit. However, rather than using a resonator 518, entanglement can be induced by inductive or capacitive coupling of a superconducting circuit or by providing another qubit, here a superconducting circuit, between the entangled qubits.

[0061] At the computational level, such systems are maintained at extremely low temperatures, e.g., tens of mK. Extreme cooling of the system helps keep the superconducting material below its critical temperature and avoid unwanted state transitions. To maintain such low temperatures, quantum information processing systems can be operated in cryostats, such as dilution refrigerators. In some implementations, control signals are generated in a hotter environment and transmitted to the quantum computer using shielded, impedance-controlled, GHz-compatible transmission lines, such as coaxial cables. In some implementations, state measurements of superconducting qubits are achieved using a distributed detection scheme. To readout or detect the state of any qubit, a probing signal, e.g., a traveling microwave, can be excited along a readout transmission line coupled to the qubit via its respective readout resonator. The frequency of the probing 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 probing signal transmitted along the readout transmission line can vary because the reflectivity of the readout resonator coupled to the qubit changes depending on the state of the qubit. This allows for qubit state detection, where during readout the qubit state collapses, i.e., is projected onto one of the basis states with respective probabilities. Multiple quantum mechanical calculations and readouts can be performed to determine the respective probabilities. Further details of superconducting quantum devices are described in, for example, EP 3830867 A1, EP 3449427 A1, U.S. 2020272925 A1, Chinese Utility Model 212061223U, and U.S. 2019019099 A1.

[0062] Figure 6 shows a schematic example of a quantum computing device based on ions in an ion trap. Similar to neutral atom traps, ion traps using, for example, positively charged calcium ions can also be used to implement quantum computing devices. Here, ions 626 are trapped in an oscillating electromagnetic field 624 in a high or ultra-high vacuum. The ions 626 are laser cooled and held within the oscillating electric field 624. Laser light 628 of different frequencies can be used for qubit operations such as superposition or entanglement.

[0063] Generally, gate-based computations can be performed on the hardware architecture of a quantum computer based on the quantum computer implementations described above. The gate-based computations are based on quantum gates. In contrast to classical gates, there are an infinite number of one-qubit quantum gates that can change the state vector of a qubit. Changing the state of a qubit's state vector is typically referred to as a one-qubit rotation, also referred to herein as a state change or one-qubit quantum gate operation. A rotation, state change, or one-qubit quantum gate operation can be mathematically represented by a 2×2 unitary matrix with complex components. A rotation corresponds to the rotation of a qubit state in Hilbert space, which can be conceptualized as the rotation of a vector on the Bloch sphere, commonly known as a geometric representation of the space of pure qubit states. A multi-qubit gate changes the quantum state of a collection of qubits. For example, a two-qubit gate rotates two qubit states as a rotation in the four-dimensional Hilbert space of the two qubits, commonly known as a Hilbert space, an abstract vector space with a dot product structure where lengths and angles are measurable. Furthermore, Hilbert spaces are complete, meaning that there are sufficient limits in the space that allow the techniques of calculus to be used.

[0064] Hereinafter, the term quantum algorithm description refers to a representation of a problem that includes a sequence of quantum operations to be applied during a quantum-mechanical computation of the problem on a gate-based quantum computer. The term "quantum operations," in the context of the present invention, may include all types of quantum gates described above and, more generally, all known operations on quantum elements on any quantum computer hardware. Furthermore, in some applications, quantum operations may also include measurement operations. This allows for the implementation of algorithms that use measurement feedback. For example, in such algorithms, a quantum computer may execute a quantum gate defined by a sequence of quantum operations, then measure only a smaller subset of qubits or other computational elements, such as boson field states, within the quantum computer, and then determine further quantum operations to be performed based on the results of one or more measurements. In particular, measurement feedback is useful for performing quantum error correction, but is not limited to its use in performing quantum error correction.

[0065] FIG. 7 schematically and illustratively illustrates one embodiment of a system for determining a solution to a problem. In particular, the example illustrated in FIG. 7 relates to determining a solution to a problem that enables the determination of a target chemical product having target technology application characteristics. However, in other embodiments, the problem may be directed to other applications related to chemical products, solid products, or even problems completely unrelated to chemical products, such as scheduling problems, encryption problems, etc. System 800, in this exemplary embodiment, also includes an apparatus 810 for generating control signals for measuring the state of quantum elements of a quantum computer, an apparatus 840 for determining a solution to the problem, and optionally, a quantum computing system 830. In general, control signal generation apparatus 810 and solution determination apparatus 840 are communicatively coupled to quantum computer 830. Quantum computer 830 may refer to any quantum computer described above and may include, for example, a gate-based quantum computer. Furthermore, solution determination apparatus 840 may optionally be communicatively coupled to a production system 850, particularly a production control system adapted to manage and control production of production system 850, for providing control signals to the production system that initiate the production of one or more chemical products 860.

[0066] The control signal generating device 810 is configured to generate control signals for measuring the states of quantum elements of a quantum computer. In particular, the control signal generating device 810 includes a problem providing unit 811, a conversion unit 812, a translation unit 813, and a control signal generating unit 814. In general, the control signal generating device may be implemented as any known classical computing system. For example, the functions provided by each unit may be performed by one or more processors of one or more classical computing devices. In particular, the control signal generating device 810 may also be implemented as a distributed computing framework, such as a cloud or network environment in which two or more computing devices are utilized to perform the functions of the devices.

[0067] The problem providing unit 811 is configured to provide a problem description indicating a problem to be solved. For example, the problem providing unit 811 may be communicatively coupled to a user interface, e.g., so that a user can indicate the selection of a respective problem to be solved from respective provided options. Generally, the problem description can be translated into a quantum mechanical description so that it can be solved by a quantum computer. In the exemplary embodiment shown in FIG. 7 , the solution to the problem indicates a technological application property of a chemical product and can therefore be used to determine the technological application property. Generally, the problem description can be provided in any format that allows the device 810 to derive respective information from the problem description; in particular, the problem description can be provided in a digital format. Preferably, the problem description refers to a mathematical description of the problem, for example, a mathematical representation of an electronic structure problem or a mathematical representation of an optimization problem. However, the problem description can be provided in any other format from which the problem providing unit 811, or optionally the conversion unit 812, can also derive respective mathematical expressions. The problem providing unit 811 can then provide the problem description to the conversion unit 812.

[0068] The transformation unit 812 is configured to transform the problem description into a quantum mechanical representation including one or more operators representing one or more observables to be measured that indicate a solution to the problem. In particular, a quantum mechanical representation refers to a representation of the problem that represents the state of a quantum mechanical system prepared in the quantum computer 830, such that each prepared state of a quantum element in the quantum computer 830 represents an operator that indicates a solution to the problem. Methods and algorithms for transforming a problem translatable into a quantum mechanical description into such a quantum mechanical representation that can be prepared in a quantum computer to solve the problem are known, some of which are described in more detail below. Furthermore, the transformation unit is configured such that the transformation additionally includes determining a unitary transformation that rotates one or more operators representing one or more observables to be measured into one or more bases, which, after application of the unitary transformation, result in a pure occupied number representation of the one or more operators. In particular, the transformation unit determines the unitary transformation necessary to transform the quantum mechanical representation into a pure occupied number representation. Depending on the specifics of the problem and the quantum mechanical representation of the problem, several different methods and algorithms are available for determining the unitary transformation, which are detailed below for each application.

[0069] The translation unit 813 is then configured to translate the quantum mechanical representation into a quantum algorithm description comprising a sequence of quantum operations to be applied to quantum elements of the quantum computer. Generally, the quantum algorithm description comprises quantum operations necessary to prepare a quantum mechanical representation of the problem on the quantum computer and to measure observable quantities in the quantum mechanical representation, and thus the states of the quantum elements, which represent a solution to the problem. Respective translation algorithms that determine the quantum algorithm description based on the respective quantum mechanical representations are known and can be utilized by the translation unit. The sequence of quantum operations, i.e., the quantum algorithm description, comprises a preparation portion and a measurement portion. The preparation portion generally comprises quantum operations that can be utilized to prepare the quantum mechanical representation of the problem on the quantum computer so that the observable quantities that represent the solution to the problem are measurable. The measurement portion of the quantum algorithm description then relates to quantum operations that are applied to the quantum elements after the preparation of the quantum mechanical representation on the quantum elements, in order to measure the respective states of the quantum elements. In particular, in the present invention, the measurement operation comprises a unitary transformation operation applied to the quantum elements. The unitary transformation operation is determined by the translation unit, in particular by utilizing the unitary transformation determined by the translation unit. In particular, the unitary transformation operation is determined such that it initiates a rotation of the state of the quantum device to respective basis states corresponding to one or more bases that result in pure occupation number representations of one or more operators representing one or more observables to be measured. In this way, the determined unitary transformation operation initiates a basis transformation of the state of the quantum device, but this basis transformation does not change the values ​​of the observables. Therefore, although the state of the quantum device in the new basis differs from the state of the quantum device before the basis transformation, the state of the quantum device still indicates, and in particular represents, the observables and thus the solution to the problem. By applying the unitary transformation operation so that the operators representing one or more observables point to pure occupation number representations, the states of each quantum device can be simultaneously measured during the same preparation of the quantum mechanical representations. However, when separately measuring the states of the quantum devices, a new quantum mechanical representation must be prepared to measure the state of each quantum device that represents an observable that is not commutative and does not have a compatible basis within the quantum device.Thus, each preparation of a quantum mechanical representation and each measurement can be saved, making it possible either to minimize the quantum computing resources required to perform the quantum computation, or to use the freed resources to compute more complex problems, i.e. problems with more variables, or to determine the problem more accurately, for example by using respective better statistics or respective error correction methods that would otherwise require excessive resources.

[0070] The control signal generation unit 814 is then configured to generate control signals for controlling the application of the determined sequence of quantum operations, i.e., the quantum algorithm description, to the quantum computer, such that a quantum mechanical representation of the problem is prepared and observables indicative of a solution to the problem are measured. In particular, the control signals may be in any format that can be read by the quantum computer 830 or the optional quantum computer management system 820. In particular, the control signals may be generated to directly enable control of the quantum computer 830, in particular the control of operational units or parts of the quantum computer 830 that operate quantum elements in accordance with the determined quantum algorithm description. In most cases, however, the quantum computer 830 will directly control the quantum computer 830, and in most cases will be provided with a quantum computer management system 820 that is further configured, for example, to schedule the respective computations. In such cases, the control signals may be generated to be readable and interpretable by the quantum computer management system 820, such that the quantum computer management system 820 controls the quantum computer 830 in accordance with the determined quantum algorithm description.

[0071] Quantum computer 830 can then provide measurements of the observables to solution determiner 840. In particular, quantum computer interface unit 841 can be utilized to receive each measurement of the observables, which can be provided in any format readable by device 840. In general, device 810 and device 840 can together form a solver, but can also be provided as independent units. In particular, solution determiner 840 can be implemented by the same hardware and / or software as control signal generator 810, e.g., realized on the same computing device or by the same computing network as part of the respective solution framework. However, solution determiner 840 can also be provided independently of control signal generator 810, e.g., provided in different hardware and / or software, e.g., in a different computing device.

[0072] The determination unit 842 of the solution determiner 840 is then configured to determine a solution to the problem based on the measurement results received from the quantum computer. For example, any known method and / or algorithm may be used that allows a solution to each problem to be determined based on measurement results of the states of the quantum devices. In particular, known mathematical formulas may be used to determine values ​​for each observable based on the measurement results. These values ​​for each observable may then be used to determine the solution to the problem. In this example, since the problem relates to determining technological application properties, each determined solution to the problem, e.g., the energy of the molecules, may then be used by the optional property determination unit 843 to determine technological application properties of the chemical product based on the determined solution to the problem.

[0073] Optionally, an iterative unit 844 may be provided that compares the determined technological application properties of the candidate chemical product with target technological application properties, i.e., the target value of the target technological application properties. If the determined technological application properties meet the target technological application properties within a predetermined limit, i.e., if the determined technological application properties meet a predetermined criterion, the chemical product can be determined as a target chemical product. If the comparison indicates that the determined technological application properties do not meet the target technological application properties within a predetermined limit, a new candidate chemical product may be provided and the determination of the technological application properties using this new candidate chemical product may be repeated. A new candidate chemical product may be provided, for example, by modifying one or more components or synthesis parameters of a previous chemical product to generate a new candidate chemical product with different properties. For example, if the chemical product refers to a polymer, each synthesis specification of the previous polymer may be modified arbitrarily or according to a predetermined rule to generate a new synthesis specification for the new polymer. Generally, this process may be performed without synthesizing or producing this chemical product until the final target chemical product is determined. The provision of new chemicals can therefore be an automated process, which can also be a supervised process in which a user is presented with candidate new chemicals and selects one or more new chemicals for further processing, or the user can provide the new chemicals. Furthermore, new candidate chemicals can also be determined by selecting new candidate chemicals from a list of previously determined candidate chemicals. For example, each problem can be provided again based on the new candidate chemicals. Notably, in most cases, the new candidate chemicals do not result in a change in the type of problem to be solved; instead, one or more constants, variables, or other quantities in the problem are changed, e.g., so that the above-described processing can be performed based on this new problem targeting the new candidate chemicals. When a final target chemical is determined at the end of the processing, control data, including, for example, a recipe and / or composition of the target chemical, can be provided to the production system 850, and the target chemical 860 can be produced based on this control data.

[0074] FIG. 8 shows a schematic and exemplary flowchart of a method for determining a solution to a problem using a quantum computer according to the present invention. In particular, this method can be implemented by using the system described above with reference to FIG. 7. In a first step, the method includes providing a problem description indicating the problem to be solved. For example, corresponding to the example given in FIG. 7, the problem concerns determining the technological application properties of a chemical product. In a next step, the problem description is converted into a quantum mechanical representation. Furthermore, a unitary transformation can be determined that rotates the operators of the quantum mechanical representation to a basis that results in a pure occupied number representation of the operators. In general, the explanations and principles already described above with reference to the device, and in particular with reference to the transformation unit, can be applied in this step. In a next step, a quantum algorithm description is determined based on the quantum mechanical representation and on the unitary transformation, such that the quantum algorithm description includes a unitary transformation operation that initiates a rotation of the states of the quantum elements of the quantum computer into respective basis states that correspond to a basis that results in a pure occupied number representation of one or more operators. In this step, the principles already described above with reference to FIG. 7, in particular with reference to the transformation unit, can also be applied. Based on the quantum algorithmic description so determined, a quantum mechanical representation can be prepared in the quantum computer to generate control signals that control the quantum computer to execute the quantum algorithmic description to measure the state of each quantum device. Thus, based on the control signals, the quantum computer can then be utilized to perform a quantum computation and provide a measurement of the state of the quantum device.

[0075] Each measurement result can then be received by a device, such as device 840, and used to determine a solution to the problem. Optionally, the method may further include, in this example, determining a property of the chemical product based on the determined solution. Each technology application property can then be verified, for example, against one or more predetermined criteria, such as a target technology application value. If the verification indicates that the technology application property meets the respective criteria, i.e., "passes," each chemical product can be determined as a target chemical product. However, if the verification indicates that the determined technology application property does not meet the predetermined criteria, i.e., "fails," a new candidate chemical product can be provided. Based on the new candidate chemical product, a corresponding new problem can be determined, and the respective process can be repeated. If the candidate chemical product is determined as the target chemical product, control data can be generated for controlling the production system to produce the chemical product. Finally, the method may then include producing the target chemical product based on the provided control data.

[0076] In the following, preferred embodiments of the present invention will be described in detail with respect to preferred application examples. Generally, quantum computing is a developing technology that utilizes quantum mechanical phenomena to perform computational tasks. Quantum computers are expected to solve certain computational problems significantly faster than classical computers. They may be used, for example, to simulate quantum mechanical systems, such as electronic structure systems, including, but not limited to, molecules, crystals, and amorphous solids. In addition, optimization problems, machine learning, and artificial intelligence are further exemplary application areas of quantum computing. In the aforementioned areas, quantum computing is expected to significantly surpass classical computing in terms of the size of problems that can be handled, the required computation time, and / or the achievable accuracy.

[0077] The basic processing unit of a quantum computer is the quantum mechanical bit (qubit). By executing an appropriate quantum circuit, e.g., based on a quantum algorithm description, via control pulses acting on the qubit, a solution to one of the above-mentioned problems or a specific subproblem is prepared in the qubit register. To read out this solution and provide a result to the user, each qubit is measured by applying a control pulse followed by a hardware-specific readout protocol that projects the state of each qubit into one of its two energy eigenstates, i.e., providing an eigenvalue of 0 or 1. The control pulses are used, for example, to rotate the qubit state into a basis that represents the solution in the qubit's measurement basis. This quantum mechanical measurement is essentially a statistical process, and to obtain meaningful results, it is necessary to average over many repeated state preparations via the above-mentioned quantum circuit and measurement. The number of measurements required typically depends on the size of the problem being investigated, the observable being measured, and therefore the number of elementary operators representing the observable being measured, the desired accuracy, and further algorithm specifications. In particular, hybrid quantum-classical computing, which combines quantum and classical computation, is particularly well suited to exploiting the limited capabilities of near-future noisy intermediate-scale quantum (NISQ) computers, but one of the main obstacles is that it typically requires many measurements.

[0078] In quantum computing, information about the system under study can be extracted by measuring observables. In general, observables can be expressed in their respective quantum mechanical formulas by operators, and hence in the following the terms operator and observable can be used interchangeably with this relationship in mind. In general, observables can be expressed in the Hermitian form

[0079]

number

[0080] and can be written as a sum of up to D Hermitian tensors V, with dimensions up to 2D.

[0081]

number

[0082] where V and D depend on the particular quantities of interest. When considering electronic structure issues,

[0083]

number

[0084] represent the electron creation and annihilation operators, respectively. The subscripts p1,...,p d ,q1,...,,q d is 1 to N, where N is proportional to the scale of the system being handled by the quantum computer.

[0085]

number

[0086] The number of individual terms in N terms ∝N 2D (2) is.

[0087] To obtain the measurement results, use the operator

[0088]

number

[0089] Quantum mechanical expectation value of

[0090]

number

[0091] needs to be determined with respect to the quantum state |Ψ> prepared in a quantum circuit, e.g., a quantum computer, by a quantum algorithm description. For this, operator averaging techniques are typically used, i.e., Nterms Each of the individual terms is rewritten as a sum of products of Pauli operators and measured individually.

[0092] Since the expectation value of equation (3) is determined probabilistically, the projective measurement on a quantum computer must be iterated over each term, which takes a total of order O(N terms / ε 2 ) state preparation and measurement. Therefore, the total number of measurements (one state preparation is required for each measurement) is N meas ∝N 2D / ε 2 (4) which clearly becomes impossible as N and / or D become large.

[0093] In the following, we consider the Hermitian operators

[0094]

number

[0095] is a general Hamiltonian that deals with the energy of electronic structures such as molecules, solids, and materials.

[0096]

number

[0097] This Hamiltonian has the general form:

[0098]

number

[0099] It has. In the most general case of a relativistic Hamiltonian, h' and v are two- and four-dimensional complex tensors (i.e., D=2), respectively. v contains two-electron integrals, and in Dirac notation,

[0100]

number

[0101] It is expressed as:

[0102]

number

[0103] is the one-electron integral

[0104]

number

[0105] together with the effective one-electron contribution arising from the two-electron integral. h is a Hermitian form, while v is symmetric with respect to the exchange of double indices pq and rs, and with respect to simultaneous exchange of p and q and r and s, has

[0106]

number

[0107] The term representing nuclear repulsion is not shown in equation (5) because it is simply a constant within the Born-Oppenheimer approximation.

[0108] In the case of a fully relativistic Hamiltonian, p, q, r, and s are N four-component complex spinors describing molecular orbitals (MOs).

[0109]

number

[0110] The first two terms, called the large components, describe spin-up and spin-down electrons. The last two terms, called the small components, describe spin-up and spin-down positrons. Because the relevant energies in typical electronic structure calculations are much lower than the electron rest energy, the creation and annihilation of electron-positron pairs can be neglected, and the restriction to the subspace of electronic states is typically a very good approximation. This so-called "pairless" approximation is also a prerequisite for stable and robust relativistic electronic structure formulations.

[0111] One-electron integral term h in the Hermitian form pq is computed via the Dirac operator in Hermitian form, which is a 4x4 matrix.

[0112]

number

[0113] c is the speed of light,

[0114]

number

[0115] is a vector of 2×2 Pauli spin matrices, and σ 0 is the 2x2 identity matrix,

[0116]

number

[0117] is the general momentum operator, and h eN is the electron-nuclear interaction potential. Additional potentials are eN can be absorbed in

[0118] In the case of a fully relativistic Hamiltonian, the electron-electron interaction is O(1 / c 2) is described by the Coulomb-Bright operator, which includes all possible interaction terms up to the complex two-electron integral term v pqrs is an operator of Hermitian form

[0119]

number

[0120] and the following holds:

[0121]

number

[0122]

number

[0123] is a vector of traceless 4x4 matrices.

[0124]

number

[0125] By neglecting the gauge term along with the magnetic contribution to the electron-electron interaction, the usual Coulomb operator (first term) in equation (7) is restored, which represents the non-relativistic limit of the electron-electron interaction.

[0126] To simplify the complexity of the underlying formulas and speed up the computation time required for the integral evaluation, a reduction to a "quasi-relativistic" purely electronic two-component Hamiltonian can be performed, which also includes to a good approximation the most important relativistic effects. For this purpose, the electronic degrees of freedom (larger component) can be completely separated from the positronic degrees of freedom (smaller component), resulting in the two-component complex spinor

[0127]

number

[0128] and the one-electron operator of the 2 × 2 matrix in Hermitian form used instead of equation (6)

[0129]

number

[0130] to reach.

[0131]

number

[0132] is the scalar relativistic contribution including the mass velocity term and the Darwinian term.

[0133]

number

[0134] describes the spin-orbit operator. It efficiently performs a reduction from a fully relativistic four-component Hamiltonian to a "quasi-relativistic" two-component Hamiltonian,

[0135]

number

[0136] There are several well-established procedures to arrive at multiple expressions for (8), such as those given by the effective core potential (ECP), the Douglas-Kroll-Hess (DKH) Hamiltonian, the Barysz-Sadlej-Snijders (BSS) Hamiltonian, the infinite-order two-component (IOTC) Hamiltonian, the exact quasi-relativistic (XQR) Hamiltonian, the exact two-component decoupling (X2C) or the zeroth-order regular approximation (ZORA).

[0137] In the case of the "quasi-relativistic" Hamiltonian, the electron-electron interaction from equation (7) is in its non-relativistic limit, i.e., the Coulomb operator

[0138]

number

[0139] is reduced to. If we neglect the spin-orbit operator in equation (8), we obtain the usual non-relativistic or scalar-relativistic Hamiltonian, where the spinor is

[0140]

number

[0141] as real-valued eigenfunctions of the spin operator, i.e., spin-up and spin-down molecular orbitals

[0142]

number

[0143] h and v in equation (1) can both be chosen as real symmetric tensors.

[0144] The measurement of the expectation value of the (relativistic) Hamiltonian for a prepared quantum state is of great importance since it allows obtaining the energy spectrum of the electronic structure system, such as a molecule or a solid. This plays an essential role in the variational hybrid quantum-classical approach, which involves repeating an iterative procedure until the lowest possible energy, e.g., the ground state, is reached. Furthermore, the obtained energy allows prediction of chemical reactivity, e.g., thermodynamic and kinetic properties as well as spectroscopic properties of the electronic structure system. The number of terms in all the above Hamiltonians is N terms ∝N 4 Therefore, in the worst case, the number of non-simultaneous measurements required is N meas ∝N 4 / ε 2Since the equation scales as , such calculations become infeasible for larger systems.

[0145] If a quantum computer cannot provide an exact solution to the complete electronic structure problem, post-processing may be required to increase the overall accuracy, and thus measurements of higher-dimensional terms (i.e., D>2) may typically be required. This is because the general worst-case scaling of the number of non-simultaneous measurements required is N meas ∝N 2D / ε 2 , which represents an even more serious measurement bottleneck.

[0146] However, several methods have been proposed to reduce the number of measurements. For example, a simple, but not general, strategy is to reduce the number of terms below a certain cutoff threshold (e.g., h in the case of the electronic structure Hamiltonian). pq and v pqrs ) are identified. These terms can therefore be ignored to reduce the number of measurements required. Furthermore, by grouping terms, measurements of several products of Pauli operators can be combined. This reduces the number of measurements by a factor of a constant. Furthermore, methods have been proposed to reduce the number of measurements by exploiting constraints arising from the structure of the problem. For an exemplary electronic structure problem, it has been shown that using n representability constraints reduces the number of measurements required by about an order of magnitude. Furthermore, with a local set of molecular orbitals, and in the asymptotic limit for very large systems, the number of measurements required can be reduced by N meas ∝N 2 / ε 2 When using the Hubbard model Hamiltonian, the number of measurements is reduced to N meas ∝1 / ε 2 Another way to reduce the number of measurements required is the classical shadow approach, which in principle reduces the dependence to the logarithmic order of the number of individual terms. However, this approach is not suitable for hybrid approaches in electronic structure theory.

[0147] To enable quantum computing to solve problems that are translatable into quantum mechanical descriptions, in particular problems involving large, i.e., large N, systems and / or higher-dimensional, i.e., large D, tensors, the measurement observables that are represented by operators connected to them must be prepared on a classical computer, the respective quantum computer measurement signals must be controlled, and the results from the quantum computer must be assembled on a classical computer to produce the general Hermitian problem operator

[0148]

number

[0149] Expected value of

[0150]

number

[0151] Solutions need to be found to reduce the number of measurements required by obtaining . Furthermore, it would be advantageous if each solution could be applied to a wide range of quantum mechanical problems, especially those that make use of relativistic formulations.

[0152] In this regard, the present invention takes advantage of the fact that terms with matching control pulse sequences can be measured within a single state preparation, for example, because different qubits are measured or one qubit is measured in the same basis for different terms. This allows the total number of state preparations and measurements to be reduced by system-dependent factors. An example of such a case is a Hamiltonian with only pure density-density interactions. In such cases, all terms can be measured simultaneously, reducing the number of state preparations to the order of O(1 / ε2). For the generic system described above, the method does not change the overall scaling.

[0153] Therefore, the solution to the above problem according to the invention is based on this principle. In particular, low-rank decomposition can be used to improve the measurement process for (relativistic) electronic structure calculations on quantum computers. Advantageously, the method is carried out for a number N of non-simultaneous measurements on a quantum computer. meas O(N 2D / ε 2 ) to O(L / ε 2 ), where L is the dimension of the rotated basis set, e.g., the number of auxiliary basis functions in the case of decomposition via the identity decomposition (RI) approximation. Examples are general one-electron operators (i.e., D=1) and two-electron operators (i.e., D=2) connected to v in the (relativistic) electronic structure Hamiltonian. To measure these, we can reduce Nmeas to O(N 2 / ε 2 ) to O(1 / ε 2 ) and O(N 4 / ε 2 ) to O(N / ε 2 ) can be reduced to. For one-electron operators, no auxiliary functions are required, but for the two-electron operators mentioned above, scaling can be improved by utilizing an appropriate set of auxiliary functions. These improvements overcome one of the major obstacles in quantum computation of (relativistic) electronic structure problems, namely the large number of measurements required. Thus, the simulation of larger problems, e.g., larger molecules, and more efficient determination of their energy spectra becomes possible through improved measurement of the (relativistic) Hamiltonian from equation (1), and more efficient determination of physicochemical properties typically associated with one-electron operators.

[0154] Furthermore, by utilizing the identity decomposition (RI) approximation to refine the measurement of two-electron terms in the Hamiltonian formula for a problem, the number of rotated basis sets is equal to the number of auxiliary basis functions used. This provides the benefits described below. In particular, the number of rotated basis sets in this case increases proportionally to the number of auxiliary basis functions and therefore also to the scale of the electronic structure problem, e.g., the size of the molecule or the number of orbitals in the molecule. Without the RI approximation, the number of rotated basis sets typically increases proportionally to the square of the scale of the electronic structure problem, or optimally, is linearly related. Furthermore, if the relationship is already asymptotically linear in this case, utilizing the RI approximation further reduces the number of rotated basis sets required, while the error due to the approximation is typically negligible. Therefore, fewer resources are required to measure the observables. Furthermore, utilizing the RI approximation eliminates the need to perform decomposition of two-electron integrals on a classical computer when preparing the problem for a quantum computer. Because decomposition can be computationally expensive depending on the problem, particularly the scale of the electronic structure problem, utilizing the RI approximation also saves classical computer resources.

[0155] In the following, preferred embodiments for solving the improved measurement process on a quantum computer are described in detail, and a general preferred overview of the preferred method is also shown in Figure 9. Figure 9 shows a schematic and exemplary flow chart of a hybrid quantum-classical implementation of a preferred method for improving the measurement process of a general electronic structure operator on a quantum computer. In this preferred embodiment, the problem is solved by solving the general Hermitian form of an electronic structure operator |Ψ> on a quantum state prepared on a quantum computer.

[0156]

number

[0157] (See also equation (1)).

[0158]

number

[0159] In the first step, we consider the problem and operators, which in this case involve the (relativistic) electronic structure problem.

[0160]

number

[0161] The physical quantities of interest, represented by , are defined in a classical computer, for example, by respective user input. Generally, an electronic structure system is defined by the types and coordinates of atoms and their charges and spin multiplicities. This information can be provided by providing a problem description, e.g., defining the chemical product to which the problem pertains. Furthermore, an appropriate basis set representing the lowest energy state and, optionally, pseudopotentials, can be selected as part of providing the problem. Furthermore, providing can also include determining a starting set of orthogonal molecular orbitals in the space spanned by the basis functions. Furthermore, the type of Hamiltonian characterizing the electronic structure, typically a non-relativistic Schrödinger-type Hamiltonian within the Born-Oppenheimer approximation, can be selected, for example, based on each chemical product to be calculated or based on user input. The following examples focus on more general Hamiltonians, particularly Hamiltonians including scalar relativistic potentials, pseudo-relativistic two-component Hamiltonians describing spin-orbit coupling, and fully relativistic four-component Dirac Hamiltonians. Further optional choices included in the problem provision may include the selection of additional potentials in the Hamiltonian to describe, for example, solvation and / or environmental effects via a continuum solvation model, such as the Conductor-Like Screening Model (COSMO), an external electric field, etc. In addition to the electronic structure system, physical quantities of interest, represented by operators, are provided as part of the problem description. These may include, for example, a (relativistic) Hamiltonian (Eq. (5)) to obtain energies, electrostatic multipole operators to obtain electrostatic multipole moments, etc.

[0162] In summary, this information provided as or with the problem can then be used to determine D (and thus d), N, and V (see equation (1)) to find the operator of interest.

[0163]

number

[0164] as a quantum mechanical representation. Preferably, the latter quantity is determined by evaluating the matrix terms of the operator in a chosen basis set on a classical computer. In general, providing a problem statement can also refer to directly providing the problem statement in this quantum mechanical representation, in which case transforming the problem statement refers only to determining a unitary transformation, as described below.

[0165] Additionally, parameters of the computational process itself, such as the number of iterations or probability measure M required to arrive at a suitable set of auxiliary functions / with the desired statistical accuracy and overall dimension L, may also be provided.

[0166] Below, we detail how operators of interest in classical computers can be prepared so that their expectation values ​​can be measured more efficiently on quantum computers. For the special cases of one- and two-electron operators, as well as general operators, more efficient approaches can be used, which are detailed below. All approaches described for complex vectors, matrices, and tensors (e.g., for relativistic electronic structure calculations) also hold for the special cases of real vectors, matrices, and tensors (e.g., for non-relativistic electronic structure calculations). When performing operations on real data rather than complex data, we replace Hermitian matrices with symmetric matrices, Hermitian conjugate matrices with transpose matrices, and complex conjugate matrices with their respective real matrices.

[0167] In the following, we describe a preferred embodiment for determining the unitary transformation, e.g., as performed by a transform unit, for the above exemplary problem. Assume that the 2d-dimensional complex tensor V defined in equation (1) is in Hermitian form with the following for simultaneous exchange of all subscripts and superscripts:

[0168]

number

[0169] If this property is not satisfied, the procedure for constructing Hermitian components described below can be applied. Furthermore, we assume that the tensor is symmetric with respect to identical simultaneous substitutions in the subscripts and superscripts:

[0170]

number

[0171] Then, in the first step, the tensor v is computed on a classical computer as a rank-3 tensor t l is suitably resolved in terms of

[0172]

number

[0173] For each particular l, t l is a Hermitian square matrix, so in a further step it can be diagonalized on a classical computer to find the eigenvalues

[0174]

number

[0175] and eigenvector U l It can be expressed by:

[0176]

number

[0177] In the case of non- or scalar relativistic formulations, the molecular orbitals are converted into actual up- and down-spin orbitals φ p↑ and φ p↓ can be written as the matrix

[0178]

number

[0179] are preferably diagonalized separately. In general, the matrices

[0180]

number

[0181] The diagonalization of can be omitted since, by construction, all components are zero. p↑ and φ p↓ has the same spatial part for all p, this can be the case in a restricted closed shell form or a restricted open shell form,

[0182]

number

[0183] can be determined such that diagonalization of either of the two matrices is sufficient. After diagonalization, inserting equation (14) into equation (13) gives:

[0184]

number

[0185] In the next step, the eigenvector U l can be absorbed into a second quantization operator, so that we get

[0186]

number

[0187] where:

[0188]

number

[0189] is U l Occupancy number operator in a basis rotated by

[0190]

number

[0191] and

[0192]

number

[0193] holds, and U l refers to a unitary transformation, and the operator

[0194]

number

[0195] yields a pure occupied number representation of In general, we refer to occupation number representations when all operators are simultaneously measurable in a quantum computer. Other examples of occupation number representations are fermionic operators that contain only occupation number operators or their products.

[0196]

number

[0197] and the annihilation operator

[0198]

number

[0199] The occupation number operator by a particular basis with

[0200]

number

[0201] An example of such an operator is the density-density interaction

[0202]

number

[0203] is. In general, all operators containing only commutative terms that can be simultaneously measured in a quantum computer after transformation into a spin system, e.g., qubits, can be defined in the context of this application as pure occupation number representations. An example is σ for all qubits. z or any operator containing only the identity Pauli operators or their products, e.g.

[0204]

number

[0205] is. All the occupied number operators in the pure occupied number representations mentioned above commute with each other, and therefore can be measured simultaneously on a quantum computer.

[0206] As can be seen from equations (16) and (17), the expected value

[0207]

number

[0208] Measuring U involves the following successive steps, which are performed on a quantum computer: preparing the quantum state |Ψ〉 on the quantum computer; l The step of rotating the state to the eigenvector basis via

[0209]

number

[0210] All occupation numbers that refer to the eigenvalues ​​of

[0211]

number

[0212] To achieve the desired statistical accuracy of the expectation, the above process needs to be repeated over M probabilistic measurements. Furthermore, the above process needs to be repeated for all l = 1,...,L. Therefore, the quantities required for quantum state preparation and expectation measurement need to be transferred to the quantum computer. To perform the improved measurement process, we can use a unitary transformation U l also need to be transferred to the quantum computer. For this transfer, the above transformations can be translated into a quantum algorithm description, for example by a transformation unit, and the respective generated control signals can be provided to the quantum computer as described below.

[0213] The first step on the quantum computer provides a control signal indicating the preparation of a desired quantum state |Ψ> in a quantum register as a result of a quantum algorithm description. This also includes hybrid quantum-classical circuits, where typically a parameterized quantum state is prepared on the quantum computer and then optimized on a classical computer to iteratively minimize an objective function, such as the (ground state relativistic) electronic structure energy. In the case of iterative, e.g., variational, procedures, the improved measurement process described here can be applied at each iteration step.

[0214] After the quantum state |Ψ〉 is prepared in the qubit register, control signals are provided that correspond to a unitary transformation operation that rotates each of the N separate qubit states |p〉 (p=1,...,N) into an eigenvector basis via a unitary transformation U l for a particular value of l.

[0215]

number

[0216] The final step in the quantum computer is to provide control signals, including hardware-specific readout protocols, to the quantum computer to calculate the N commutative occupation number operators for a particular value of l.

[0217]

number

[0218] Simultaneously measure all eigenvalues ​​of N. Either a 0 or a 1 is returned for each of the N qubits.

[0219]

number

[0220] After measuring these occupation numbers, the state of the qubit register is the corresponding ground state

[0221]

number

[0222] After all values ​​have been collected and transferred to the classical computer, the state of the qubit register can be reset to |00...0>.

[0223] In the following steps, the final expected value

[0224]

number

[0225] is evaluated on the classical computer using the measurement results from the quantum computer according to equation (16), and the solution to the problem is then determined, for example, by the decision unit. In particular, for the example shown in Figure 9, the occupation number measured on the quantum computer is

[0226]

number

[0227] is transferred to a classical computer, and the eigenvalues

[0228]

number

[0229] and is added to the current expectation for a given value of l according to

[0230]

number

[0231] The preparation and measurement of the quantum state on the quantum computer is repeated M times, where M is the expectation value

[0232]

number

[0233] is the number of probabilistic measurements required to achieve the desired statistical accuracy of . This entire sub-procedure is then repeated additionally for all l=1,...,L.

[0234] Finally, the expectations determined above are then summed over all l to give

[0235]

number

[0236] The expected value of

[0237]

number

[0238] is obtained according to A preferred embodiment allows for a further reduction in the number of measurements required and the number of operations to rotate the qubit state into an appropriate basis by separating the operators of the quantum mechanical representation representing the observable to be measured into a first part containing the first operator and a second part containing the second operator. An example of this embodiment for the above exemplary problem is described below. In this example, equation (1) is separated into a first part containing operators that can be accurately measured in the original basis and a second part containing operators that are advantageously measured in the rotated basis, as follows:

[0239]

number

[0240] First part

[0241]

number

[0242] can be measured exactly in the original basis, whereas the second part

[0243]

number

[0244] is a unitary transformation

[0245]

number

[0246] Therefore, the eigenvalue

[0247]

number

[0248] are measured as above in a rotated basis defined using

[0249]

number

[0250] Rather than decomposing

[0251]

number

[0252] is obtained by decomposing δ pq is the Kronecker delta. In summary, as mentioned above, the method, also called low-rank decomposition, aims to improve measurement processing on quantum computers and involves the use of operators

[0253]

number

[0254] The number of non-simultaneous measurements N to determine the expected value of meas O(N 2d / ε 2 ) to O(L / ε 2 ) mainly because, according to equation (1), 2d ), is achieved by simultaneously measuring the expectation values ​​of all N occupation number operators for a particular rotated basis l = 1,...,L. To provide advantages in practical applications, the number of rotated bases L is preferably efficiently truncated. We will show below that this can be achieved relatively straightforwardly for the cases of one- and two-electron operators. Furthermore, the method is compatible with a large number of other cutting-edge methods that further refine the measurement process.

[0255] In general, the method reduces the number of measurements required on a quantum computer, thereby enabling quantum computing to be used for simulating large (relativistic) electronic structure problems (large N) and / or calculating quantities connected to operators involving higher-dimensional tensors (large D). Examples include calculating energy levels and physicochemical properties of large electronic structure systems, such as large molecules. The method works particularly well when relativistic effects, such as spin-orbit coupling, are important. The method also works in the nonrelativistic limit. The calculated properties and / or the results of multiple energy calculations, which can be used to calculate energy differences, can be used to determine relevant quantities, such as technological application properties for real-world application problems linked to molecules and solids. This can lead to recommendations for designing new materials and chemical products, improving chemical processes, tailoring molecules, solids, and materials to desired properties, and significantly streamlining research activities by reducing costly experimentation and prototyping.

[0256] 10 shows a schematic and exemplary embodiment of the present invention that allows for improved measurement of one-electron operators. The following example highlights possible modifications that can be made to efficiently measure one-electron operators in a quantum computer.

[0257] For the one-electron operator, in the example problem represented by equation (1), the dimension is d = D = 1. The resulting one-electron operator therefore has the same form as the first term of the (relativistic) electronic structure Hamiltonian in equation (5), which represents the quantum mechanical representation in this example.

[0258]

number

[0259] Number of non-simultaneous measurements in a quantum computer, N meas If there are no further improvements, 2 / ε 2 ) is scaled by

[0260] The improved measure described above allows scaling to be O(1 / ε 2 ) can be reduced to. In the case of one-electron operators, the auxiliary basis set and the loop over l are not required, i.e., L=1 in all the above equations. If the one-electron operator considered is the one-electron contribution to the (relativistic) Hamiltonian in equation (5), then the integral h in the basis of the (molecular) orbitals pq is preferably determined using, for example, a (relativistic) Hartree-Fock calculation. The result of the Hartree-Fock calculation can then also serve as a starting point for preparing the quantum state on a quantum computer. Because a loop over l is not required, the decomposition described above can be omitted and the matrix h can be directly diagonalized as described above. After the quantum mechanical representation is prepared, the qubit state is rotated and transformed into an eigenvector basis, and finally all N occupation numbers are measured simultaneously on the quantum computer. Because there is no loop over l, this subprocess is repeated over M stochastic measurements to obtain the expectation value

[0261]

number

[0262] The final result is obtained. Besides their contribution to the (relativistic) Hamiltonian and thus the energy spectrum of a system's electronic structure, single-electron operators typically represent important observables that allow the prediction of physicochemical properties. Associated with single-electron operators are, for example, relativistic corrections such as mass velocity and Darwinian corrections to energies based on non-relativistic wave functions, electrostatic multipole moments, magnetic moments and spin polarizations, hyperfine couplings, electric fields and their gradients for Mössbauer spectroscopy, and diamagnetic shielding for nuclear magnetic resonance (NMR) spectroscopy. In many cases, the influence of relativistic effects on these properties is crucial for a better understanding of the systems and problems under investigation.

[0263] 11 shows a schematic and exemplary embodiment of the present invention, which allows for improved measurement of two-electron operators. The following description focuses on modifications that can be implemented in order to efficiently measure two-electron operators in a quantum computer.

[0264] For the two-electron operator, the dimension is d = D = 2 for the example problem represented by equation (1). The resulting two-electron operator therefore has the same form as the second term of the (relativistic) electronic structure Hamiltonian in equation (5), which represents the quantum mechanical representation in this example.

[0265]

number

[0266] Number of non-simultaneous measurements in a quantum computer, N meas is O(N 4 / ε 2 ), but when considering large electronic structures, this can become a computational bottleneck and prevent further improvement.

[0267] The improved measures mentioned above generally reduce the scaling to O(L / ε 2 ), where L is the dimension of the set of rotated bases. If the two-electron operator under consideration is the two-electron contribution to the (relativistic) Hamiltonian in equation (5), the two-electron integral Vpqrs in the basis of the (molecular) orbitals is preferably determined using, for example, a (relativistic) Hartree-Fock calculation. Again, the result of the Hartree-Fock calculation can serve as a starting point for preparing the quantum state in a quantum computer. If the two-electron integral is real, the factor t l In a preferred embodiment, V is obtained by applying diagonalization or pivoted Cholesky decomposition, as shown in Figure 11. In a further advantageous alternative embodiment, V pqrsThe identity decomposition (RI) approximation of is preferably used for its simplicity in that it considers only the Coulomb interaction, i.e., no Bright contribution, and it works for both real and complex two-electron integrals. After diagonalizing the factors on a classical computer and rewriting the two-electron (interaction) operator only in terms of density-density interactions, the quantum state is prepared on a quantum computer, the qubit state is rotated and transformed into the eigenvector basis l, and finally all occupation numbers are measured simultaneously on the quantum computer as described above. This subprocess is then repeated over M stochastic measurements and over all rotated bases l to obtain the expectation value σ as described above.

[0268]

number

[0269] Variations of this method may include the above-described specifics regarding separating the operators of the quantum mechanical representation representing the observable being measured into a first portion including the first operator and a second portion including the second operator to further reduce the number of measurements required and the number of operations to rotate the qubit states and transform them into an auxiliary basis.

[0270] Efficient measurement of the two-electron operators contributing to the (relativistic) Hamiltonian in equation (5) is crucial for virtually all electronic structure calculations, as it allows for efficient determination of the energy levels of larger electronic structure problems. As an example, variational hybrid quantum-classical algorithms require the calculation of the total energy at each iteration step to determine whether a desired energy state, e.g., the ground state, has been reached and the iterative procedure has converged. Furthermore, calculating the energy difference between different electronic states of an electronic structure system, e.g., a molecule, enables the prediction of spectroscopic properties, which are important for understanding the interaction of radiation with materials, e.g., in organic electronics. Another example is chemical reactivity. Here, the energy difference between derivatives, products, and transition states, e.g., the energy maxima along a reaction pathway, allows for the prediction of chemical reactivity, e.g., the thermodynamic and kinetic properties of a chemical reaction. Finally, energy differences must be calculated to predict the magnetocrystalline anisotropy of magnetic materials.

[0271] The influence of relativistic effects on the above-mentioned energies and properties is preferably taken into account whenever heavy elements with high atomic numbers, such as heavy main group elements, transition metals, lanthanides, and actinides, are involved. In such cases, to obtain accurate results for the above-mentioned energies and properties, it is preferable to consider additional relativistic effects beyond the quantum mechanical description and problem solution. Relativistic effects generally refer to discrepancies between model solutions that take relativity into account, such as those using Hamiltonian operators and those that do not. Therefore, in the above cases, to obtain accurate results, it is preferable to consider both quantum mechanical theory and relativity theory. A notable example is the description of the color of gold. Due to relativistic effects, gold is not silvery like most other metals. Relativistic effects are suitable for permanent magnets or catalysts, where heavy elements such as platinum and iridium play an important role, and also for chelating agents that interact with heavy metal ions. Relativistic effects are often suitably considered when only relatively light elements are involved in describing and understanding "spin-forbidden" transitions between different electronic states, such as level shifts and splitting in spectroscopy, and phosphorescence and intersystem crossing, both of which are facilitated by spin-orbit coupling and are suitable for organic electronic materials.

[0272] In the following, we describe in more detail the use of the identity decomposition (RI) approximation as shown in the first step of Figure 11, first for real two-electron integrals and then for multiple two-electron integrals. p The two-electron Coulomb repulsion integral between ,... is defined as:

[0273]

number

[0274] The identity decomposition (RI) method uses an additional set of functions, the auxiliary basis set χ, to approximate the product of two orbits. l Introduce.

[0275]

number

[0276]

number

[0277] is the two orbits φ p and φ q are the coefficients in the linear expansion of each product of A preferred choice of auxiliary basis set is to use Gaussian basis functions. In many cases, a set of auxiliary basis set parameters tailored for a particular molecular orbital basis set can be predetermined and then stored so that these sets can be accessed, for example, based on the problem for which the transformation unit is provided, for example, based on the chemical or solid product to which the problem relates. Therefore, these sets can also be applied in the context of quantum computations without extra effort. Furthermore, known procedures can be used to automatically generate auxiliary basis sets for molecular orbital basis sets. Furthermore, any type of basis function can be used. Generally, when an auxiliary basis set is tailored to each problem, the error introduced by the RI approximation can be significantly smaller than the error introduced by simulation methods or finite molecular orbital basis sets, and therefore the error introduced by the RI approximation can be ignored.

[0278] By expanding the product of orbitals as a linear combination of auxiliary functions, the two-electron repulsion integral can be written as

[0279]

number

[0280] where J is the matrix of electron repulsion integrals between auxiliary basis functions.

[0281]

number

[0282] The formula in (A3) is an approximation of the exact two-electron repulsion integral. For simplicity, v pqrs Starting from equation (A3), refers to the integrals following the RI approximation, rather than the exact value of each integral. Therefore, the equal sign "=" is used instead of the "approximately equal" symbol "≒" that appears in equation (A2).

[0283] To take advantage of the RI approximation in a low-rank decomposition, the matrix J is preferably pre-decomposed as follows:

[0284]

number

[0285] To obtain the matrix L in equation (A5), suitable methods available, for example, by a transformation unit, include the Cholesky decomposition of J or the matrix square root

[0286]

number

[0287] This includes the calculation of Comparison with equation (13) shows that the two-electron quadruple integral can be decomposed into a triple integral as follows:

[0288]

number

[0289] and

[0290]

number

[0291] Typically, the size of the auxiliary basis set grows linearly with the system size N. This means that N meas is equal to the dimension of the auxiliary basis set, which implies that it grows linearly with the size of the system. Therefore, the general method described above combined with the RI approximation gives Nmeas O(N / ε 2 ) The advantage of this method over other alternatives that do not utilize the RI approximation is that the decomposition of a large matrix containing all the two-electron repulsion integrals, e.g., by Cholesky decomposition with diagonalization or pivoting, reduces to the factor

[0292]

number

[0293] This is to be avoided in order to obtain There are various variations of the RI method, and the coefficients

[0294]

number

[0295] The methods for obtaining RI differ. Below, we describe Coulomb fitting and other fitting schemes that can be used in each embodiment. A variant of the RI approximation is Coulomb fitting, where the expansion coefficient is selected to minimize the Coulomb self-repulsion of the density error.

[0296]

number

[0297] The coefficients that minimize equation (A8) are

[0298]

number

[0299] where

[0300]

number

[0301] is. In practice, the most straightforward way to resolve the electron repulsion integral via the available Coulomb fitting is, e.g., by the transformation unit,

[0302]

number

[0303] The method involves calculating the following steps, but does not include explicit calculation of the following formula:

[0304]

number

[0305] In the first step, the integral defined in equation (A10)

[0306]

number

[0307] and J as defined in formula (A4) lm In the second step, matrix J is multiplied by matrix LL T (see equation (A5)). Suitable methods include Cholesky decomposition or matrix square root. In the last step, the factor

[0308]

number

[0309] This can be done by performing the steps in the previous equation, for example, by inverting the matrix L and calculating each B pq However, in particular when computing L by Cholesky decomposition, the preferred numerical procedure is to solve the linear equation

[0310]

number

[0311] The coefficient

[0312]

number

[0313] The goal is to solve the following problem.

[0314]

number

[0315] Note that there is no need to explicitly solve for A possible modification of the Coulomb fitting scheme is an alternative to equation (A9) or equation (A11), which is preferably used when the matrix J is unsatisfactory or singular.

[0316] Coefficients fitted by the conversion unit using several schemes other than the Coulomb fitting in equation (A8)

[0317]

number

[0318] One of the possibilities available is overlap fitting, where the objective function to be minimized is the self-overlap of the errors in the fitted density.

[0319]

number

[0320] Overlap-fitted coefficients

[0321]

number

[0322] is a linear equation:

[0323]

number

[0324] Meet the following. Many other fitting schemes, such as alternatives to Coulomb fitting and overlap fitting, can also be used explicitly or implicitly in place of equation (A8) or equation (A13), and the coefficients

[0325]

number

[0326] It depends on the type of metric used to obtain it. In particular, the RI / DF approximation is preferably used in connection with complex Hamiltonian components. This is immediately true, for example, if we consider a fully relativistic four-component Hamiltonian or a "quasi-relativistic" two-component Hamiltonian. Complex multicomponent functions in an interacting four-component Dirac-Coulomb Hamiltonian or an interacting two-component Hamiltonian

[0327]

number

[0328] Consider the tensor of the two-electron Coulomb repulsion integral between

[0329]

number

[0330] As with real numbers, a tensor can be decomposed according to:

[0331]

number

[0332] Complex Coefficients

[0333]

number

[0334] is the fitting coefficient equivalent to equation (A7)

[0335]

number

[0336] and the factor L lm It is the product of For example, a suitable implementation of the method in a transform unit is

[0337]

number

[0338] Using the complex fitting coefficients

[0339]

number

[0340] In that situation, the matrix L is obtained in the same way as in the real case. As in the Coulomb fitting for real integrals, the coefficients

[0341]

number

[0342] teeth,

[0343]

number

[0344] Note that the method can be directly determined without explicitly calculating the auxiliary function

[0345]

number

[0346] It is also possible to implement it so that the matrix J is itself complex. lm is complex symmetric and has a factor L lm can be obtained by suitable techniques such as Takagi decomposition or Cholesky decomposition for complex symmetric matrices. In both cases, the respective equations are similar to those presented for the real two-electron integral above, except that the complex multi-component function φ p and φ r are their Hermitian conjugates

[0347]

number

[0348] whereas φ q and φ s Note that remains non-conjugated in the above equation.

[0349] For example, the complex two-electron integral v of the Hamiltonian as part of the determination of the unitary transformation pqrs The use of the identity decomposition (RI) approximation to decompose (13) as described above is particularly advantageous because it can significantly reduce the scaling of the number of terms that are measured non-simultaneously in a quantum computer. In addition, existing optimized auxiliary basis sets from classical quantum chemistry can be used to omit the decomposition by diagonalization to obtain (13).

[0350]

number

[0351] is therefore simply a density-fitted triple integral in either a basis of real molecular orbitals p,q or a basis of complex molecular spinors p,q. In both cases, the density-fitted triple integral is calculated in the basis of real atomic orbitals and then suitably fitted with either real molecular orbital coefficients or complex molecular spinor coefficients, e.g., by transformation units.

[0352]

number

[0353] where l is an auxiliary function. The number of auxiliary functions scales linearly with the system size without invoking further screening criteria, i.e., L ∝ O(N), and therefore the number of non-simultaneous measurements N meas is O(N 4 / ε 2 ) to O(N / ε 2 ) can be reduced to

[0354] Two-electron integrals can be complicated, for example, with several relativistic Hamiltonians. Using the RI approximation, v pqrs Unless explicit decomposition of v is to be avoided, it is preferable to modify the double decomposition procedure as shown in Figure 11. As in the real case, the first step is to pqrs From the above, we form a supermatrix whose rows are labeled with double subscripts pq and whose columns are labeled with double subscripts rs. A complex matrix is ​​symmetric with respect to the exchange of rows and columns, i.e., v pqrs =v rspq is.

[0355] One possibility for decomposing a symmetric complex matrix is ​​the Takagi decomposition, also called the Orton-Takagi decomposition, described for example in Corollary 4.4.4 of the book "Matrix Analysis", 2nd edition, Cambridge University Press, by RA Horn and CR Johnson.

[0356]

number

[0357]

number

[0358] are the elements of the unitary supermatrix obtained from the Takagi decomposition. Its rows are labeled by the double subscript pq and its columns are labeled by the subscript l. The entry s l is the supermatrix v pqrs contains singular values ​​that are non-negative real numbers.

[0359]

number

[0360] is preferably obtained as follows:

[0361]

number

[0362] Takagi decomposition is a special kind of singular value decomposition. For each particular l, the matrix t l is diagonalized according to equation (14). For real two-electron integrals, the Takagi decomposition reduces to the diagonalization.

[0363] A second possibility to perform the decomposition of a symmetric complex matrix is ​​the result of the pivoted Cholesky decomposition to obtain:

[0364]

number

[0365] An implementation of an algorithm for performing pivoted Cholesky decomposition of a complex symmetric matrix is ​​described, for example, in "A dense complex symmetric indefinite solver for the Fujitsu AP3000", P. Strazdins, Technical Report TR-CS-99-01, Canberra 0200 ACT, Australia, 1999: http: / / hdl.handle.net / 1885 / 40733.

[0366] Figure 12 shows the adaptation of the above method to allow improved measurements of quantities associated with contracted density matrices of any order, in particular to problems where a symmetric or more general Hermie-form tensor V is not available. In what follows we will again focus only on the necessary modifications.

[0367] In general, the expected value of the considered operator (Eq. (1)) is the trace

[0368]

number

[0369] and the dth order density matrix is:

[0370]

number

[0371] For example, in the general method described with respect to Figure 9, the problem results in a tensor V that has the symmetries outlined in equations (11) and (12). If the problem results in a tensor V that does not have the above symmetries, the method preferably includes introducing symmetries. Instead of the expression in equation (31), the normal ordered density

[0372]

number

[0373] Utilizing this, we obtain the following:

[0374]

number

[0375] Using an appropriate normal order density, equation (30) becomes

[0376]

number

[0377] where:

[0378]

number

[0379] are coefficients derived from V and associated with the normal order density. The formula without normal order (equation (30)) and the formula with occurrence order (equation (33)) are related via the anti-commutative relation of the second quantization operator.

[0380]

number

[0381] First, it is preferable to establish a permutation symmetry according to equation (12). This kind of symmetry is obtained by constructing a normal-order d-th density

[0382]

number

[0383] For d indices, there are d! unique permutations P n {p1...p d Equation (33) can therefore be equivalently expressed as:

[0384]

number

[0385] Note that the ordering of superscripts and subscripts is always defined under the identity permutation. Second, the symmetry with respect to the exchange of superscripts and subscripts (equation (11)) is well established for real quantities by the symmetry of the density matrix.

[0386]

number

[0387] As in the case of expectation values ​​of operators that represent observable physical quantities such as energy,

[0388]

number

[0389] If you know that is real, then

[0390]

number

[0391] Only the Hermitian components of are needed.

[0392]

number

[0393] Similarly,

[0394]

number

[0395] Only the imaginary part of is obtained when

[0396]

number

[0397] is replaced by its anti-Hermitian component. In general, equation (33) can then be suitably converted to the formula

[0398]

number

[0399] where:

[0400]

number

[0401] teeth,

[0402]

number

[0403] Through symmetrization with respect to the substitution of

[0404]

number

[0405] or regarding the exchange of subscripts

[0406]

number

[0407] Hermitianization of, for example, symmetrization in the real case

[0408]

number

[0409] or a combination of both.

[0410]

number

[0411] Symmetrized tensors using anticommutative relations for the second quantized creation and annihilation operators or by other algebraic means

[0412]

number

[0413] is a non-normal ordered form suitable for decomposition

[0414]

number

[0415] is converted to Finally, the expected value of the operator is

[0416]

number

[0417] is expressed as equation (30).

[0418]

number

[0419] Thereafter, the method may proceed as already described above with respect to, for example, FIGS.

[0420]

number

[0421] Proceed to process and expect value

[0422]

number

[0423] Modifications of this method may include the variations described above. Using any of the above methods,

[0424]

number

[0425] The number of non-simultaneous measurements N on a quantum computer to determine meas O(N 2d / ε 2 ) to O(L / ε 2 ), potentially overcoming a serious computational bottleneck, especially for quantities with d>2, when combined with an appropriately truncated set of auxiliary functions of dimension L. Measurements of higher-order contracted density matrices can be important for perturbation methods, where additional post-processing on classical computers can improve the overall accuracy of results, e.g., energies, when an exact solution of the complete electronic structure problem cannot be prepared on a quantum computer. Examples of such methods are second-order n-electron valence state perturbation theory (NEVPT2) and second-order complete active space perturbation theory (CASPT2), which yield third- and fourth-order contracted density matrices, i.e., d=3 and 4, resulting in O(N 8 / ε 2 ) instead of O(L / ε 2) Furthermore, the generally applicable quantum subspace expansion method for determining electronically excited states and / or alleviating decoherence, described for example in the paper "Hybrid quantum-classical hierarchy for mitigation of decoherence and determination of excited states" McClean et al. Phys. Rev. A 95, 042308 (2017), also requires measurements of higher-order reduced density matrices, i.e., d>2. Therefore, the above-mentioned measurement method can further improve the efficiency.

[0426] The above-described method and its embodiments may also be applied to other problems besides the electronic structure problems exemplarily described above, such as problems of mixed fermion-boson systems, e.g., electron-photon (radiation-matter interactions), electron-phonon, etc. The method may also be applied in the calculation of nuclear wave functions or mixed nuclear / electronic wave functions.

[0427] In general, the invention described above improves upon known methods and algorithms by improving the measurements to be applicable to operators present in problems that utilize the formulation of relativistic electronic structure problems, which is particularly advantageous for the applications described above. Furthermore, in contrast to known methods, the invention described above advantageously utilizes an identity decomposition approximation to improve the measurement of two-electron terms in the Hamiltonian operator formulation of the problem, thereby optimally reducing the measurement effort while minimizing the approximation error.

[0428] Other variations to the disclosed embodiments can be understood and effected by those skilled in the art from the drawings, the disclosure, and the appended claims in practicing the claimed invention.

[0429] For the processes and methods disclosed herein, the actions performed in the processes and methods may be performed in different orders. Furthermore, the outlined actions are presented only as examples, and some actions are optional and may be combined to reduce steps and actions, supplemented with further actions, or expanded into additional actions, without departing from the essence of the disclosed embodiments.

[0430] In the claims, the word "comprising" does not exclude other elements or steps, and the indefinite article "a" or "an" does not exclude a plurality.

[0431] A single unit or device may fulfill the functions of several items recited in the claims. The mere fact that certain measures are recited in mutually different dependent claims does not indicate that a combination of these measures cannot be used to advantage.

[0432] The procedures performed by one or more units or devices, such as providing a problem description, transforming the problem description, translating quantum mechanical expressions, generating control signals, etc., may be performed by any number of other units or devices. These procedures may be implemented as program code means of a computer program and / or as dedicated hardware.

[0433] The computer program product may be stored / distributed by any suitable medium, such as an optical storage medium or a solid-state medium, supplied together with or as part of other hardware, but may also be distributed in other forms, for example via the Internet or other wired or wireless telecommunications systems.

[0434] Any unit described herein may be a processing unit that is part of a classical computing system. A processing unit may include a general-purpose processor, a field programmable gate array (FPGA), an application-specific integrated circuit (ASIC), or any other dedicated circuit. Any memory may be physical system memory, which may be volatile, nonvolatile, or a combination of both. The term "memory" may include computer-readable storage media, such as non-volatile mass storage. If a computing system is distributed, processing and / or storage capabilities may also be distributed. A computing system may include multiple structures as "executable elements." The term "executable element" is a structure well understood in the computing field, which may be software, hardware, or a combination thereof. For example, when implemented in software, those skilled in the art will understand that executable element structures may include software objects, routines, methods, etc. that can be executed on a computing system. This may include both executable elements in the computing system's heap or on a computer-readable storage medium. Executable element structures may reside on a computer-readable medium such that, when interpreted by one or more processors, e.g., processor threads, of the computing system, cause the computing system to perform a function. Such structures may be directly computer readable by a processor, such as when the executable elements are binary, or may be interpretably structured and / or compiled to generate binary directly interpretable by a processor, whether in one stage or multiple stages, for example. In other examples, the structures may be hard-coded or hard-wired logic gates implemented exclusively or nearly exclusively in hardware, such as in a field programmable gate array (FPGA), application specific integrated circuit (ASIC), or other dedicated circuitry. Thus, the term "executable element" refers to a structure, whether implemented in software, hardware, or a combination thereof, as would be well understood by one of ordinary skill in the computing arts. Any embodiments herein are described with reference to operations that are performed by one or more processing units of a computing system.When such operations are implemented in software, one or more processors direct the operation of the computing system in response to executing the computer-executable instructions that make up the executable elements. A computing system may also include communication channels that allow the computing system to communicate with other computing systems, for example, over a network. A "network" is defined as one or more data links that allow electronic data to be transmitted between computing systems and / or modules and / or other electronic devices. When information is transferred or provided to a computing system via a network or another communications connection, e.g., wired, wireless, or a combination of wired and wireless, the computing system properly considers the connection to be a transmission medium. Transmission media may include networks and / or data links that can be used to carry desired program code means in the form of computer-executable instructions or data structures and that can be accessed by a general-purpose or special-purpose computing system, or a combination thereof. While not all computing systems require a user interface, in some embodiments, a computing system includes a user interface system for interacting with a user. The user interface serves as an input or output mechanism for the user, for example, via a display.

[0435] Those skilled in the art will appreciate that at least portions of the present invention may be implemented in networked computing environments having many types 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, cellular phones, PDAs, pagers, routers, switches, data centers, wearable devices such as eyeglasses, etc. The present invention may also be practiced in distributed system environments where tasks are performed together by local and remote computing systems that are connected either through a network, for example, by wired data links, wireless data links, or a combination of wired and wireless data links. In a distributed system environment, program modules may be located in both local and remote memory storage devices.

[0436] Those skilled in the art will also understand that at least a portion of the present invention may be implemented in a cloud computing environment. A cloud computing environment may be distributed, but this is not required. When distributed, a cloud computing environment may be distributed internationally within an organization and / or may have elements held across multiple organizations. For purposes of this specification and the claims that follow, "cloud computing" is defined as a model that enables on-demand network access to a shared pool of configurable computing resources, such as networks, servers, storage, applications, and services. The definition of "cloud computing" is not limited to any of the many other benefits that may be gained from such a model when deployed. The computing system in the figures, as described above, includes various elements or functional blocks that may implement various embodiments disclosed herein. The various elements or functional blocks may be implemented in a local computing system or in a distributed computing system that includes elements that reside in the cloud or that implement aspects of cloud computing. The various elements or functional blocks may be implemented as software, hardware, or a combination of software and hardware. The computing system shown may include more or fewer elements than those shown, and some of the elements may be combined where circumstances permit.

[0437] Any reference signs in the claims should not be construed as limiting the scope of the invention. The present invention relates to an apparatus for generating control signals for measuring the states of quantum elements of a quantum computer. A providing unit provides a problem description. A transforming unit transforms the problem description into a quantum mechanical representation. The transforming includes determining a unitary transformation that rotates an operator representing an observable to be measured into a basis that results in a pure occupied number representation. A translating unit translates the quantum mechanical representation into a sequence of quantum operations that includes a unitary transformation operation to be applied to the quantum element. The translation includes determining a unitary transformation operation based on the determined unitary transformation. A generating unit generates control signals for controlling the application of the determined sequence of quantum operations to a quantum computer such that a quantum mechanical representation of the problem is prepared and an observable indicative of a solution to the problem is measured.

Claims

1. 1. An apparatus for generating control signals for measuring states of quantum elements of a quantum computer (830), the measured states representing observables that indicate a solution to a problem that is translatable into a quantum mechanical description, the apparatus (810) comprising: a problem provision unit (811) for providing a problem description representing the problem to be solved, the problem description being translatable into a quantum mechanical description; a transformation unit (812) for transforming the problem statement into a quantum mechanical representation that describes the solution to the problem and includes one or more operators that represent one or more observables to be measured, the transformation further comprising determining a unitary transformation that rotates the one or more operators that represent one or more observables to be measured into one or more bases, the one or more bases resulting in pure occupation number representations of the one or more operators after application of the unitary transformation; a translation unit (813) for translating the quantum mechanical representation into a quantum algorithm description comprising a sequence of quantum operations to be applied to quantum elements of the quantum computer (830), the sequence of quantum operations comprising: a) a preparation portion comprising quantum operations to prepare the quantum mechanical representation on the quantum computer (830) such that the observables indicative of the solution to the problem are measurable; and b) a measurement portion comprising quantum operations to measure the observables by measuring the states of the quantum elements after the preparation of the quantum mechanical representation, the measuring operation comprising a unitary transformation operation applied to the quantum elements, the translation comprising determining, based on the determined unitary transformation, the unitary transformation operation to initiate a rotation of the states of the quantum elements to respective basis states corresponding to the one or more bases that result in the pure occupation number representations of the one or more operators representing the one or more observables to be measured; a control signal generation unit (814) for generating control signals for controlling the application of the determined sequence of quantum operations to the quantum computer (830) such that the quantum mechanical representation of the problem is prepared and the observables indicative of the solution to the problem are measured according to the quantum algorithmic description; 1. An apparatus comprising:

2. 2. The apparatus of claim 1, wherein the transform unit is adapted to determine the unitary transformation by: i) applying a decomposition to a tensor representation of one or more operators of the one or more observables to be measured; and ii) applying a diagonalization to resulting matrix terms of the decomposed tensor representation of the one or more operators.

3. 3. The apparatus of claim 2, wherein the transformation unit is adapted to determine, for each matrix term of the decomposed tensor representation, an eigenvalue and a corresponding eigenvector for the diagonalization of the matrix terms in the decomposed tensor representation of the one or more operators, and to determine the measured observable as an expression in terms of the corresponding eigenvectors and eigenvalues ​​of the decomposed tensor representation of the operator.

4. 10. An apparatus according to any one of the preceding claims, wherein the problem description is translatable into a relativistic Hamiltonian description of the problem.

5. The apparatus of claim 4 , wherein the transform unit (812) is adapted to apply Takagi decomposition or pivoted Cholesky decomposition to determine the unitary transform.

6. 10. The apparatus of claim 1, wherein the transformation unit is adapted to separate an operator of the quantum mechanical representation representing the observable quantity to be measured into a first part including a first operator and a second part including a second operator, and the transformation unit is adapted to transform the second operator into a quantum mechanical representation including only pure occupation number representations of the operators representing the one or more observable quantities to be measured.

7. 10. The apparatus of claim 1, wherein the quantum mechanical representation includes a two-electron operator representing an observable quantity to be measured, and the conversion unit (812) is adapted to convert the two-electron operator into a density-density interaction term.

8. The apparatus of claim 7, wherein the transformation unit (812) is adapted to transform the two-electron operator into a density-density interaction term by utilizing an identity decomposition approximation.

9. 10. The apparatus of claim 1, wherein the quantum mechanical representation comprises operators that refer to contracted density matrices of any order and tensors of any order, and the transformation unit (812) is adapted to symmetrize and / or Hermitianize the tensors of any order before determining the unitary transformation.

10. 1. A system for performing quantum mechanical calculations on a quantum computer (830), comprising: a quantum computer (830) adapted to perform quantum mechanical calculations based on the provided control signals; 10. An apparatus (810) according to any one of the preceding claims, adapted to provide control signals to said quantum computer (830) for controlling the execution of quantum mechanical calculations; A system including:

11. 1. A computer-implemented method for generating control signals for measuring states of quantum elements of a quantum computer (830), the measured states representing observables that indicate a solution to a problem that is translatable into a quantum mechanical description, the method comprising: providing a problem statement describing the problem to be solved, the problem statement being translatable into a quantum mechanical statement; transforming the problem statement into a quantum mechanical representation that describes the solution to the problem, the representation including one or more operators that represent one or more observables to be measured, the transformation further comprising determining a unitary transformation that rotates the one or more operators that represent one or more observables to be measured into one or more bases, the one or more bases resulting in pure occupation number representations of the one or more operators after application of the unitary transformation; translating the quantum mechanical description into a quantum algorithmic description comprising a series of quantum operations to be applied to quantum elements of the quantum computer (830), the series of quantum operations comprising: a) a preparation portion comprising quantum operations for preparing the quantum mechanical representation in the quantum computer (830) such that the observables indicative of the solution to the problem are measurable; and b) a measurement portion comprising quantum operations for measuring the observables by measuring the states of the quantum elements after the preparation of the quantum mechanical representation, the measurement operations comprising unitary transformation operations applied to quantum elements, the translation comprising determining, based on the determined unitary transformation, the unitary transformation operation to initiate a rotation of the states of the quantum elements to respective basis states corresponding to the one or more bases that result in the pure occupation number representations of the one or more operators representing the one or more observables to be measured; providing control signals to control application of the determined sequence of quantum operations to the quantum computer (830) such that the quantum mechanical representation of the problem is prepared and the observables indicative of the solution to the problem are measured according to the quantum algorithmic description; 11. A computer-implemented method comprising:

12. A computer program product for generating control signals for measuring states of quantum elements of a quantum computer (830), the computer program product comprising program code means for causing an apparatus (810) or a system (800) according to claims 1 to 9 or 10, respectively, to perform the method according to claim 11.

13. 1. A solver for determining a solution to a problem translatable into a quantum mechanical description, comprising: An apparatus (810) according to any one of claims 1 to 9 for generating a control signal for controlling a quantum computer (830); a quantum computer interface unit (841) for interfacing with the quantum computer (830) to provide the control signals to the quantum computer (830) and to receive results for the measured observables; a determination unit (843) configured to determine a solution to the problem based on the received measurements; A solving device including:

14. 1. A property determination device for determining a technical application property of a chemical or solid product based on a solution of a problem relating to said chemical or solid product, said problem being translatable into a quantum mechanical description, said device comprising: An apparatus (810) according to any one of claims 1 to 9 for generating a control signal for controlling a quantum computer (830); a quantum computer interface unit (841) for interfacing with the quantum computer (830) to provide the control signals to the quantum computer (830) and to receive results for the measured observables; one or more processors configured to determine the technical application characteristics of the chemical or solid product based on the received measurement results; A characteristic determination device comprising:

15. 1. An apparatus for determining a target chemical or solid product including target technology application characteristics, comprising: an input interface configured to provide target technology application properties and candidate chemical or solid products; An apparatus (810) according to any one of claims 1 to 9 for generating a control signal for controlling a quantum computer (830) based on the candidate chemical or solid product and based on the target technology application characteristics; a quantum computer interface unit (841) for interfacing with the quantum computer (830) to provide the control signals to the quantum computer (830) and to receive results for the measured observables; one or more processors, a) determining technological application characteristics of the candidate chemical or solid product based on the received measurement results; b) comparing the determined technological application properties of the candidate chemical product or solid product with the target technological application properties, and based on the comparison, either i) determining the candidate chemical product or solid product as the target chemical product or solid product, or ii) providing a new candidate chemical product or solid product, and repeating the determination of the technological application properties using the new candidate chemical product or solid product. one or more processors configured to perform an output interface configured to provide a control signal for producing the determined target chemical or solid product; An apparatus comprising:

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