Quantum computing support program, quantum computing support method, and information processing device.

Abstract

The items to be measured simultaneously and the sample size should be determined appropriately. [Solution] The processing unit 12 obtains first information 13 that shows the term-specific variance and the pairwise covariance of multiple terms when simultaneous measurement is performed for multiple terms included in the Hamiltonian corresponding to the problem to be solved by the variational quantum eigenvalue method, and for multiple terms that can be simultaneously measured by a quantum computer. Based on the constraint that the change in the mean of the sum of the multiple terms is less than or equal to a predetermined value, the processing unit 12 generates an optimization problem based on the first information 13 that minimizes the sum of the term-specific variance and pairwise covariance of the multiple terms. By solving the optimization problem, the processing unit 12 determines multiple first terms from among the multiple terms that will be subject to simultaneous measurement by a quantum computer. The processing unit 12 calculates the number of samples for simultaneous measurement based on the minimized sum.

Description

[Technical Field]

[0001] This invention relates to a quantum computing support program, a quantum computing support method, and an information processing device. [Background technology]

[0002] In the field of quantum computing, the practical application of NISQ (Noisy Intermediate-Scale Quantum Computer) is highly anticipated. NISQ is a medium-scale quantum computer without error correction capabilities. One application of NISQ is computation using the Variational Quantum Eigensolver (VQE). VQE is a variational algorithm for finding the ground state of a quantum many-body system. VQE can be used, for example, in quantum chemical calculations on NISQ. Quantum chemical calculations involve solving the Schrödinger equation to obtain information about molecular states and physical properties. Currently, various studies are underway to realize practical applications of VQE-based computations.

[0003] In VQE, the Hamiltonian is described as a linear combination of tensor products of Pauli matrices. That is, the Hamiltonian is expressed as the sum of multiple terms. Each term includes the tensor product of Pauli matrices and its weight coefficients. The expected value of each term in the Hamiltonian is statistically calculated by sampling measurement results from a quantum computer. Generally, the number of measurement samples is estimated based on a predetermined tolerance, assuming term-specific independence where each term is measured individually. The number of samples is sometimes called the number of shots.

[0004] Here, for example, a technique has been proposed for the simultaneous measurement of multiple observables, each of which is a tensor product of Pauli matrices. According to this technique, it is possible to measure multiple observables with a single quantum circuit.

[0005] Furthermore, there is a proposed system for generating trial states for VQE that selects the number of samples to take from the qubit for a particular trial state. Furthermore, there are proposed quantum optimization methods that use classical computers to estimate the expectation value of the Hamiltonian in VQE for a quantum state, and then transform either the Hamiltonian or the quantum state, or both, to reduce the expectation value of the Hamiltonian.

[0006] Furthermore, there is a proposed system for solving optimization problems by representing them with a cost function in the form of QUBO (Quadratic Unconstrained Binary Optimization) and using the VQE algorithm to find the minimum eigenvalue of the Hamiltonian representing that cost function. [Prior art documents] [Patent Documents]

[0007] [Patent Document 1] International Publication No. 2022 / 269712 [Patent Document 2] International Publication No. 2019 / 057317 [Patent Document 3] U.S. Patent Application Publication No. 2020 / 0057957 Specification [Patent Document 4] U.S. Patent Application Publication No. 2023 / 0244979 [Non-patent literature]

[0008] [Non-Patent Document 1] J. Tilly, et al., “The Variational Quantum Eigensolver: a review of methods and best practices”, [online], November 9, 2021, Cornell University, [Retrieved January 8, 2025], Internet<URL:https: / / arxiv.org / abs / 2111.05176> [Overview of the project] [Problems that the invention aims to solve]

[0009] Simultaneous measurement of each simultaneously measurable term in the Hamiltonian can sometimes improve the efficiency of expectation value measurement. In this case, the terms being measured simultaneously are not necessarily independent of each other. Therefore, the sample size estimated based on the assumption of independence of each term, as described above, will be inaccurate.

[0010] Furthermore, some terms in the Hamiltonian contribute very little to the energy obtained as the sum of the expected values ​​of each term. Including such terms in the measurement and energy calculation processes of a quantum computer increases the overall processing time in VQE.

[0011] In one aspect, the present invention aims to appropriately select the terms to be measured simultaneously and determine the number of samples. [Means for solving the problem]

[0012] In one embodiment, a quantum computing support program is provided. This quantum computing support program causes a computer to perform the following processes: The computer obtains first information showing the term-specific variance and pairwise covariance of multiple terms that are simultaneously measured by a quantum computer, for multiple terms included in the Hamiltonian corresponding to the problem to be solved by the variational quantum eigenvalue method, and for multiple terms that can be simultaneously measured by a quantum computer. Based on the first information, the computer generates an optimization problem that minimizes the sum of the term-specific variance and pairwise covariance of multiple terms, based on the constraint that the change in the mean of the sum of the multiple terms is less than or equal to a predetermined value. By solving the optimization problem, the computer determines multiple first terms from among the multiple terms to be targeted for simultaneous measurement by a quantum computer, and calculates the number of samples for simultaneous measurement based on the minimized sum.

[0013] In one embodiment, a method for supporting quantum computing performed by a computer is provided. In one embodiment, an information processing device having a storage unit and a processing unit is provided. [Effects of the Invention]

[0014] In one respect, it allows for the appropriate selection of the terms to be measured simultaneously and the determination of the sample size. [Brief explanation of the drawing]

[0015] [Figure 1] This is a diagram illustrating the information processing device of the first embodiment. [Figure 2] This figure shows an example of a quantum computing system according to the second embodiment. [Figure 3] This figure shows an example of a quantum computing system's hardware. [Figure 4] This figure shows an example of the functionality of a quantum computing system. [Figure 5] This figure shows an example of the functionality of a quantum computing system (continued). [Figure 6] This flowchart shows an example of how to obtain mean and covariance information. [Figure 7] This flowchart shows an example of term selection and sample size calculation. [Figure 8] This flowchart shows an example of VQE execution. [Modes for carrying out the invention]

[0016] This embodiment will be described below with reference to the drawings. [First Embodiment] A first embodiment will be described.

[0017] Figure 1 is a diagram illustrating an information processing device of a first embodiment. The information processing device 10 supports quantum computing in a quantum computing system that performs VQE. The quantum computing system includes a quantum computer and a classical computer. A classical computer is also called a von Neumann computer. The quantum computing system is not shown in Figure 1. The information processing device 10 may be a classical computer that performs VQE in cooperation with a quantum computer. The information processing device 10 may be a classical computer separate from the classical computer that performs VQE in cooperation with a quantum computer. The information processing device 10 has a storage unit 11 and a processing unit 12.

[0018] The memory unit 11 may be a volatile semiconductor memory such as RAM (Random Access Memory), or a non-volatile storage such as an HDD (Hard Disk Drive) or flash memory. The processing unit 12 is a processor such as a CPU (Central Processing Unit), GPU (Graphics Processing Unit), or DSP (Digital Signal Processor). However, the processing unit 12 may also include application-specific electronic circuits such as an ASIC (Application Specific Integrated Circuit) or FPGA (Field Programmable Gate Array). The processor executes programs stored in memory such as RAM (which may also be the memory unit 11). A collection of multiple processors is sometimes called a "multiprocessor" or simply a "processor."

[0019] Here, the second quantized Hamiltonian in the field of quantum chemistry is expressed by equation (1).

[0020]

number

[0021] 'a' is an annihilation operator. Here, a caret "^" is placed above 'a' in mathematical formulas, but the caret is omitted in text. , a , a , , a , , a ,

[0029] is a creation operator. h corresponding to each subscript is a coefficient. The Hamiltonian obtained by converting the creation and annihilation operators in Equation (1) into quantum gates is represented by Equation (2).

[0022]

Number

[0023] P a is the tensor product of Pauli matrices. w a is a weight coefficient. P is the number of terms included in the Hamiltonian H. The Pauli matrix is represented by Equation (3).

[0024]

Number

[0025] In VQE, quantum computation based on the Hamiltonian in Equation (2) is executed. In the energy calculation of VQE, the process of solving the optimization problem represented by Equation (4) for the parameter θ of the unitary matrix U is performed.

[0026]

Number

[0027] In solving the optimization problem, the quantum computing system is <0|U † (θ)P a U(θ)|0>. Each term of is statistically obtained by sampling P a . It is known that the standard deviation ε of the error of the statistical process is represented by Equation (5) based on the central limit theorem.

[0028]

Number

[0029] Var(P a ) is the variance of P a . m a is P aThis is the sample size for the measured values. The sample size for the entire Hamiltonian H is m. a The total number m' is expressed by equation (6).

[0030]

number

[0031] Equation (5) shows the sample size m a all P a Assuming that they are equal, equation (7) holds.

[0032]

number

[0033] In equation (7), m' provides an estimate of the number of samples needed to achieve the error ε. However, the estimate given by equation (7) is P a It is assumed that all measurements are performed independently. Therefore, a certain P a Measurement values ​​and other P a In cases where the covariance with the measured value is not zero, the estimation using equation (7) is inappropriate.

[0034] Here, the quantum computing system groups the terms of the Hamiltonian into terms that can be measured simultaneously. Being able to measure simultaneously corresponds to being interchangeable as operators. The quantum computing system uses a quantum computer to perform simultaneous measurements of each term belonging to each group. In this case, P belonging to a certain group... a Measurement values ​​and other P a There are cases where the covariance with the measured value is not zero. Therefore, the sample size m' obtained in equation (7) is inappropriate when simultaneous measurements are performed for each group. Thus, the information processing device 10 executes the quantum computing support method shown below.

[0035] A linear combination of terms belonging to a group of simultaneously measurable terms is called a partial Hamiltonian. Partial Hamiltonian A αThis is represented by equation (8), where α is the group identifier.

[0036]

number

[0037] P α c is the set of tensor products of Pauli matrices. k This is the weighting coefficient. The expectation value H of the Hamiltonian H for the state vector of matter |ψ> - H can be found using equation (9). - The character "H" has a hyphen "-" above it.

[0038]

number

[0039] L is the number of groups. α Expected value A α - This is expressed by equation (10).

[0040]

number

[0041] A α,i This is the i-th measurement. α - is, m α A measured multiple times α,i This is the average. From equation (8), A α Average Ave ψ (A α ) is expressed by equation (11).

[0042]

number

[0043] Ave ψ (P j) is expressed by equation (12).

[0044]

number

[0045] Also, A α Variance Var ψ (A α ) is expressed by equation (13).

[0046]

number

[0047] Cov ψ (P j ,P k ) is P j and P k This is the covariance of Cov. ψ (P j ,P k ) is expressed by equation (14).

[0048]

number

[0049] Note that the measurement or calculation of equations (12) and (14) requires a state vector (wave function) |ψ>. For this state vector, the ground state |ψ0> obtained by classical calculations such as the HF (Hartree-Fock) method is used.

[0050] The data for each term on the right-hand side of equations (12) and (14) can be obtained through classical computational simulations or experimental measurements using quantum computers. α Covariance σ ij and mean μ i Each of these is defined by equations (15) and (16) by reassigning the subscripts.

[0051]

number

[0052]

number

[0053] n is A α The Pauli product term P is included in this term. i It is the number of [number]. A α The variance-covariance matrix S is σ ij It is defined by equation (17) using .

[0054]

number

[0055] A α The mean vector μ is μ i It is defined by equation (18) using .

[0056]

number

[0057] Var ψ (A α ) can be expressed using the variance-covariance matrix S in equation (19).

[0058]

number

[0059] Ave ψ (A α ) can be expressed using the mean vector μ in equation (20).

[0060]

number

[0061] 1 n This is an n-dimensional column vector where all elements are 1.n This is expressed by equation (21).

[0062]

number

[0063] The subscript T indicates transpose. The processing unit 12 performs, for example, A using a quantum computer. α Based on the results of simultaneous measurement of each term included in the expression, the first information 13 representing the variance-covariance matrix S and the mean vector μ are obtained. The processing unit 12 may also obtain the first information 13 representing the variance-covariance matrix S and the mean vector μ based on the results of a simulation of the simultaneous measurement on a classical computer.

[0064] The processing unit 12 processes the partial Hamiltonian A α From each term, select the term to actually use in calculating the expected value. The selection of terms is done by selecting one of the terms in equations (19) and (20). n The binary variable vector b n This is expressed by changing it to b n This is expressed by equation (22).

[0065]

number

[0066] For example, b i =1 is b i This indicates that the term corresponding to this will be the subject of measurement. i =0 is b i This indicates that the term corresponding to this will not be included in the measurement. The criterion for term selection is the variance value σ of equation (23). A_α 2 This is the minimization of A. "A_α" is A α This indicates.

[0067]

number

[0068] b as a constraint on term selection n T A of μ α An inequality is given that limits the change from the mean value to a predetermined value δ or less. The criteria and constraints for term selection are expressed as an optimization problem in equation (24).

[0069]

number

[0070] The processing unit 12 processes the partial Hamiltonian A α The problem of selecting which terms from each term to actually use in calculating the expected value is formulated as the optimization problem of equation (24). The optimization problem of equation (24) is called an integer quadratic programming problem.

[0071] The processing unit 12 solves the optimization problem of equation (24). The processing unit 12 uses existing techniques to solve the optimization problem. For example, the processing unit 12 may solve the optimization problem using an existing mathematical programming solver program. Alternatively, the processing unit 12 solves the optimization problem of equation (24) using σ A_α 2* The optimization problem may be formulated as a QUBO-form evaluation function that includes the evaluation formula and constraint formula. The processing unit 12 may solve the optimization problem formulated as a QUBO-form evaluation function using techniques such as simulated annealing or quantum annealing.

[0072] The processing unit 12 solves the optimization problem of equation (24) to obtain solution b. * and, b * Corresponding variance value σ A_α 2* We obtain the following. Here, the variance value σ A_α 2* This does not necessarily have to be a global minimum; it may also be a local minimum, i.e., a local minimum. For this reason, the criterion for term selection mentioned above is the variance σ. A_α 2 It can also be said that this is a minimization of b. In actual quantum computing, b * Only terms whose element is 1 are subject to simultaneous measurement. That is, b* Terms with an element of 0 become non - measurement targets by pruning. The optimization problem of Equation (24) can also be said to be a problem of minimizing the total sum of variances for each term and covariances for each pair among a plurality of terms, based on a constraint that the amount of change in the average value of the sum of a plurality of terms is below a predetermined value, with respect to the selection of terms to be simultaneously measured among the plurality of terms.

[0073] Note that the terms subject to term selection may be those after preliminary selection using existing technologies or the like. For example, terms that have been found to have a contribution to H less than a threshold among all terms included in H, or terms corresponding to unimportant orbits may be pruned in advance.

[0074] The processing unit 12 calculates the number of measurement samples m based on the central limit theorem. The number of samples m is represented by Equation (25).

[0075]

Equation

[0076] ε is the allowable error. The value of ε is given in advance according to the problem to be solved by VQE. The processing unit 12 calculates b * and the number of samples m for each partial Hamiltonian included in the Hamiltonian H.

[0077] In this way, the processing unit 12 can simultaneously realize the selection of terms of the Hamiltonian and the estimation of the number of samples by solving the optimization problem of Equation (24). The number of samples m in Equation (25) is an appropriate value considering the covariance between each term in the partial Hamiltonian.

[0078] The processing unit 12 inputs b * and the number of samples m for each partial Hamiltonian to the quantum computing system, and can execute VQE based on b * , m. For example, the processing unit 12 can use b *Cause the quantum computer to perform simultaneous measurements of a plurality of terms shown by, obtain m measurement values for each term to be simultaneously measured from the quantum computer, and these may be used for the energy calculation of VQE.

[0079] According to the information processing apparatus 10, the first information 13 is acquired. The first information 13 indicates the variance for each term and the covariance for each pair of two terms when simultaneous measurements are performed for a plurality of terms that can be simultaneously measured by the quantum computer. The plurality of terms are some of the terms included in the Hamiltonian corresponding to the problem to be solved by the variational quantum eigenvalue method (VQE). An optimization problem is generated based on the first information 13. The optimization problem is a problem of minimizing the sum (σ A_α 2* ) of the variances for each term and the covariances for each pair in the plurality of terms, based on the constraint that the amount of change in the average value of the sum of the plurality of terms is less than or equal to a predetermined value. By solving the optimization problem, among the plurality of terms, a plurality of first terms to be the objects of simultaneous measurement by the quantum computer are determined. The number of samples for simultaneous measurement is calculated based on the minimized sum (σ A_α 2* ).

[0080] Thereby, the information processing apparatus 10 can appropriately select the terms to be simultaneously measured and determine the number of samples. The information processing apparatus 10 can cause the quantum computing system to execute VQE based on the result of the selection of the terms and the determined number of samples. The information processing apparatus 10 can reduce the terms to be measured by the quantum computer by narrowing down the terms to be actually measured among the plurality of terms that can be simultaneously measured, and can improve the efficiency of the VQE calculation. The information processing apparatus 10 can appropriately balance the error and the calculation speed, which are in a trade-off relationship, by optimizing the number of samples.

[0081] [Second Embodiment] Next, the second embodiment will be described. Figure 2 shows an example of a quantum computing system according to the second embodiment. The quantum computing system 400 performs quantum chemical calculations using VQE. The quantum computing system 400 is connected to a terminal device 31 via a network 20. The terminal device 31 transmits a request for quantum computing to the quantum computing system 400 in response to user operations.

[0082] The quantum computing system 400 comprises classical computers 100 and 200 and a quantum computer 300. The classical computers 100 and 300 are connected by a communication interface. The classical computers 100 and 200 are connected via a network 40 in the quantum computing system 400.

[0083] Classical computers 100 and 200 are von Neumann architecture computers. Classical computer 100 performs tasks such as generating quantum circuits and optimizing the parameters used for quantum circuit calculations. Quantum computer 300 is a computer that performs quantum chemical calculations by performing quantum gate-based operations on qubits. Quantum computer 300 performs quantum chemical calculations using the VQE algorithm according to the quantum circuits and parameters generated by classical computer 100.

[0084] The classical computer 200 supports the quantum computation of VQE by the classical computer 100 and the quantum computer 300. The classical computer 200 is an example of the information processing device 10 of the first embodiment.

[0085] Figure 3 shows an example of the hardware of a quantum computing system. The classical computer 100 is controlled as a whole by a processor 101. The processor 101 is connected to memory 102 and several peripheral devices via a bus 109. The processor 101 may be a multiprocessor. The processor 101 is, for example, a CPU, an MPU (Micro Processing Unit), or a DSP. At least some of the functions that the processor 101 implements by executing a program may be implemented by electronic circuits such as ASICs and PLDs (Programmable Logic Devices).

[0086] Memory 102 is used as the main memory of the classical computer 100. Memory 102 temporarily stores at least a portion of the OS (Operating System) program and application programs that are to be executed by the processor 101. Memory 102 also stores various data used for processing by the processor 101. For memory 102, a volatile semiconductor memory device such as RAM is used.

[0087] Peripheral devices connected to bus 109 include storage device 103, GPU 104, input interface 105, optical drive device 106, device connection interface 107, and network interfaces 108a and 108b.

[0088] The storage device 103 electrically or magnetically writes and reads data from its built-in recording medium. The storage device 103 is used as an auxiliary storage device for the classical computer 100. The storage device 103 stores the OS program, application programs, and various data. The storage device 103 is, for example, an HDD or an SSD (Solid State Drive).

[0089] The GPU104 is a processing unit that performs image processing. The GPU104 is an example of a graphics controller. A monitor 41 is connected to the GPU104. The GPU104 displays images on the screen of the monitor 41 according to instructions from the processor 101. The monitor 41 can be a display device using organic EL (Electro Luminescence) or a liquid crystal display device.

[0090] The input interface 105 is connected to a keyboard 42 and a mouse 43. The input interface 105 transmits signals from the keyboard 42 and mouse 43 to the processor 101. Note that the mouse 43 is just one example of a pointing device; other pointing devices can also be used. Other pointing devices include touch panels, tablets, touchpads, and trackballs.

[0091] The optical drive device 106 uses laser light or the like to read data recorded on the optical disc 44 or write data to the optical disc 44. The optical disc 44 is a portable recording medium on which data is recorded in a way that makes it readable by the reflection of light. Examples of optical discs 44 include DVD (Digital Versatile Disc), DVD-RAM, CD-ROM (Compact Disc Read Only Memory), and CD-R (Recordable) / RW (ReWritable).

[0092] The device connection interface 107 is a communication interface for connecting peripheral devices to the classical computer 100. For example, a memory device 45 and a memory reader / writer 46 can be connected to the device connection interface 107. The memory device 45 is a recording medium equipped with a communication function with the device connection interface 107. The memory reader / writer 46 is a device that writes data to or reads data from the memory card 47. The memory card 47 is a card-type recording medium.

[0093] The network interface 108a is connected to the network 40. The network interface 108a transmits and receives data to and from other computers or communication devices via the network 40. The network interface 108a is a wired communication interface, for example, connected by cable to a wired communication device such as a switch or router. Alternatively, the network interface 108a may be a wireless communication interface, connected by radio waves to a wireless communication device such as a base station or access point.

[0094] The network interface 108b is an interface for connecting to the quantum computer 300. The processor 101 transmits quantum circuits to the quantum computer 300 via the network interface 108b, causing the quantum computer 300 to perform quantum computations. The processor 101 also obtains the results of the quantum computations via the network interface 108b.

[0095] Although not shown in the diagram, the classical computer 100 may have a network interface that connects to the network 20. However, the network 40 may also be connected to the network 20. In that case, the classical computer 100 may communicate with the terminal device 31 via the network 40.

[0096] The classical computer 200 has hardware similar to that of the classical computer 100. The quantum computing system 400 implements the processing functions of the second embodiment using the above hardware. The information processing device 10 of the first embodiment can also be implemented using hardware similar to that of the classical computer 100 shown in Figure 3. Here, the processor that executes one of the multiple processes performed by the classical computer 200 and the processor that executes a different process from the multiple processes may be different. The processor may also be called a "processor circuitry". The processor of the classical computer 200 is an example of the processing unit 12 of the first embodiment. The memory and storage device of the classical computer 200 is an example of the storage unit 11 of the first embodiment.

[0097] Classical computers 100 and 200 realize the processing functions of the second embodiment by executing a program recorded on, for example, a computer-readable recording medium. The program describing the processing to be executed by classical computers 100 and 200 can be recorded on various recording media.

[0098] For example, a program to be executed by the classical computer 100 is stored in the storage device 103. The processor 101 loads at least a portion of the program from the storage device 103 into the memory 102 and executes the program. A program to be executed by the classical computer 200 is stored in the storage device of the classical computer 200. The processor of the classical computer 200 loads at least a portion of the program from the storage device into the memory of the classical computer 200 and executes the program.

[0099] Programs to be executed by classical computers 100 and 200 can be recorded on portable recording media such as optical discs 44, memory devices 45, and memory cards 47. Programs stored on portable recording media can be installed in storage devices 103, for example, under control from processor 101, and then become executable on classical computer 100. Programs stored on portable recording media can be installed in the storage device of classical computer 200, for example, under control from the processor of classical computer 200, and then become executable on classical computer 200. Alternatively, processor 101 or the processor of classical computer 200 can directly read and execute programs from portable recording media.

[0100] The quantum computer 300 comprises a control device 310 and a qubit device 320. The control device 310 performs gate operations on the qubits in the qubit device 320 according to a quantum circuit. The qubit device 320 has multiple qubits. The qubit device 320 is, for example, a QPU (Quantum Processing Unit).

[0101] In the quantum computing system 400, the classical computer 100 and the quantum computer 300 work in conjunction to perform quantum chemical calculations using VQE. Figure 4 shows an example of the functionality of a quantum computing system. The classical computer 100 has a data input unit 110, a classical computing unit 120, a quantum computing control unit 130, and a statistical computing unit 140. The data input unit 110, the classical computing unit 120, the quantum computing control unit 130, and the statistical computing unit 140 are realized by the execution of a program stored in memory 102 by the processor 101.

[0102] The data input unit 110 receives first input data. The first input data may be input from the terminal device 31 to the classical computer 100. The first input data includes compound data and first specified conditions. The compound data is information indicating the Hamiltonian in VQE. Each term included in the Hamiltonian is grouped together with terms that can be measured simultaneously. α is a group identifier. The first specified condition is the initial value m of the sample number. α Includes m α m is given in advance for each group of terms that can be measured simultaneously. α This is used to determine the number of samples m for the actual test for group α. α The values ​​can be the same.

[0103] The classical computation unit 120 solves the ground state |ψ0> using classical computation. For example, the classical computation unit 120 may find the ground state |ψ0> using the HF method or the like. This ground state |ψ0> is used as the initial state for the trial in VQE.

[0104] The quantum computing control unit 130 instructs the quantum computer 300 to perform sampling based on the first specified condition for each term belonging to group α. For multiple terms that can be measured simultaneously, the measured values ​​can be sampled by a single quantum circuit. For example, the quantum computing control unit 130 inputs information about the quantum circuit and information about |ψ0> to the quantum computer 300 and causes the quantum circuit to execute.

[0105] The quantum computer 300, in response to instructions from the quantum computing control unit 130, samples each term belonging to group α by simultaneous measurement according to the first specified condition, and responds to the quantum computing control unit 130 with the measured value of each term.

[0106] Here, the quantum computing control unit 130 specifies all terms belonging to group α in order to determine the actual sample size m, and the sample size m αThe quantum computer 300 is instructed to perform sampling. The quantum computing control unit 130 obtains the sampling results of the measured values ​​of each term for all groups included in the Hamiltonian, group by group. The sampling results for group α are obtained for each term belonging to group α. α Includes individual measurements.

[0107] Furthermore, the quantum computing control unit 130 may perform sampling by simultaneous measurement of each term in group α through a simulation that simulates the operation of the quantum computer 300. In other words, the quantum computing control unit 130 may obtain measurement values ​​for the simultaneous measurement of each term in group α through the simulation, rather than performing actual measurements using the quantum computer 300.

[0108] The statistical calculation unit 140 calculates the Ave of equation (12) based on the sampling results of each term belonging to group α. ψ (P j ) and Cov of formula (14) ψ (P j ,P k The statistical calculation unit 140 calculates Cov ψ (P j ,P k Based on ), the σ of equation (15) ij The statistical calculation unit 140 calculates the variance-covariance matrix S of equation (17). ψ (P j Based on ), μ in equation (16) i The mean vector μ of equation (18) is generated by calculating the mean and covariance. The statistical calculation unit 140 outputs mean-covariance information including S and μ. The mean-covariance information is input to the classical computer 200.

[0109] The classical computer 200 has a data input unit 210, an optimization calculation unit 220, and an output unit 230. The data input unit 210, the optimization calculation unit 220, and the output unit 230 are realized by executing a program stored in the memory of the classical computer 200 by the processor of the classical computer 200.

[0110] The data input unit 210 receives the second input data. The second input data includes mean-covariance information and a second specified condition. The second specified condition may be input by the terminal device 31. The data input unit 210 stores the second input data in the storage unit of the classical computer 200. This storage unit is implemented by the memory or storage device of the classical computer 200. The illustration of this storage unit is omitted in Figure 4. The second specified condition includes the allowable error ε of equation (25) and the predetermined value δ of equation (24). ε and δ may be specified for each group.

[0111] The optimization calculation unit 220 generates the optimization problem given by equation (24) based on mean-covariance information. The optimization problem given by equation (24) is an integer quadratic programming problem. The optimization calculation unit 220 performs the calculation of the optimization problem to obtain solution b * , and, b * σ corresponding to A_α 2* Here, the optimization calculation unit 220 generates an optimization problem for each group and performs the solution. The optimization calculation unit 220 calculates b for each group. * ,σ A_α 2* To obtain.

[0112] The optimization calculation unit 220 can solve integer quadratic programming problems, for example, using an existing mathematical programming solver program. The optimization calculation unit 220 may also formulate the optimization problem in equation (24) using an evaluation function in QUBO form and solve it using methods such as simulated annealing or quantum annealing.

[0113] The optimization calculation unit 220 calculates σ A_α 2* Based on this, the sample size m in equation (25) is calculated. The sample size m is calculated for each group. Output unit 230 outputs item selection result b * The system outputs term selection and sampling information, including the sample size m, for each group. This term selection and sampling information is input to the classical computer 100 during the actual VQE execution.

[0114] Figure 5 shows an example of the functions of a quantum computing system (continued). The classical computer 100 has a data input unit 110, a quantum computing control unit 130, and an output unit 150. The output unit 150 is realized when a program stored in memory 102 is executed by the processor 101. The classical computing unit 120 and the statistical computing unit 140 are not shown in Figure 5.

[0115] The data input unit 110 receives the third input data. The third input data includes compound data and third specified conditions. The compound data is the same as the compound data in Figure 4. The third specified conditions include item selection and sampling information for each group.

[0116] The quantum computing control unit 130 works in conjunction with the quantum computer 300 to execute the actual VQE based on the third input data. Specifically, the quantum computing control unit 130 instructs the quantum computer 300 to perform sampling based on term selection and sampling information for group α. For example, the quantum computing control unit 130 inputs information on the quantum circuit reflecting the term selection results and information on |ψ0> to the quantum computer 300 and causes the quantum circuit to execute. Note that |ψ0> is calculated by the classical computing unit 120. In response to the instructions of the quantum computing control unit 130, the quantum computer 300 samples only the selected terms from each term belonging to group α by simultaneous measurement with a sample size m, and responds the sampling results to the quantum computing control unit 130.

[0117] The quantum computing control unit 130 can calculate the partial Hamiltonian Aα corresponding to each group based on the sampling results from the quantum computer 300, and perform energy calculations corresponding to the Hamiltonian H. Based on these energy calculations, the quantum computing control unit 130 works in cooperation with the quantum computer 300 to optimize the parameter θ in equation (4).

[0118] The output unit 150 outputs the quantum chemical calculation results. The quantum chemical calculation results include, for example, the ground state and the ground state energy based on the optimized parameter θ. Next, we will explain the processing procedure of the quantum computing system 400.

[0119] Figure 6 is a flowchart showing an example of obtaining mean and covariance information. (S10) The data input unit 110 reads the compound data. The data input unit 110 reads the sample size m α The input is accepted. Compound data includes information on Hamiltonian H in formula (2). Also, Hamiltonian H is a partial Hamiltonian A α It is expressed as the sum of m samples. α The input is entered for each group α of terms that can be measured simultaneously. Furthermore, steps S11 to S15 below are executed for each group α.

[0120] (S11) The classical computation unit 120 performs the calculation of the ground state |ψ0> using classical computation. (S12) The quantum computing control unit 130 uses the quantum computer 300 to perform the Pauli matrix product P included in the Hamiltonian H. j and P j P k The expected value of <ψ0|P j |ψ0>,<ψ0|P j P k The measurement of |ψ0> is performed. The quantum computation control unit 130 adds 1 to the number of repetitions of step S12. The initial value of the number of repetitions of step S12 is 0.

[0121] Furthermore, the quantum computing control unit 130 simulates the operation of the quantum computer 300, and determines the expected value <ψ0|P j |ψ0>,<ψ0|P j P k You may also perform the calculation of |ψ0>.

[0122] (S13) The quantum computation control unit 130 determines that the number of repetitions of step S12 is the number of samples m. α Determine whether or not the target has been reached. The number of iterations is the sample size m. α If this is reached, the process proceeds to step S14. The number of iterations is the number of samples m. αIf the condition has not been reached, the process proceeds to step S12.

[0123] (S14) The statistical calculation unit 140 generates mean-covariance information by statistical calculation based on the measurement results of step S12. The mean-covariance information is A α The variance-covariance matrices S and A α It includes the mean vector μ. Mean and covariance information is generated for each group α.

[0124] (S15) The statistical calculation unit 140 outputs mean-covariance information. Then, the acquisition of mean-covariance information is completed. The mean-covariance information is input to the classical computer 200. Figure 7 is a flowchart showing an example of term selection and sample size calculation. Steps S20 to S24 are performed for each group α.

[0125] (S20) The data input unit 210 obtains the mean vector μ and the variance-covariance matrix S based on the variance-covariance information. (S21) The optimization calculation unit 220 generates an integer quadratic programming problem based on the mean vector μ and the variance-covariance matrix S. The integer quadratic programming problem is expressed by equation (24).

[0126] (S22) The optimization calculation unit 220 solves the integer quadratic programming problem. The optimization calculation unit 220 obtains the term selection result b as the solution result. * and variance value σ A_α 2* To obtain. (S23) The optimization calculation unit 220 calculates the number of samples m based on the solution result. The number of samples m is expressed by equation (25).

[0127] (S24) Output unit 230 outputs item selection result b * The number of samples, m, is then output. The selection of terms and the calculation of the number of samples are then completed. Note: Item selection result b *The number of samples m is output as term selection and sampling information. The term selection and sampling information is output for each group α. For example, the output unit 230 can input the term selection and sampling information corresponding to each α into the classical computer 100, thereby allowing the actual VQE to be executed based on that term selection and sampling information. Next, an example of executing the actual VQE will be explained.

[0128] Figure 8 is a flowchart showing an example of VQE execution. (S30) The data input unit 110 receives the term selection result b for each partial Hamiltonian. * The specified conditions, including the number of samples m, are obtained. The data input unit 110 also obtains the compound data from step S10.

[0129] (S31) The quantum computing control unit 130 works in conjunction with the quantum computer 300 to perform the actual VQE by sampling based on specified conditions. The sampling is performed using the partial Hamiltonian A α Item selection result b from each item * The procedure is performed for each term specified by the method, for a sample size of m. Based on the results of this sampling, A α A is calculated. α The energy is calculated by taking the sum of the values. The quantum computing control unit 130 obtains the ground state and ground energy as the VQE execution result.

[0130] (S32) The output unit 150 outputs the VQE execution result. Then the VQE execution is completed. Thus, by solving the optimization problem in equation (24), the classical computer 200 can simultaneously select terms in the Hamiltonian and estimate the number of samples. The number of samples m in equation (25) is an appropriate value that takes into account the covariance between each term in the partial Hamiltonian.

[0131] In this way, the classical computer 200 can appropriately select the terms to be measured simultaneously and determine the number of samples. Based on the selection of the terms and the determined number of samples, the classical computer 200 can cause the quantum computing system 400 to perform VQE. By narrowing down the terms to be actually measured from among multiple terms that can be measured simultaneously, the classical computer 200 can reduce the number of terms to be measured by the quantum computer 300, thereby improving the efficiency of the VQE calculation. By optimizing the number of samples, the classical computer 200 can appropriately balance the trade-off between error and calculation speed.

[0132] As explained above, the classical computer 200 performs the following processes. The data input unit 210 obtains first information about multiple terms included in the Hamiltonian corresponding to the problem to be solved by the variational quantum eigenvalue method, which can be simultaneously measured by the quantum computer. The first information shows the variance for each term and the covariance for each pair of terms when simultaneous measurement is performed. The optimization calculation unit 220 generates an optimization problem based on the first information. The optimization problem is to minimize the sum of the variance for each term and the covariance for each pair of terms, based on the constraint that the change in the mean value of the sum of the multiple terms must be less than or equal to a predetermined value, for the selection of terms to be simultaneously measured from among the multiple terms. By solving the optimization problem, the optimization calculation unit 220 determines multiple first terms from among the multiple terms that will be simultaneously measured by the quantum computer 300. The optimization calculation unit 220 calculates the number of samples for simultaneous measurement based on the minimized sum.

[0133] This allows the classical computer 200 to appropriately select the terms to be measured simultaneously and determine the number of samples. The variance-covariance matrix S is an example of first information. The optimization problem can be expressed, for example, by equation (24). Variance value σ A_α 2* This corresponds to the sum of the term-specific variances and pairwise covariances across multiple terms.

[0134] The optimization calculation unit 220 calculates the number of samples by dividing the minimized sum by the square of the tolerance error. This allows the classical computer 200 to appropriately determine the number of samples. The number of samples is calculated using equation (25).

[0135] The output unit 230 may input multiple first terms and the number of samples determined to be the targets of simultaneous measurement to the quantum computer 300. The output unit 230 may cause the quantum computer 300 to perform simultaneous measurements on multiple first terms based on the number of samples. This allows the classical computer 200 to perform quantum computation of VQE more efficiently. Furthermore, the classical computer 200 can improve the accuracy of the calculation results obtained by VQE by optimizing the number of samples and the selection of terms.

[0136] The Hamiltonian H may contain multiple groups of terms that can be measured simultaneously. The optimization calculation unit 220 can determine the number of first terms to be measured simultaneously and calculate the number of samples for each group by generating and solving an optimization problem. This allows the classical computer 200 to appropriately select the terms to be measured simultaneously and determine the number of samples for each group included in the Hamiltonian H.

[0137] The information processing in the first embodiment can be achieved by having the processing unit 12 execute a program. The information processing in the second embodiment can be achieved by having the processor 101 execute a program. The program can be recorded on a computer-readable recording medium 113.

[0138] For example, a program can be distributed by distributing a recording medium 113 on which the program is stored. Alternatively, the program may be stored on another computer and distributed via a network. A computer may, for example, store (install) a program stored on the recording medium 113 or a program received from another computer into a storage device such as RAM 102 or HDD 103, and then read and execute the program from that storage device. [Explanation of symbols]

[0139] 10 Information Processing Devices 11 Storage section 12 Processing Units 13 First information

Claims

1. For a plurality of terms included in the Hamiltonian corresponding to a problem to be solved by variational quantum eigenvalue method, and for a plurality of terms that can be simultaneously measured by a quantum computer, first information is obtained showing the variance for each term and the covariance for each pair of terms when the simultaneous measurement is performed. Based on the constraint that the change in the mean of the sum of the aforementioned multiple terms is less than or equal to a predetermined value, an optimization problem is generated based on the first information to minimize the sum of the variances of each term and the covariances of each pair in the aforementioned multiple terms. By solving the optimization problem, a plurality of first terms to be targeted for simultaneous measurement by the quantum computer are determined from among the plurality of terms, and the number of samples for the simultaneous measurement is calculated based on the minimized sum. A quantum computing support program that allows a computer to perform a process.

2. In calculating the sample size, the sample size is calculated by dividing the minimized sum by the square of the tolerance error. The quantum computing support program according to claim 1.

3. The plurality of first terms and the number of samples determined to be the targets of the simultaneous measurement are input to the quantum computer, and the quantum computer is made to perform the simultaneous measurement on the plurality of first terms based on the number of samples. The quantum computing support program according to claim 1.

4. The Hamiltonian includes multiple groups of the multiple terms that can be measured simultaneously, For each group, the determination of the plurality of first terms to be measured simultaneously and the calculation of the sample size are performed. The quantum computing support program according to claim 1.

5. Computers For a plurality of terms included in the Hamiltonian corresponding to a problem to be solved by variational quantum eigenvalue method, and for a plurality of terms that can be simultaneously measured by a quantum computer, first information is obtained showing the variance for each term and the covariance for each pair of terms when the simultaneous measurement is performed. Based on the constraint that the change in the mean of the sum of the aforementioned multiple terms is less than or equal to a predetermined value, an optimization problem is generated based on the first information to minimize the sum of the variances of each term and the covariances of each pair in the aforementioned multiple terms. By solving the optimization problem, a plurality of first terms to be targeted for simultaneous measurement by the quantum computer are determined from among the plurality of terms, and the number of samples for the simultaneous measurement is calculated based on the minimized sum. Quantum computing support method.

6. A storage unit stores first information indicating the variance for each term and the covariance for each pair of terms when the simultaneous measurement is performed for a plurality of terms included in the Hamiltonian corresponding to a problem to be solved by variational quantum eigenvalue method, which can be simultaneously measured by a quantum computer. A processing unit generates an optimization problem based on first information to minimize the sum of the variances for each term and the covariances for each pair in the plurality of terms, based on the constraint that the change in the mean of the sum of the plurality of terms is less than or equal to a predetermined value, solves the optimization problem to determine a plurality of first terms from the plurality of terms that will be the target of the simultaneous measurement by the quantum computer, and calculates the number of samples for the simultaneous measurement based on the minimized sum, An information processing device having

Images