Quantum chemistry calculation program, quantum chemistry calculation method, and information processing device

Abstract

To attain efficient calculation of VQE.SOLUTION: An information processing device 10 repeats update processing of a value of a coefficient in a third expression and exploration processing of a ground state of a multi-electron system. The third expression is an expression obtained by adding a term obtained by multiplying a coefficient to a second expression related to the number of electrons in the multi-electron system, to a first expression which calculates physical quantity of the multi-electron system. The exploration processing is the exploration processing in a variational quantum characteristic value solver method which explores the ground state of the multi-electron system by changing a quantum state of the multi-electron system so that an expectation value of the third expression according to the quantum state of the multi-electron system lowers. The information processing device 10, in k+1-th exploration processing, sets an end state of the multi-electron system in any of first to k-th exploration processing, as an initial state of the multi-electron system in the k+1-th exploration processing, and changes the quantum state of the multi-electron system so that the expectation value of the third expression lowers, from the initial state.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] The present invention relates to a quantum chemical calculation program, a quantum chemical calculation method, and an information processing device. [Background technology]

[0002] One of the quantum chemical calculations using a quantum computer is a calculation method called the Variational Quantum Eigensolver (VQE). VQE is a method for calculating the eigenvalues ​​(e.g., minimum energy eigenvalues) and eigenstates of physical quantities in quantum mechanical multi-electron systems. In VQE, the energy expectation value (minimum energy eigenvalue) of the ground state of a molecule is calculated, for example, using the following procedure. 1. Under control of a classical computer, a trial state "|ψ(θ)>" in a quantum mechanical multi-electron system is generated within the quantum computer (θ is a real parameter). 2. The quantum computer calculates the expectation value of the energy of the trial state, "<ψ(θ)|H|ψ(θ)>" (H is the Hamiltonian). 3. Based on the calculation result of the energy expectation value, the classical computer updates the value of the parameter θ so as to reduce the expected value "<ψ(θ)|H|ψ(θ)>".

[0003] The classical and quantum computers work together to repeat the above process until the expected value of the energy, <ψ(θ)|H|ψ(θ)>, converges. This allows us to find an approximate minimum energy value and its state.

[0004] The functional form of the trial state "|ψ(θ)>" is selected to be computationally efficient on a quantum computer. Depending on the functional form selected, a state that deviates from the expected conditions (for example, a state with an incorrect number of electrons) may be obtained. In such cases, a VQE calculation is performed to find the state that minimizes the expectation value of H(μ), for example, using the formula "H(μ):=H+μC" (μ is a coefficient, C is the number of electrons in the H state), which adds a penalty term to the operator (Hamiltonian H) that obtains the energy.

[0005] For example, a hybrid algorithm for solving discrete quadratic models has been proposed as a computational approach using penalty terms on quantum computers. A method for transforming cost functions in quantum approximate optimization has also been proposed. Techniques have also been proposed to improve systems for handling inequality constraints in mixed binary optimization problems on quantum computers, significantly improving system performance. Furthermore, a system has been proposed that facilitates quantum-enhanced feature generation optimization. [Prior art documents] [Patent documents]

[0006] [Patent Document 1] Special Publication No. 2023-507139 [Patent Document 2] Special Publication No. 2021-504805 [Patent Document 3] U.S. Patent Application Publication No. 2021 / 0216897 [Patent Document 4] US Patent Application Publication No. 2023 / 0143072 Summary of the Invention [Problem to be solved by the invention]

[0007] In VQE calculations using functions that include penalty terms, the VQE calculation is repeatedly performed while updating the coefficient value of the penalty term. Therefore, repeated VQE calculations increase the calculation time required to determine the energy basis value.

[0008] In one aspect, the present invention aims to improve the efficiency of VQE calculations. [Means for solving the problem]

[0009] In one proposal, the following quantum chemistry calculation program is provided. The computer alternately repeats a process of updating the value of a coefficient in a third equation obtained by adding a term obtained by multiplying a coefficient in a second equation related to the number of electrons in the multi-electron system to a first equation that calculates a physical quantity of the multi-electron system, and a search process using a variational quantum eigenvalue solver method that searches for the ground state of the multi-electron system by changing the quantum state of the multi-electron system so that the expected value of the third equation according to the quantum state of the multi-electron system decreases. Then, in the (k+1)th search process (k is a natural number), the computer sets the final state of the multi-electron system in any of the 1st to kth search processes as the initial state of the multi-electron system in the (k+1)th search process, and changes the quantum state of the multi-electron system from the initial state so that the expected value of the third equation decreases. [Effects of the Invention]

[0010] According to one aspect, the efficiency of VQE calculation can be improved. [Brief explanation of the drawings]

[0011] [Figure 1] FIG. 1 is a diagram illustrating an example of a quantum chemical calculation method according to a first embodiment. [Figure 2] FIG. 1 is a diagram illustrating an example of the configuration of a quantum computing system. [Figure 3] FIG. 1 is a diagram illustrating an example of hardware of a device that constitutes a quantum computing system. [Figure 4] FIG. 10 is a diagram illustrating an example of a procedure for calculating VQE using an equation to which a penalty term including a coefficient μ is added. [Figure 5] FIG. 1 is a block diagram showing an example of the functionality of a classical computer for performing quantum chemical calculations. [Figure 6] FIG. 10 is a diagram illustrating an example of a method for adjusting a coefficient μ of a penalty term. [Figure 7] 1 is a flowchart showing an example of a procedure for quantum chemistry calculation processing by VQE. [Figure 8] FIG. 10 is a diagram illustrating an example in which the conversion of the coefficient μ using Newton's method is not monotonic. [Figure 9] FIG. 10 is a diagram illustrating an example of a method for determining an initial value of a parameter θ for the next VQE calculation from the results of multiple past VQE calculations. [Figure 10] 11 is a flowchart showing an example of a procedure for quantum chemistry calculation processing by VQE according to the third embodiment. DETAILED DESCRIPTION OF THE INVENTION

[0012] The present embodiment will be described below with reference to the drawings. Note that each embodiment can be implemented in combination with a plurality of other embodiments within a range that does not contradict each other. [First embodiment] The first embodiment is a quantum chemical calculation method for improving the efficiency of VQE calculations.

[0013] Fig. 1 is a diagram showing an example of a quantum chemistry calculation method according to a first embodiment. Fig. 1 shows an information processing device 10 that performs the quantum chemistry calculation method. The information processing device 10 performs quantum chemistry calculation in cooperation with a quantum computer 1. The information processing device 10 can perform the quantum chemistry calculation method by, for example, executing a quantum chemistry calculation program.

[0014] The information processing device 10 includes a storage unit 11 and a processing unit 12. The storage unit 11 is, for example, a memory or a storage device included in the information processing device 10. The processing unit 12 is, for example, a processor or an arithmetic circuit included in the information processing device 10.

[0015] The storage unit 11 stores, for example, a quantum chemistry calculation program, information about a multi-electron system to be solved, and the like. The processing unit 12 determines the ground state (the state where the energy is minimum) of the many-electron system by VQE. For example, the processing unit 12 defines a third equation "H(μ)=H+μ(C)" (the H on the left side is marked with a ^) by adding a term obtained by multiplying a second equation "C" related to the number of electrons in the many-electron system by a coefficient "μ" to a first equation for calculating the physical quantity of the many-electron system. The term obtained by multiplying a coefficient to the second equation related to the number of electrons in the many-electron system is, for example, a penalty term for preventing the number of electrons included in the quantum state of the many-electron system during the calculation process from deviating significantly from the correct number of electrons.

[0016] The quantum state of a multi-electron system is expressed as |Ψ(θ)>. This quantum state changes depending on the value of the parameter θ. The parameter θ is, for example, vector data containing multiple real-valued values ​​as elements.

[0017] The processing unit 12 alternately repeats the process of updating the coefficient values ​​in the third equation and the search for the ground state of the many-electron system by VQE using the third equation. In the process of updating the coefficient values, the processing unit 12 updates the coefficient values ​​so that, for example, the number of electrons included in the quantum state of the many-electron system approaches the correct number of electrons.

[0018] In the process of searching for the ground state of the multi-electron system, the processing unit 12 changes the quantum state of the multi-electron system so that the expected value of the third equation corresponding to the quantum state of the multi-electron system decreases. For example, the processing unit 12 calculates the expected value "<Ψ(θ)|H|Ψ(θ)>" (H is marked with a ^) of the third equation corresponding to the quantum state of the multi-electron system, and optimizes the value of the parameter θ so that the expected value decreases. Then, the processing unit 12 obtains the quantum state of the multi-electron system when the expected value converges as the final state.

[0019] In the (k+1)th (k is a natural number) search process for the ground state of the multi-electron system, the processing unit 12 sets the final state of the multi-electron system in any of the first to k-th search processes for the ground state of the multi-electron system as the initial state of the multi-electron system in the (k+1)th search process. Then, the processing unit 12 changes the quantum state of the multi-electron system from the initial state so that the expected value of the third equation decreases.

[0020] The processing unit 12 changes the quantum state of the multi-electron system, for example, by allowing fluctuations in the number of electrons in the multi-electron system.The processing unit 12 then determines the final state of the multi-electron system when the number of electrons in the multi-electron system in the final state satisfies a predetermined requirement as the ground state of the multi-electron system.The predetermined requirement is, for example, a requirement that the difference between the number of electrons in the final state of the multi-electron system and the number of electrons that should originally be included in the multi-electron system be within an allowable range indicated by a threshold value.

[0021] For example, the processing unit 12 first sets a predetermined real value to the coefficient μ as the initial value "μ1." In the first VQE calculation, the processing unit 12 sets a predetermined value to the parameter θ as the initial value. For example, the processing unit 12 sets the parameter θ to the initial value "0" (the values ​​of all elements included in the parameter θ are "0").

[0022] The processing unit 12 optimizes the value of the parameter θ so that the expected value "<Ψ(θ)|H(μ1)|Ψ(θ)>" (H is followed by a ^) of the third equation corresponding to the quantum state of the multi-electron system decreases. When the value of the parameter θ becomes "θ1", the expected value is considered to have converged. The quantum state "|Ψ(θ1)>" of the multi-electron system when the expected value has converged is the final state in the first VQE. The number of electrons in the quantum state "|Ψ(θ1)>" of the multi-electron system that has become the final state may be significantly different from the correct number of electrons of the multi-electron system.

[0023] If the number of electrons in the final state "|Ψ(θ1)>" of the multi-electron system in the first VQE satisfies a predetermined requirement, the processing unit 12 determines that the final state "|Ψ(θ1)>" is the ground state of the multi-electron system. If the number of electrons in the final state "|Ψ(θ1)>" of the multi-electron system in the first VQE does not satisfy the predetermined requirement, the processing unit 12 updates the value of the coefficient μ (μ = μ2). Thereafter, the search for the ground state by VQE and the update of the coefficient μ are repeated until the predetermined requirement regarding the number of electrons is satisfied.

[0024] In the VQE calculation, the final state of the previous VQE calculation is used as the initial state of the multi-electron system. The quantum state of the multi-electron system is specified by the value of the parameter θ.

[0025] For example, the initial state of the multi-electron system in the k+1th VQE calculation is the final state of the multi-electron system in the kth VQE calculation, |Ψ(θ k )>" is applied. In other words, the initial value of the parameter θ in the (k+1)th VQE is "θ k In the k-th VQE calculation, the processing unit 12 calculates the initial state of the multi-electron system |Ψ(θ k )>”, we obtain the expectation value 〈Ψ(θ)|H(μ k+1 Optimize θ so that )|Ψ(θ)> (H is marked with a ^) decreases.

[0026] In such quantum chemical calculations, the quantum state obtained as a result of the kth VQE is used as the initial state for the k+1th VQE. This allows the expectation value to converge efficiently in the VQE calculation. As a result, the calculation efficiency of the entire quantum system calculation process using VQE is improved. In other words, if the update width of the penalty term coefficient μ is small each time, the quantum state that minimizes the expectation value of "H(μ)" (H with a ^) is thought to not change significantly. Therefore, if the final state of the kth VQE calculation is used as the initial state for the k+1th VQE calculation, the final state will be reached in the k+1th VQE calculation with few changes from the initial state. This reduces the processing time for the k+1th VQE.

[0027] The process of using the final state of the kth VQE as the initial state of the k+1th VQE is particularly effective when the value of the coefficient μ changes monotonically. If the value of the coefficient μ does not change monotonically, it may be more efficient to use the final state of a VQE calculation other than the immediately preceding VQE calculation.

[0028] Therefore, the processing unit 12 can also determine an appropriate quantum state as the initial state for the k+1th VQE calculation based on the difference between the value of the coefficient μ applied to each of the first to kth VQE calculations and the value of μ for the k+1th VQE calculation.

[0029] For example, the processing unit 12 selects one of the values ​​of the coefficient μ applied to the first through k-th VQE calculations based on the difference between each value of the coefficient μ of "H(μ)" (H is followed by a ^) used in the first through k-th VQE calculations and the value of the coefficient μ used in the (k+1)-th VQE calculation. For example, the processing unit 12 selects the value that has the smallest difference from the value of the coefficient μ used in the (k+1)-th VQE calculation. The processing unit 12 sets the final state of the multi-electron system in the VQE performed using "H(μ)" (H is followed by a ^) with the selected value as the coefficient value as the initial state of the multi-electron system in the (k+1)-th VQE.

[0030] This allows each VQE calculation to search for the ground state from an appropriate initial state of the multi-electron system, even if the value of the coefficient μ does not change monotonically, making the VQE calculation process more efficient.

[0031] Second Embodiment The second embodiment is a quantum computing system in which, when repeating VQE calculations while updating the coefficients of the penalty terms, the state obtained as a result of the previous VQE calculation is set as the initial value of the quantum bit state for each VQE calculation.

[0032] 2 is a diagram showing an example of the configuration of a quantum computing system. The quantum computing system 300 is a computer system that uses quantum devices. The quantum computing system 300 includes a classical computer 100 and a quantum computer 200. A terminal device 400 is connected to the classical computer 100 via a network 20. The terminal device 400 is a computer used by a user who requests quantum computing by the quantum computing system 300. The classical computer 100 receives information about a multi-electron system (e.g., a molecule) to be solved from the terminal device 400.

[0033] Based on the information about the multi-electron system received from the terminal device 400, the classical computer 100 generates a quantum circuit that calculates the expected energy value of the ground state of the multi-electron system. The quantum circuit indicates the order of operations on quantum bits by arranging elements such as quantum gates. A quantum bit is a bit that can represent a superposition of a "0" state and a "1" state. The classical computer 100 instructs the quantum computer 200 to perform quantum computation according to the quantum circuit. The classical computer 100 also obtains measurement results for each quantum bit from the quantum computer 200.

[0034] The quantum computer 200 has a plurality of quantum bits and devices for manipulating each of the plurality of quantum bits. The plurality of quantum bits of the quantum computer 200 can be realized by, for example, a superconducting system, an ion trap system, a diamond spin system, a cold atom system (sometimes called a neutral atom system), or the like.

[0035] FIG. 3 is a diagram showing an example of hardware of a device that constitutes a quantum computing system. A classical computer 100 is entirely controlled by a processor 101. A memory 102 and multiple peripheral devices are connected to the processor 101 via a bus 109. The processor 101 may be a multiprocessor. The processor 101 is, for example, a CPU (Central Processing Unit), an MPU (Micro Processing Unit), or a DSP (Digital Signal Processor). At least some of the functions realized by the processor 101 executing a program may be realized by an electronic circuit such as an ASIC (Application Specific Integrated Circuit) or a PLD (Programmable Logic Device).

[0036] The memory 102 is used as a main storage device of the classical computer 100. The memory 102 temporarily stores at least a portion of the OS (Operating System) program and application programs to be executed by the processor 101. The memory 102 also stores various data used in processing by the processor 101. As the memory 102, for example, a volatile semiconductor storage device such as a RAM (Random Access Memory) is used.

[0037] The peripheral devices connected to the bus 109 include a storage device 103, a GPU (Graphics Processing Unit) 104, an input interface 105, an optical drive device 106, a device connection interface 107, and network interfaces 108a and 108b.

[0038] The storage device 103 writes and reads data electrically or magnetically to and from a 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. Note that the storage device 103 may be, for example, an HDD (Hard Disk Drive) or an SSD (Solid State Drive).

[0039] The GPU 104 is an arithmetic unit that performs image processing. The GPU 104 is an example of a graphics controller. The GPU 104 is connected to a monitor 21. The GPU 104 displays an image on the screen of the monitor 21 in accordance with an instruction from the processor 101. The monitor 21 may be a display device using organic EL (Electro Luminescence) or a liquid crystal display device.

[0040] The input interface 105 is connected to a keyboard 22 and a mouse 23. The input interface 105 transmits signals sent from the keyboard 22 and the mouse 23 to the processor 101. The mouse 23 is an example of a pointing device, and other pointing devices can also be used. Examples of other pointing devices include a touch panel, a tablet, a touch pad, and a trackball.

[0041] The optical drive device 106 uses a laser beam or the like to read data recorded on an optical disc 24 or write data to the optical disc 24. The optical disc 24 is a portable recording medium on which data is recorded so that it can be read by reflected light. The optical disc 24 includes a DVD (Digital Versatile Disc), a DVD-RAM, a CD-ROM (Compact Disc Read Only Memory), a CD-R (Recordable) / RW (Rewritable), and the like.

[0042] The device connection interface 107 is a communication interface for connecting peripheral devices to the classical computer 100. For example, a memory device 25 or a memory reader / writer 26 can be connected to the device connection interface 107. The memory device 25 is a recording medium equipped with a function for communicating with the device connection interface 107. The memory reader / writer 26 is a device for writing data to the memory card 27 or reading data from the memory card 27. The memory card 27 is a card-type recording medium.

[0043] The network interface 108a is connected to the network 20. The network interface 108a transmits and receives data to and from other computers or communication devices via the network 20. The network interface 108a is a wired communication interface connected by a cable to a wired communication device such as a switch or a router. The network interface 108a may also be a wireless communication interface connected by radio waves to a wireless communication device such as a base station or an access point.

[0044] The network interface 108b is an interface for connecting to the quantum computer 200. The processor 101 transmits a quantum circuit to the quantum computer 200 via the network interface 108b and causes the quantum computer 200 to execute a quantum computation. The processor 101 also obtains the result of the quantum computation via the network interface 108b.

[0045] The classical computer 100 can realize the processing functions of the second embodiment by using the hardware described above. Note that the information processing device 10 shown in the first embodiment can also be realized by using hardware similar to that of the classical computer 100 shown in FIG.

[0046] The classical computer 100 realizes 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 the classical computer 100 can be recorded on various recording media. For example, the program to be executed by the classical computer 100 can be stored in a storage device 103. The processor 101 loads at least a portion of the program in the storage device 103 into the memory 102 and executes the program. The program to be executed by the classical computer 100 can also be recorded on a portable recording medium such as an optical disk 24, a memory device 25, or a memory card 27. The program stored on the portable recording medium becomes executable after being installed on the storage device 103, for example, under the control of the processor 101. The processor 101 can also read and execute the program directly from the portable recording medium.

[0047] Quantum computer 200 includes control device 201 and quantum device 202. Control device 201 executes gate operations on quantum bits in quantum device 202 according to a quantum circuit. Quantum device 202 includes multiple quantum bits. Quantum device 202 is, for example, one or multiple quantum processing units (QPUs).

[0048] Quantum chemical calculations using VQE are efficiently performed by the above-described quantum computing system 300. Quantum chemical calculations include, for example, calculations of the ground state of a multi-electron system. For example, consider a multi-electron system where the number of electrons present in the system is m (m is a natural number). The quantum state of the multi-electron system can be expressed as follows:

[0049] The classical computer 100 first approximately solves the Schrödinger equation to obtain the states that a single electron can take. Although there can be an infinite number of single-electron states obtained as solutions, here we limit the number to a finite number (n: n is a natural number) for the convenience of numerical calculations.

[0050] According to the Pauli exclusion principle, multiple electrons cannot occupy the same single-electron state. The state of a multi-electron system is determined by specifying which m of n single-electron states (e.g., molecular orbitals) are occupied by electrons. Therefore, the classical computer 100 prepares n quantum bits for use in VQE on the quantum computer 200, corresponding to the n single-electron states.

[0051] If the state of the i-th qubit (i is a natural number) is |0>, then that state indicates that the i-th single-electron state is not occupied by an electron. If the state of the i-th qubit is |1>, then that state indicates that the i-th single-electron state is occupied by an electron.

[0052] The approximate lowest energy state is a state in which the m lowest energy single-electron states among the n single-electron states are occupied by an electron. This state is called a Hartree-Fock state, and is expressed on the quantum computer 200 as follows: |ψ Hartree-Fock >=|1···1100···0> The sequence on the right side of the Hartree-Fock state is the quantum bit states corresponding to each of the n single-electron states, arranged from left to right in ascending order of quantum bit number. The smaller the quantum bit number, the lower the energy single-electron state associated with each quantum bit. In the Hartree-Fock state, the m quantum bits with the smallest quantum bit numbers are in |1> states, and the remaining nm quantum bits are in |0> states.

[0053] The Hartree-Fock state represents a state in which m electrons are arranged in order from the lowest energy single-electron state. Because the Hartree-Fock state has m electrons in low energy states, it can be considered that the overall state represents an approximate lowest energy state.

[0054] On the other hand, there are states that are not considered in the Hartree-Fock approximation. In quantum mechanics, superposition states exist, so states such as the one below also exist. |ψ1>=c0|1···1100···0>+c1|1···1010···0>+c2|1···0011···0> c0, c1, and c2 are real constants. To find the exact lowest energy state, we search the state space including all superposition states.

[0055] The quantum computing system 300 assumes the following subspace in the quantum state space of a multi-electron system, making it easy to search for the lowest energy state. First, the quantum computing system 300 assumes the following annihilation operator a i , generation operator a i + Define a i |···1····>=|···0···>,a i | 0 >= 0 a i + |···0····>=|···1···>,a i + | 1 >= 0 a i changes the state where the value of the i-th quantum bit is |1> to |0>. a i + changes the state where the value of the i-th quantum bit is |0> to the state |1>.

[0056] Consider the following state, where a creation or annihilation operator acts on a Hartree-Fock state. |Ψ(θ)>=exp(iΣ k,p θ k,p a p + a k +iΣ k,l,p,q θ k,l,p,q a q + a p + a l a k )|ψHartree-Fock > a p + a k represents a single-electron excitation that changes an electron occupying the k-th single-electron state to the p-th single-electron state. q + a p + a l a k represents a dielectronic excitation in which an electron occupying the kth single-electron state and an electron occupying the lth single-electron state change to the pth single-electron state and the qth single-electron state.

[0057] The method of limiting the quantum state of a multi-electron system to the quantum state expressed by the above "|Ψ(θ)>" is called UCCSDansatz. In the quantum computer 200, a qubit state corresponding to a Hartree-Fock state is first prepared, and then annihilation operators a i , generation operator a i + The gate operation of the quantum gate corresponding to is performed.

[0058] In the case of UCCSDansatz, the number of quantum gates executed by the quantum computer 200 becomes large, making it difficult to realize quantum circuit calculations in many cases. Therefore, various other ansatzes have been proposed to enable realization with fewer quantum gates. For example, in UCCSDansatz, the number of electrons in the system remains constant even when the value of the parameter θ is changed, but in order to prioritize reducing the number of quantum gates, an ansatz that does not preserve the number of electrons in the system has also been devised.

[0059] Therefore, the quantum computing system 300 uses an equation that allows for a state in which the number of electrons is not conserved as the functional form of the trial state "|ψ(θ)>" that is computationally efficient. For example, the quantum computing system 300 repeatedly performs a VQE calculation to find a state that minimizes the expected value of the equation "H(μ)" (H is followed by a ^) to which a penalty term including a coefficient μ is added, while updating the value of μ.

[0060] 4 is a diagram showing an example of a VQE calculation procedure using an equation to which a penalty term including a coefficient μ is added. For example, when the classical computer 100 receives a calculation request for quantum computation using VQE from the terminal device 400, it decomposes the problem to be solved into multiple Hamiltonians. For each decomposed Hamiltonian, the classical computer 100 generates a quantum circuit parameterized by the parameter θ.

[0061] The classical computer 100 instructs the quantum computer 200 to perform a VQE calculation using the divided quantum circuit. The instruction for the initial VQE calculation includes the values ​​of the coefficients for each divided Hamiltonian, the initial value of the coefficient μ of the penalty term, and the initial value of the parameter θ that indicates the quantum state.

[0062] The quantum computer 200 performs quantum computation using a quantum circuit for VQE computation based on the specified information. The quantum computation yields the expected value "<ψ(θ)|H|ψ(θ)>" (where H is followed by a ^) of the physical quantity + penalty term of the quantum state specified by the parameter θ. The quantum computer 200 transmits the expected value of the physical quantity + penalty term to the classical computer 100. The classical computer 100 then updates the parameter θ so that the expected value of the physical quantity + penalty term decreases, and transmits the updated value of the parameter θ to the quantum computer 200.

[0063] In one VQE calculation, quantum computation is repeatedly performed while updating the value of the parameter θ. The classical computer 100 ends the first VQE calculation when the expected value of the physical quantity+penalty term obtained as the quantum computation result converges.

[0064] Each time a VQE calculation is completed, the classical computer 100 updates the value of the coefficient μ of the penalty term so that the number of electrons in the final state of the VQE calculation is the correct number of electrons for the multi-electron system. Then, the classical computer 100 transmits the initial value of the parameter θ for the next VQE calculation and the updated value of the penalty term μ to the quantum computer 200, and starts the next VQE calculation. At this time, the classical computer 100 sets the value of the parameter θ, which indicates the state of each quantum bit in the previous VQE calculation, as the initial value of the parameter θ for the next VQE calculation.

[0065] In this way, the VQE calculation is repeatedly performed by the classical computer 100 and the quantum computer 200 while updating the value of the coefficient μ. Then, the classical computer 100 ends the repetition of the VQE calculation if the number of electrons is correct when the expected value of the physical quantity+penalty term calculated by VQE converges. The classical computer 100 outputs, as the calculation result, the value of the parameter θ that minimizes the expected value of the physical quantity+penalty term when the repetition of the VQE calculation ends.

[0066] 5 is a block diagram showing an example of the functions of a classical computer for performing quantum chemical calculations. The classical computer 100 includes a quantum calculation manager 110, a penalty term coefficient adjuster 120, and a VQE execution unit 130 to perform the quantum chemical calculations.

[0067] The quantum computing management unit 110 receives a VQE calculation request from, for example, the terminal device 400. The quantum computing management unit 110 transmits information on the multi-electron system to be solved, which is indicated in the calculation request, to the penalty term coefficient adjustment unit 120. The quantum computing management unit 110 also acquires the VQE result from the penalty term coefficient adjustment unit 120 and transmits the calculation result to the terminal device 400.

[0068] The penalty term coefficient adjustment unit 120 generates a Hamiltonian equation including a penalty term based on information about the multi-electron system to be solved, determines the coefficient of the penalty term, generates a quantum circuit for calculating the solution of the generated equation using VQE, and transmits the generated quantum circuit to the VQE execution unit 130.

[0069] Furthermore, upon receiving the VQE calculation result from the VQE execution unit 130, the penalty term coefficient adjustment unit 120 determines whether the number of electrons indicated in the calculation result is correct, and if so, determines that the quantum chemistry calculation has ended. When the quantum chemistry calculation has ended, the penalty term coefficient adjustment unit 120 transmits the energy expectation value as the calculation result to the quantum calculation management unit 110. If there is an error in the number of electrons, the penalty term coefficient adjustment unit 120 updates the coefficient of the penalty term and instructs the VQE execution unit 130 to perform the VQE calculation applying the updated coefficient.

[0070] When the VQE execution unit 130 acquires a quantum circuit for VQE calculation, it executes VQE based on the acquired quantum circuit in cooperation with the quantum computer 200. Furthermore, when the value of the coefficient of the penalty term is updated, the VQE execution unit 130 executes VQE applying the updated coefficient in cooperation with the quantum computer 200. To execute VQE, the VQE execution unit 130 has a parameter update unit 131 that optimizes a parameter θ used in VQE.

[0071] For example, the VQE execution unit 130 first specifies an initial value for the parameter θ and instructs the quantum computer 200 to execute the quantum circuit using the parameter θ. The VQE execution unit 130 obtains an energy expectation value as the execution result of the quantum circuit. Upon obtaining the energy expectation value, the parameter update unit 131 updates the parameter θ so as to decrease the energy expectation value. The VQE execution unit 130 instructs the quantum computer 200 to execute the quantum circuit using the updated parameter θ.

[0072] The VQE execution unit 130 repeats updating the parameter θ and executing the quantum circuit with the updated parameter θ until the VQE calculation result (e.g., the energy expectation value) converges. When the energy expectation value converges, the VQE execution unit 130 transmits the value of the parameter θ, which indicates the state at that time, to the penalty term coefficient adjustment unit 120 as the VQE calculation result.

[0073] The quantum computer 200 has an energy expectation calculation unit 210. The energy expectation calculation unit 210 performs gate operations on the quantum bits based on the quantum circuit input from the classical computer 100, and measures the final state of the quantum bits. The energy expectation calculation unit 210 then calculates the expectation value of the physical quantity + penalty term from the measurement result, and transmits it to the classical computer 100. Note that the process of calculating the expectation value of the physical quantity + penalty term from the measurement result may be performed by the VQE execution unit 130 of the classical computer 100.

[0074] The functions of the elements in the classical computer 100 shown in FIG. 5 can be realized, for example, by having the processor 101 execute a program module corresponding to the element.

[0075] Next, we will explain how to update the coefficient of the penalty term. The Hamiltonian (physical quantity + penalty term) H(μ) (H has a ^) with the penalty term added is expressed by the following equation (1).

[0076]

number

[0077] The third term (last term) on the right side of equation (1) is the penalty term. The penalty term is the operator (Σ p =1 N a p + a p ) multiplied by the coefficient μ. The penalty term coefficient adjustment unit 120 adjusts the coefficient μ of the penalty term using, for example, a function for determining the error in the number of electrons.

[0078] 6 is a diagram showing an example of a method for adjusting the coefficient μ of the penalty term. To adjust the coefficient μ of the penalty term, the penalty term coefficient adjustment unit 120 defines a function f(μ) that executes the processing shown in the function processing content 31. The processing executed according to the function f(μ) is as follows: [Process 1] Obtain the quantum state that minimizes the expectation value of H(μ) (H is followed by ^) using VQE. [Process 2] The process of outputting the number of electrons in the electronic state obtained by VQE - the correct number of electrons as the return value. The penalty term coefficient adjustment unit 120 uses the return value of the function f(μ) to search for μ that satisfies f(μ)=0 using, for example, the Newton method.

[0079] Graphs 32 to 34 show examples of updating the value of μ according to the function f(μ). The horizontal axis of graphs 32 to 34 shows the value of the coefficient μ, and the vertical axis shows the value f obtained by the function f(μ). For example, the penalty term coefficient adjustment unit 120 first sets the coefficient μ to an initial value μ0 and executes the function f(μ). In the first iteration (iteration: 1), the penalty term coefficient adjustment unit 120 finds the intersection between the tangent line that touches the curve representing the function f(μ) at the position μ=μ0 and the line at f=0. The penalty term coefficient adjustment unit 120 sets the value of μ at the found intersection as the updated value μ1 of the coefficient μ.

[0080] Next, the penalty term coefficient adjustment unit 120 sets the coefficient μ to the updated value μ1 and executes the function f(μ). In the second iteration (iteration: 2), the penalty term coefficient adjustment unit 120 finds the intersection between the tangent line that touches the curve representing the function f(μ) at the position μ=μ1 and the line where f=0. The penalty term coefficient adjustment unit 120 sets the value of μ at the found intersection as the updated coefficient value μ2.

[0081] In this way, the penalty term coefficient adjustment unit 120 updates the value of the coefficient μ, so that the value obtained by the function f(μ) approaches "0" (no error). Finally, an appropriate value of the coefficient μ of the penalty term is obtained.

[0082] Next, the procedure for quantum chemical calculation processing using VQE will be described in detail. 7 is a flowchart showing an example of the procedure for quantum chemistry calculation processing using VQE. The processing shown in FIG. 7 will be explained below in order of step number.

[0083] [Step S101] The penalty term coefficient adjustment unit 120 sets an initial value for the coefficient μ of the penalty term. [Step S102] The penalty term coefficient adjustment unit 120 generates an equation "H(μ)" (H is marked with a ^) by adding a penalty term to an equation for obtaining the expected value of a physical quantity (e.g., energy). The penalty term coefficient adjustment unit 120 then executes the function f(μ) shown in FIG. 6. When the penalty term coefficient adjustment unit 120 starts executing the function f(μ), it first instructs the VQE execution unit 130 to perform a VQE calculation based on "H(μ)" (H is marked with a ^). The VQE execution unit 130 performs a VQE calculation to find a quantum state "|Ψ(θ)>" that minimizes "<Ψ(θ)|H(μ)|Ψ(θ)>" (H is marked with a ^). The VQE calculation procedure is as follows: Steps S103 to S108.

[0084] [Step S103] The VQE execution unit 130 sets an initial value for the parameter θ of the trial state “|Ψ(θ)>”. For example, the VQE execution unit 130 sets an initial value for the parameter θ prev does not exist, the initial value of θ is set to 0. This state corresponds to the Hartree-Hock state. prev If θ exists, prev The value of is set as the initial value of θ.

[0085] [Step S104] The VQE execution unit 130 instructs the quantum computer 200 to calculate the expected value "<Ψ(θ)|H(μ)|Ψ(θ)>" (H is followed by a ^) of the physical quantity+penalty term in the trial state. In accordance with the instruction, the quantum computer 200 obtains the expected value "<Ψ(θ)|H(μ)|Ψ(θ)>" (H is followed by a ^) of the physical quantity+penalty term through quantum calculation. A specific method for calculating "<Ψ(θ)|H(μ)|Ψ(θ)>" (H is followed by a ^) is described below.

[0086] In a many-electron system, if the single-electron state occupied by an electron is given, the operator for calculating the energy of that state can be expressed as follows (second quantized Hamiltonian):

[0087]

number

[0088] a appearing on the right-hand side i + ,a j + is the creation operator in the one-electron state. j ,a k ,a l is the annihilation operator in the one-electron state. h i,j ,h i,j,k,l is a real number. The first term on the right-hand side is the one-electron Hamiltonian, which is a term derived from the kinetic energy of the electron and the Coulomb attractive energy between the electron and the nucleus. The second term on the right-hand side is the two-electron Hamiltonian, which is a term derived from the Coulomb repulsive energy between two electrons. The process of applying the operators of these terms to the state "|Ψ(θ)>" can be realized by applying quantum gates to quantum bits on the quantum computer 200.

[0089] The equation obtained by rewriting the second quantized Hamiltonian in a language corresponding to a quantum gate is called a qubit Hamiltonian. Quantum computer 200 executes a quantum circuit corresponding to the qubit Hamiltonian to calculate the expected value of the physical quantity of the state plus the penalty term, "<Ψ(θ)|H(μ)|Ψ(θ)>" (where H is followed by a ^).

[0090] [Step S105] The VQE execution unit 130 obtains from the quantum computer 200 the calculation result of the expected value of the physical quantity+penalty term in the trial state, "<Ψ(θ)|H(μ)|Ψ(θ)>" (H is marked with a ^).

[0091] [Step S106] The parameter update unit 131 of the VQE execution unit 130 updates the value of the parameter θ to minimize the expected value of the physical quantity+penalty term. Here, the expected value of the physical quantity+penalty term, "E(θ)=<Ψ(θ)|H(μ)|Ψ(θ)>" (H is followed by a ^), is a continuous function of the parameter θ. Therefore, one method for updating the parameter θ to minimize the objective function is, for example, gradient descent. The gradient descent is expressed by the following equation.

[0092]

number

[0093] η is a real number. The differential coefficient "∂E(θ) / ∂θ" can be calculated, for example, by numerical differentiation. In this case, when the VQE execution unit 130 causes the quantum computer 200 to execute quantum computation, it causes the VQE execution unit 130 to calculate not only the value of E(θ) but also the value of "E(θ+δ)". The parameter update unit 131 calculates the value of the updated θ according to equation (3) using the acquired E(θ) and E(θ+δ).

[0094] [Step S107] The VQE executing unit 130 determines whether the update step of the parameter θ (the difference between the value of the parameter θ before and after the update) is equal to or less than a threshold. That is, when the value of the parameter θ converges and the update step becomes equal to or less than the threshold, it is considered that the expected value of the physical quantity+penalty term has also converged. If the update step is equal to or less than the threshold, the VQE executing unit 130 proceeds to step S108. If the update step exceeds the threshold, the VQE executing unit 130 proceeds to step S104.

[0095] [Step S108] The VQE execution unit 130 obtains the error of the expected value "<Ψ(θ)|N|Ψ(θ)>" (N is followed by a ^) of the number of electrons in the obtained quantum state "|Ψ(θ)>" from the correct number of electrons. For example, the number of electrons in a state in a multi-electron system can be obtained by counting the number of single-electron states occupied by electrons. Therefore, the operator for calculating the number of electrons can be expressed as follows:

[0096]

number

[0097] a appearing on the right side of equation (4) i + ,a i are the creation operator and annihilation operator for the one-electron state, respectively. The expectation value of the number of electrons in the state, "<Ψ(θ)|N|Ψ(θ)>" (N is followed by a ^), is also obtained as a result of quantum circuit calculation on the quantum computer 200.

[0098] The VQE execution unit 130 transmits the obtained error in the number of electrons to the penalty term coefficient adjustment unit 120 . [Step S109] The penalty term coefficient adjustment unit 120 determines whether the error in the number of electrons is equal to or less than a threshold. When a ground state with the correct number of electrons is ultimately found, the threshold for the error in the number of electrons is "0." If the error in the number of electrons is equal to or less than the threshold, the penalty term coefficient adjustment unit 120 transmits the calculation results, such as the expected value of the physical quantity (e.g., energy) at that time and the value of the parameter θ at that time, to the quantum computing management unit 110, and ends the process. If the error in the number of electrons exceeds the threshold, the penalty term coefficient adjustment unit 120 proceeds to step S110.

[0099] [Step S110] The penalty term coefficient adjustment unit 120 adjusts the current value of θ by θ prev The data is stored in the memory 102 or the storage device 103 as the data. [Step S111] The penalty term coefficient adjustment unit 120 updates the value of the penalty term coefficient μ, and then the penalty term coefficient adjustment unit 120 proceeds to step S102.

[0100] In this way, the quantum computing system 300 can efficiently calculate the expected value of the physical quantity + penalty term through VQE calculations in which the number of electrons is not conserved. By repeating the VQE calculations until the error in the number of electrons becomes equal to or less than a threshold, the expected value of the physical quantity + penalty term for the correct number of electrons can finally be obtained. Furthermore, in the second and subsequent VQE calculations, the value of the parameter θ obtained in the previous VQE calculation is set as the initial value of the parameter θ for the next VQE calculation. This allows the expected value of the physical quantity + penalty term in the VQE calculation to converge with fewer iterations, thereby shortening the calculation time per VQE calculation.

[0101] Third Embodiment In the third embodiment, the VQE calculation that is closest to the value of the coefficient μ set in the kth VQE calculation is selected from the 1st to the (k-1)th VQE calculations, and the state obtained as a result of that VQE calculation is set as the initial value of the kth VQE calculation. This method of updating the coefficient μ is effective when the conversion of μ using the Newton method is not monotonic (monotonically increasing or monotonically decreasing).

[0102] Figure 8 shows an example of a case where the conversion of the coefficient μ using the Newton method is not monotonic. A case where the change in the coefficient μ is monotonic is when the value of μ decreases as the number of times the VQE calculation is performed (the subscript of μ) increases, such as "μ0>μ1>μ2>...". Conversely, a case where the value of μ increases as the number of times the VQE calculation is performed is also considered to be a monotonic change.

[0103] Graphs 41 to 43 show examples of updating the value of the coefficient μ according to the function f(μ) when the value of the coefficient μ does not change monotonically. The horizontal axis of graphs 41 to 43 shows the value of the coefficient μ, and the vertical axis shows the value f obtained by the function f(μ).

[0104] For example, the penalty term coefficient adjustment unit 120 first sets the coefficient μ to an initial value μ0 and executes the function f(μ). Executing the function f(μ) performs a VQE calculation, and obtains the minimum value of the expected value of the physical quantity+penalty term in the first iteration (iteration: 1). The value of the parameter θ when the minimum value of the expected value of the physical quantity+penalty term is obtained can be expressed as follows:

[0105]

number

[0106] In the first iteration, the penalty term coefficient adjustment unit 120 finds the intersection between the tangent line that touches the curve representing the function f(μ) at the position μ=μ0 and the line of f=0. The penalty term coefficient adjustment unit 120 sets the value of μ at the found intersection as the updated value μ1 of the coefficient μ.

[0107] Next, the penalty term coefficient adjustment unit 120 sets the coefficient μ to the updated value μ1 and executes the function f(μ). By executing the function f(μ), the VQE calculation is performed by the VQE execution unit 130, and the minimum value of the expected value of the physical quantity+penalty term in the second iteration (iteration: 2) is obtained. The value of the parameter θ when the minimum value of the expected value of the physical quantity+penalty term is obtained can be expressed as follows:

[0108]

number

[0109] In the second iteration, the penalty term coefficient adjustment unit 120 finds the intersection between the tangent line that touches the curve representing the function f(μ) at the position μ=μ1 and the line where f=0. The penalty term coefficient adjustment unit 120 sets the value of μ at the found intersection as the updated coefficient value μ2.

[0110] In the example of Figure 8, "μ0>μ2>μ1" holds, and the change in the value of the coefficient μ is not monotonous. Also, the value of μ2 is closer to μ0 than μ1 (μ0-μ2<μ2-μ1). In this case, it is considered that the VQE calculation efficiency will be better if the value of equation (5) obtained in the first iteration is used as the initial value of parameter θ in the third iteration (iteration: 3) rather than the value of equation (6) obtained in the second iteration.

[0111] Therefore, in the example of FIG. 8, the penalty term coefficient adjustment unit 120 sets the value of the parameter θ when the minimum expected value of the physical quantity+penalty term is obtained in the first iteration as the initial value of the parameter θ for the VQE calculation in the third iteration.

[0112] 9 is a diagram showing an example of a method for determining the initial value of the parameter θ for the next VQE calculation from the results of multiple past VQE calculations. For example, a history list 140 is provided in the memory 102 or storage device 103 of the classical computer 100. The history list 140 stores the value of the parameter θ when the expected value of the physical quantity + penalty term in a previously executed VQE calculation is minimized, in association with the value of the coefficient μ set in that VQE calculation. The parameter θ is data including multiple parameter values ​​that indicate, for example, the rotation angle of a rotation operation by each of multiple rotation gates included in a quantum circuit used in the VQE calculation.

[0113] The penalty term coefficient adjustment unit 120 adjusts the value μ of the coefficient μ to be applied to the k-th VQE calculation. k Then, the penalty term coefficient adjustment unit 120 determines the equation H(μ k ) to the VQE execution unit 130.

[0114] The VQE execution unit 130 calculates μ from the value of the coefficient μ set in the history list 140. k The VQE execution unit 130 searches for a value closest to the coefficient μ. The VQE execution unit 130 extracts the value of the parameter θ corresponding to the relevant value of the coefficient μ from the history list 140. The VQE execution unit 130 sets the extracted value of the parameter θ as the initial value of the parameter θ in the VQE calculation, and executes the VQE calculation. The VQE execution unit 130 then transmits the result of the k-th VQE calculation to the penalty term coefficient adjustment unit 120. The penalty term coefficient adjustment unit 120 then transmits the value μ of the coefficient μ applied to the k-th VQE calculation. k and the value θ of the parameter θ when the expected value of the physical quantity + penalty term is minimized in the kth VQE calculation. k The set of and is added to the history list 140 as one record 141.

[0115] Fig. 10 is a flowchart showing an example of the procedure of quantum chemistry calculation processing by VQE in the third embodiment. Among the processing shown in Fig. 10, the processing of steps S201 to S202, S204 to S209, and S211 is the same as the processing of steps S101 to S102, S104 to S109, and S111 (see Fig. 7) in the second embodiment, respectively. The processing of steps S203 and S210 that differ from the second embodiment is as follows.

[0116] [Step S203] The VQE execution unit 130 references the history list 140 generated in the process of step S210 below to set the initial value of the parameter θ of the trial state "|Ψ(θ)>". Note that the history list 140 is empty in the first iteration of VQE. In this case, for example, the VQE execution unit 130 sets the initial value of the parameter θ to "0" (Hartree-Fock state).

[0117] If the history list is not empty, the VQE execution unit 130 identifies from the history list a record (μ, θ) having μ closest to the current value of μ. The VQE execution unit 130 then sets the value of θ set in the identified record as the initial value of the parameter θ for the current VQE calculation.

[0118] Thereafter, the VQE execution unit 130 and the quantum computer 200 cooperate to execute the VQE calculation. When the expected value of the physical quantity+penalty term obtained by the VQE calculation converges to a minimum value, the VQE execution unit 130 transmits the calculation result to the penalty term coefficient adjustment unit 120. If there is an error exceeding a threshold in the number of electrons in the state indicated by the calculation result, the penalty term coefficient adjustment unit 120 performs the process of step S210.

[0119] [Step S210] The penalty term coefficient adjustment unit 120 adds to the history list 140 a record containing the value of the coefficient μ applied to the most recently executed VQE calculation and the value of the parameter θ when the expected value of the physical quantity+penalty term obtained in that VQE calculation was the minimum value.

[0120] Thereafter, the value of the coefficient μ is updated by the penalty term coefficient adjustment unit 120, and the VQE calculation is performed using the updated value of the coefficient μ. In this way, even if the value of the coefficient μ does not monotonically increase or decrease, an appropriate value is set as the initial value of the parameter θ for each VQE calculation.

[0121] Although the embodiments have been described above, the configuration of each part shown in the embodiments can be replaced with other parts having similar functions. Also, any other components or processes may be added. Furthermore, any two or more configurations (features) of the above-described embodiments may be combined. [Explanation of symbols]

[0122] 1. Quantum computers 10. Information processing equipment 11 Storage section 12 Processing section

Claims

1. alternately repeating a process of updating a coefficient value in a third equation obtained by adding a term obtained by multiplying a coefficient to a second equation relating to the number of electrons in a multi-electron system to a first equation for calculating a physical quantity of the multi-electron system, and a search process using a variational quantum eigenvalue solver method for searching for a ground state of the multi-electron system by changing the quantum state of the multi-electron system so that the expected value of the third equation according to the quantum state of the multi-electron system decreases; In the k+1th (k is a natural number) search process, a final state of the multi-electron system in any one of the first to kth search processes is set as an initial state of the multi-electron system in the k+1th search process, and the quantum state of the multi-electron system is changed from the initial state so that the expected value of the third equation decreases. Quantum chemistry calculation program.

2. In the (k+1)th search process, the final state of the multi-electron system in the kth search process is set as the initial state of the multi-electron system in the (k+1)th search process. The quantum chemical calculation program according to claim 1.

3. In the (k+1)th search process, a value is selected based on the difference between each of the coefficient values ​​of the third equation used in the first to kth search processes and the coefficient value of the third equation used in the (k+1)th search process, and a final state of the multi-electron system in the search process executed using the third equation in which the selected value is the coefficient value is set as the initial state of the multi-electron system in the (k+1)th search process. The quantum chemical calculation program according to claim 1.

4. In the search process, the quantum state of the multi-electron system is changed by allowing the number of electrons in the multi-electron system to vary, and the final state of the multi-electron system when the number of electrons in the multi-electron system in the final state of the multi-electron system satisfies a predetermined requirement is determined to be the ground state of the multi-electron system. The quantum chemical calculation program according to claim 1.

5. alternately repeating a process of updating a coefficient value in a third equation obtained by adding a term obtained by multiplying a coefficient to a second equation relating to the number of electrons in a multi-electron system to a first equation for calculating a physical quantity of the multi-electron system, and a search process using a variational quantum eigenvalue solver method for searching for a ground state of the multi-electron system by changing the quantum state of the multi-electron system so that the expected value of the third equation according to the quantum state of the multi-electron system decreases; In the k+1th (k is a natural number) search process, a final state of the multi-electron system in any one of the first to kth search processes is set as an initial state of the multi-electron system in the k+1th search process, and the quantum state of the multi-electron system is changed from the initial state so that the expected value of the third equation decreases. Quantum chemical calculation method.

6. a processing unit that alternately repeats an update process of a coefficient in a third equation obtained by adding a term obtained by multiplying a coefficient of a second equation related to the number of electrons in the multi-electron system to a first equation for calculating a physical quantity of the multi-electron system, and a search process using a variational quantum eigenvalue solver method that searches for a ground state of the multi-electron system by changing the quantum state of the multi-electron system so that an expected value of the third equation corresponding to the quantum state of the multi-electron system decreases, and in a k+1th search process (k is a natural number), a final state of the multi-electron system in any of the 1st to kth search processes is set as an initial state of the multi-electron system in the k+1th search process, and changes the quantum state of the multi-electron system from the initial state so that the expected value of the third equation decreases; An information processing device having the above.

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