Quantum computation control program, quantum computation control method, and information processing device

Abstract

To shorten the computation time for an expected value of a ground state energy of a molecule.SOLUTION: An information processing device 10 creates multiple quantum bit pairs, each of which is formed by combining a first quantum bit and a second quantum bit. The first quantum bit corresponds to a first orbital in which an electron is present in the initial configuration. The second quantum bit corresponds to a second orbital in which an electron is not present in the initial configuration. The information processing device 10 generates a quantum circuit 3 which applies two-qubit gates 4a to 4j to at least a part of the multiple quantum bit pairs. The two-qubit gates 4a to 4j are quantum gates which generate a superposition state according to a parameter value between a first state in which the states of the first and second quantum bits are not swapped and a second state in which the states are swapped. An expected value of a ground state energy of a molecule is acquired by causing a quantum computer 1 to repeatedly execute the quantum circuit 3.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] The present invention relates to a quantum computing control program, a quantum computing control 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. Examples of trial states include UCC (Unitary Coupled-Cluster) ansatz and Symmetry Preserving Ansatz.

[0005] Techniques related to VQE have been proposed, for example, methods for estimating expectation values ​​of quantum mechanical observables that reduce the number of state preparation and measurement iterations and implement operator averaging within quantum or classical-quantum algorithms. Systems have also been proposed for achieving hardware-efficient VQE for quantum computing machines. Furthermore, computer-implemented methods for determining the measurement values ​​of each operator among multiple operators have been proposed. [Prior art documents] [Patent documents]

[0006] [Patent Document 1] Japanese Patent Publication No. 2023-99003 [Patent Document 2] Special Publication No. 2020-534607 [Patent Document 3] Special Publication No. 2022-544926 [Non-patent literature]

[0007] [Non-Patent Document 1] Bryan T. Gard, Linghua Zhu, George S. Barron, Nicholas J. Mayhall, Sophia E. Economou & Edwin Barnes, "Efficient symmetry-preserving state preparation circuits for the variational quantum eigensolver algorithm", npj Quantum Information volume 6, Article number: 10 (2020), 28 January 2020 Summary of the Invention [Problem to be solved by the invention]

[0008] Compared to UCCansatz, Symmetry Preserving Ansatz can realize the superposition of Hartree-Fock states and excited states with simple quantum gates. However, since Symmetry Preserving Ansatz only performs gate operations on pairs of adjacent qubits, obtaining accurate results requires repeated gate operations on pairs of adjacent qubits. As a result, as the circuit length of the ansatz increases, the number of parameters also increases. A longer circuit length requires longer calculation times for each energy expectation value. Furthermore, a larger number of parameters requires more iterations until the energy expectation value converges, resulting in a longer calculation time for the entire VQE calculation. As such, with conventional techniques, it takes a long time to calculate the ground state energy expectation value of a molecule using VQE with high accuracy.

[0009] In one aspect, the present invention aims to reduce the calculation time of the energy expectation value of the ground state of a molecule. [Means for solving the problem]

[0010] In one proposal, a quantum computing control program is provided that causes a computer to perform the following processes. The computer creates multiple quantum bit pairs, each of which is a combination of a first quantum bit corresponding to a first orbital in which an electron exists in the initial configuration and a second quantum bit corresponding to a second orbital in which an electron does not exist in the initial configuration, among multiple quantum bits that indicate the presence or absence of an electron in each of multiple orbitals of the molecule. The computer generates a quantum circuit that causes a two-qubit gate to operate on at least some of the multiple quantum bit pairs, generating a superposition state, depending on the value of a parameter, between a first state in which the states of the first quantum bit and the second quantum bit are not swapped and a second state in which the states are swapped. The computer then obtains the energy expectation value in the ground state of the molecule by repeatedly executing the quantum circuit on the quantum computer while updating the value of the parameter of the two-qubit gate. [Effects of the Invention]

[0011] According to one aspect, the calculation time for the energy expectation value of the ground state of a molecule can be reduced. [Brief explanation of the drawings]

[0012] [Figure 1] FIG. 2 is a diagram illustrating an example of a quantum computing control method according to the 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 UCCansatz. [Figure 5] FIG. 10 is a diagram illustrating an example of Symmetry Preserving Ansatz. [Figure 6] FIG. 10 is a diagram showing an example of an ansatz circuit in which the number of quantum gate boxA is reduced. [Figure 7] FIG. 1 is a block diagram showing an example of the functionality of a classical computer for performing quantum chemical calculations. [Figure 8] 1 is a flowchart showing an example of a procedure for quantum chemical calculation. [Figure 9] 10 is a flowchart illustrating an example of a procedure for a VQE execution process. [Figure 10] FIG. 1 is a diagram illustrating an example of an ansatz circuit for VQE. [Figure 11] FIG. 10 is a diagram illustrating an example of a VQE execution result. [Figure 12] FIG. 10 is a diagram showing a first example of an ansatz circuit that causes the quantum gate boxA to act only on quantum bit pairs that are highly effective in lowering the energy expectation value. [Figure 13] FIG. 11 is a diagram showing an example of a function for quantum chemical calculation in the third embodiment. [Figure 14] 10 is a flowchart showing an example of a procedure for quantum chemical calculation in the third embodiment. [Figure 15]FIG. 10 is a diagram showing a second example of an ansatz circuit that applies the quantum gate boxA only to quantum bit pairs that are highly effective in lowering the energy expectation value. [Figure 16] FIG. 13 is a diagram showing an example of a function for quantum chemical calculation in the fourth embodiment. [Figure 17] 13 is a flowchart showing an example of a procedure for quantum chemical calculation in the fourth embodiment. [Figure 18] 10 is a flowchart illustrating an example of a procedure for calculating an energy expected value derivative. DETAILED DESCRIPTION OF THE INVENTION

[0013] 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 computation control method that can efficiently calculate the energy expectation value of the ground state of a molecule while minimizing the decrease in calculation accuracy.

[0014] Fig. 1 is a diagram illustrating an example of a quantum computing control method according to a first embodiment. Fig. 1 illustrates an information processing device 10 that implements the quantum computing control method. The information processing device 10 can implement the quantum computing control method by, for example, executing a quantum computing control program.

[0015] 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.

[0016] The storage unit 11 stores molecular information 2 of a molecule for which the ground state energy expectation value is to be calculated. The molecular information 2 includes, for example, information such as the number of orbitals, the number of electrons, a Hamiltonian, and an active space.

[0017] The processing unit 12 works in cooperation with the quantum computer 1 to calculate the expected energy value of the ground state of the molecule based on the molecular information 2. For example, the processing unit 12 determines the initial arrangement of electrons in multiple orbitals of the molecule. For example, when the Hartree-Fock state is set as the initial state, the processing unit 12 sets each orbital, starting from the lowest energy, corresponding to the number of electrons, as the arrangement destination of electrons in the initial arrangement. The orbital (occupied orbital) to which electrons are arranged in the initial arrangement is set as the first orbital. Furthermore, the orbital (unoccupied orbital) to which electrons are not arranged in the initial arrangement is set as the second orbital.

[0018] The processing unit 12 uses the same number of quantum bits as the number of orbitals as quantum bits to be used in the calculation. The state of the quantum bits used in the calculation represents the presence or absence of electrons occupying each of the multiple orbitals of the molecule. For example, the state of a quantum bit corresponding to an orbital in which an electron is located is represented by |1>, and the state of a quantum bit corresponding to an orbital in which an electron is not located is represented by |0>.

[0019] Here, the quantum bit corresponding to the first orbit is referred to as the first quantum bit, and the quantum bit corresponding to the second orbit is referred to as the second quantum bit. Processing unit 12 creates a plurality of quantum bit pairs by combining one first quantum bit and one second quantum bit from the plurality of quantum bits.

[0020] Processing unit 12 generates quantum circuit 3 based on a plurality of quantum bit pairs. For example, processing unit 12 generates quantum circuit 3 including a circuit that applies predetermined two-qubit gates 4a to 4j to at least some of the plurality of quantum bit pairs. Two-qubit gates 4a to 4j are quantum gates that generate a superposition state, depending on the value of a parameter, between a first state in which the states of the first quantum bit and the second quantum bit are not swapped and a second state in which the states are swapped.

[0021] If the electrons remain in their initial positions, in the first state, the first quantum bit is |1> and the second quantum bit is |0>. In the second state, which is the result of swapping the states of the first quantum bit and the second quantum bit, the first quantum bit is |0> and the second quantum bit is |1>. The transition of the first quantum bit and the second quantum bit from the first state to the second state represents the excitation of an electron in the first orbital and its movement to the second orbital. The probability of entering the first state and the probability of entering the second state depend on, for example, the values ​​of the parameters of the two-qubit gates 4a to 4j. The parameters of each of the two-qubit gates 4a to 4j are independent of each other.

[0022] The circuit that causes two-qubit gates 4a to 4j to act on at least some of the plurality of qubit pairs is an ansatz circuit 3a that constructs a trial state (also called a trial wave function or an ansatz) for the calculus of variations.

[0023] Processing unit 12 acquires the expected energy value in the ground state of the molecule by repeatedly executing the quantum circuit on quantum computer 1 while updating the parameter values ​​of two-qubit gates 4a to 4j. For example, processing unit 12 calculates the expected energy value in the ground state of the molecule by VQE in cooperation with quantum computer 1.

[0024] According to this quantum computing control method, in the quantum circuit 3, two-qubit gates 4a-4j are arranged for a qubit pair consisting of a first qubit corresponding to a first orbital in which an electron is present in the initial configuration and a second qubit corresponding to a second orbital in which no electron is present in the initial configuration. On the other hand, two-qubit gates that create a superposition state are not arranged between the first qubits or between the second qubits. The first qubits correspond to the first orbital in which an electron is present, and no state change occurs when the first qubits are exchanged with each other. Similarly, the second qubits correspond to the second orbital in which an electron is absent, and no state change occurs when the second qubits are exchanged with each other. Therefore, the calculation accuracy of the expected energy value is not reduced even if two-qubit gates that create a superposition state between the first qubits and the second qubits are not applied. Furthermore, by suppressing unnecessary gate operations and reducing the number of parameters to be updated, the processing unit 12 can efficiently calculate the expected energy value of the ground state of the molecule.

[0025] The processing unit 12 can also apply a two-qubit gate that creates a superposition state only to a qubit pair among the multiple qubit pairs that has a high effect of reducing the energy expectation value. For example, the processing unit 12 calculates an evaluation value for each of the multiple qubit pairs regarding the effect of reducing the energy expectation value of the molecule by applying a two-qubit gate that creates a superposition state. Then, based on the evaluation value, the processing unit 12 determines the qubit pair on which to apply the two-qubit gate that creates a superposition state. For example, the processing unit 12 compares the evaluation value of the qubit pair with a predetermined threshold, and if the evaluation value is greater than or equal to the threshold, determines to apply a two-qubit gate that creates a superposition state to the qubit pair, and adds the two-qubit gate to the quantum circuit 3.

[0026] By using a two-qubit gate that generates a superposition state only on qubit pairs that are highly effective in reducing the energy expectation value, processing efficiency is improved while minimizing the decrease in the accuracy of the energy expectation value.

[0027] The effect of reducing the expected energy value by applying a two-qubit gate that creates a superposition state to a qubit pair can be evaluated using, for example, an ansatz circuit that applies the two-qubit gate only to that qubit pair. In this case, processing unit 12 evaluates each of multiple qubit pairs and generates an evaluation quantum circuit for each of the qubit pairs. The evaluation quantum circuit is a circuit that applies a two-qubit gate that creates a superposition state to the qubit pair that is being evaluated, but does not apply a two-qubit gate that creates a superposition state to qubit pairs that are not being evaluated.

[0028] Processing unit 12 sets the minimum expected energy value obtained by repeatedly executing the evaluation quantum circuit on quantum computer 1 while updating the parameter values ​​of the two-qubit gate to be acted on as the evaluation value. For example, if the minimum expected energy value when acting on a two-qubit gate that produces a superposition state only on a qubit pair is equal to or less than a predetermined threshold, processing unit 12 determines that the qubit pair is the target on which the qubit gate is to be acted on.

[0029] In this way, by calculating the energy expectation value using an ansatz circuit that operates a two-qubit gate that generates a superposition state only for the qubit pair, the processing unit 12 can correctly evaluate the effectiveness of placing a two-qubit gate on the qubit pair. As a result, the quantum circuit 3 suppresses the placement of a two-qubit gate on a qubit pair that has a small effect on reducing the energy expectation value, among multiple qubit pairs. As a result, the processing unit 12 can suppress a decrease in the accuracy of the energy expectation value and improve the efficiency of calculating the energy expectation value.

[0030] The effect of reducing the energy expectation value by applying a two-qubit gate that generates a superposition state to a quantum bit pair can also be evaluated by, for example, the differential coefficient obtained by differentiating the energy expectation value with the parameter of the two-qubit gate. For example, the processing unit 12 generates an evaluation quantum circuit for each of a plurality of quantum bit pairs, and applies a two-qubit gate that generates a superposition state only to that quantum bit pair. The processing unit 12 executes the evaluation quantum circuit on the quantum computer 1 to obtain the differential coefficient of the energy expectation value when the parameter of the two-qubit gate that generates the superposition state has a predetermined value. For example, the predetermined value is set to a parameter value representing a Hartree-Fock state. The processing unit 12 then uses the obtained differential coefficient as the evaluation value. For example, if the differential coefficient obtained by applying a two-qubit gate that generates a superposition state only to a quantum bit pair is equal to or greater than a predetermined threshold, the processing unit 12 adds a two-qubit gate to the quantum circuit 3 to operate on that quantum bit pair.

[0031] The processing unit 12 can correctly evaluate the effectiveness of the placement of a two-qubit gate on a quantum bit pair by calculating the derivative of the energy expectation value using an ansatz circuit that operates a two-qubit gate that generates a superposition state only for the quantum bit pair. This prevents the placement of a two-qubit gate on a quantum bit pair that has a low effect of reducing the energy expectation value. As a result, the processing unit 12 can prevent a decrease in the accuracy of the energy expectation value and improve the efficiency of calculating the energy expectation value. Moreover, the calculation load of the derivative is lighter than when calculating the minimum value of the energy expectation value, allowing the processing unit 12 to efficiently calculate the evaluation value.

[0032] Note that molecular orbitals are divided into orbitals in which α-spin electrons are located and orbitals in which β-spin electrons are located. Depending on the molecule being calculated, the number of α-spin electrons and the number of β-spin electrons may be conserved. In this case, processing unit 12 may suppress the application of a two-qubit gate that generates a superposition state for a qubit pair corresponding to orbitals with different spin directions.

[0033] For example, processing unit 12 inhibits the creation of a quantum bit pair between a first quantum bit corresponding to a first orbital in which α-spin electrons can be arranged and a second quantum bit corresponding to a second orbital in which β-spin electrons can be arranged. Processing unit 12 also inhibits the creation of a quantum bit pair between a first quantum bit corresponding to a first orbital in which β-spin electrons can be arranged and a second quantum bit corresponding to a second orbital in which α-spin electrons can be arranged.

[0034] This omits unnecessary two-qubit gates in the calculation of the energy expectation value, and reduces the number of parameters, allowing the processing unit 12 to efficiently calculate the energy expectation value.

[0035] Second Embodiment The second embodiment is a quantum computing system that improves processing efficiency without reducing the accuracy of quantum chemistry calculations using VQE by performing gate operations that place only quantum bit pairs that are effective in improving calculation accuracy into a superposition state.

[0036] 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, from the terminal device 400, molecular information related to molecules of a problem to be solved.

[0037] Based on the molecular information 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 molecule. 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.

[0038] 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, or the like.

[0039] 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).

[0040] 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.

[0041] 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.

[0042] 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).

[0043] 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.

[0044] 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.

[0045] 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.

[0046] 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.

[0047] 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.

[0048] 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.

[0049] 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.

[0050] 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.

[0051] Quantum computer 200 includes control device 210 and quantum device 220. Control device 210 executes gate operations on quantum bits in quantum device 220 according to a quantum circuit. Quantum device 220 includes multiple quantum bits. Quantum device 220 may be, for example, one or multiple quantum processing units (QPUs).

[0052] The quantum chemistry calculation using VQE is efficiently performed by the quantum computing system 300 described above. In the quantum chemistry calculation using VQE, a trial state is first constructed. The quantum computing system 300 improves the function system of the trial state to improve the efficiency of the quantum chemistry calculation using VQE.

[0053] UCCansatz, one of the trial state function systems, creates various excited states and sets the trial state as a superposition of the Hartree-Fock state and the excited state.

[0054] The Hartree-Fock state is the lowest energy state when there is no superposition. For example, in the case of a molecule with six orbitals and four electrons, if there is no superposition, the lowest energy state would be one in which electrons are placed in the four lowest energy orbitals out of the six orbitals. If lower energy orbitals are assigned lower numbered quantum bits, and the presence or absence of an electron occupying an orbital is represented by the corresponding quantum bit, the Hartree-Fock state would be |111100>.

[0055] The excited state is created by the creation operator a † and the annihilation operator a. 4 is a diagram showing an example of UCCansatz. The trial state 30 of UCCansatz is expressed by Equation (1).

[0056]

number

[0057] In equation (1), for the Hartree-Fock state |111100>, "exp(Σ j,k θ j,k (a k † a j -a j † a k )+···)" where j is the number of the quantum bit corresponding to the orbital where an electron is annihilated. k is the number of the quantum bit corresponding to the orbital where an electron is created. The annihilation operator that annihilates an electron from the orbital corresponding to the fourth quantum bit is "a4". The creation operator that creates an electron in the orbital corresponding to the fifth quantum bit is "a5". † ". The Hartree-Fock state has "a4" and "a5" † When " is applied, the result is |111010>.

[0058] θ j,k is a parameter related to the possibility of generating an excited state in which an electron is annihilated from the orbital corresponding to the jth quantum bit and an electron is generated in the orbital corresponding to the kth quantum bit.

[0059] UCCansatz is designed based on a physical interpretation of, for example, which orbital to excite an electron from and to. If all the possible excited states were superimposed on the Hartree-Fock state, the number of quantum gates would be too large. Therefore, Symmetry Preserving Ansatz is being considered.

[0060] In Symmetry Preserving Ansatz, a superposition state of a Hartree-Fock state and an excited state is generated using the operation "A," which can be realized with a small number of quantum gates.

[0061] FIG. 5 is a diagram showing an example of a Symmetry Preserving Ansatz. The operation of annihilating an electron from an orbit corresponding to a j-th quantum bit and generating an electron for a quantum bit corresponding to a k-th quantum bit is called "A j,k For example, for the Hartree-Fock state |111100>, the operation "A" 31 that annihilates an electron from the orbit corresponding to the fourth quantum bit and creates an electron in the orbit corresponding to the fifth quantum bit is expressed by equation (2).

[0062]

number

[0063] The quantum gates that perform gate operations corresponding to such calculations are referred to as quantum gate boxes A32a to A32h. The quantum gate boxes A32a to A32h are an example of two-qubit gates that produce a superposition state in the first embodiment.

[0064] In the ansatz circuit 32, a gate operation of a superposition operation is performed between adjacent quantum circuits by a quantum gate boxA. The operation of the quantum gate boxA can be expressed as a matrix with bases |00>, |01>, |10>, and |11>, as shown in equation (3).

[0065]

number

[0066] Although the parameter φ is included in equation (3), the value of the parameter φ can be set to "0" (φ = 0). In addition, the parameter θ of each of the multiple quantum gates boxA is independent, and if "θ = 0" for all parameters θ, the initial Hartree-Fock state is maintained.

[0067] The ansatz circuit 32 was designed with ease of calculation in a quantum computer as a priority. For example, quantum gate boxA can realize gate operations without changing the number of electrons with a relatively simple circuit. Furthermore, in the ansatz circuit 32, for ease of implementation, the gate operations of quantum gate boxA are performed only between adjacent quantum bits.

[0068] Although the ansatz circuit 32 is easier to implement than the UCCansatz, to obtain accurate results, the gate operation of the quantum gate boxA must be repeated many times.

[0069] For example, a set of quantum circuits that act on all two adjacent quantum bits with quantum gate boxA is defined as one base layer. In ansatz circuit 32, the set of quantum gate boxes A32a to 32d and the set of quantum gate boxes A32e to 32h are each a base layer.

[0070] In one basic layer, only two adjacent qubits are superimposed, so to superimpose the states of two non-adjacent qubits, the gate operation of the basic layer must be repeated multiple times. The more basic layers there are, the more accurate the VQE calculation becomes.

[0071] On the other hand, as the number of base layer stages increases, the ansatz circuit 32 becomes longer and the number of parameters θ to be optimized by VQE increases. The longer the circuit, the longer the processing time for a single quantum calculation on a quantum computer in VQE. Furthermore, as the number of parameters θ increases, it takes longer for the VQE calculation results to converge, and the number of iterative calculations in VQE increases. As a result, the overall quantum chemistry calculation time using VQE increases.

[0072] Therefore, the quantum computing system 300 constructs a trial state using an ansatz circuit that reduces the number of quantum gates boxA without degrading accuracy as much as possible. Reducing the number of quantum gates boxA to be executed reduces the number of parameters θ to be optimized during the VQE calculation process. Reducing the number of parameters θ makes it easier to perform calculations to update the parameters θ. Furthermore, reducing the depth of the circuit reduces the time required for one quantum calculation.

[0073] Specifically, the quantum computing system 300 generates an ansatz that applies the gate operation of the quantum gate boxA only to quantum bit pairs that combine quantum bits with different initial states, among the quantum bit pairs that can be generated by selecting two quantum bits.

[0074] Fig. 6 is a diagram showing an example of an ansatz circuit in which the number of quantum gates boxA is reduced. As shown in Fig. 6, there are quantum bits whose initial state is |1> and quantum bits whose initial state is |0>. A quantum bit whose initial state is |1> corresponds to an orbital (occupied orbital) in which an electron is located in the initial state. A quantum bit whose initial state is |0> corresponds to an orbital (unoccupied orbital) in which an electron is not located in the initial state.

[0075] The smaller the quantum bit number (the quantum bit set higher in the quantum circuit), the lower the energy orbital it is associated with. If the initial state is a Hartree-Fock state, the initial state of a certain number of quantum bits (number of electrons placed) from the smallest quantum bit number will be |1>, and the initial state of the other quantum bits will be |0>.

[0076] In the ansatz circuit 33 that constructs the trial state proposed in the second embodiment, the gate operation of the quantum gate boxA is applied to all pairs of quantum bits corresponding to occupied orbitals and unoccupied orbitals. That is, in the ansatz circuit 33, quantum gates boxA33a,...,33k,33l,33m,33n are arranged for all combinations of quantum gates whose initial state is |1> and quantum gates whose initial state is |0>. On the other hand, in the ansatz circuit 33, the gate operation of the quantum gate boxA is not performed on quantum bit pairs whose initial states are both |1> and quantum bit pairs whose initial states are both |0>.

[0077] If the two quantum bits on which the quantum gate boxA operates are both |1> or both |0>, the state does not change even if the quantum gate boxA operates. Therefore, gate operations of the quantum gate boxA on such a quantum bit pair are wasteful. In the quantum computing system 300, the efficiency of quantum chemistry calculations using VQE is improved by suppressing the execution of quantum gate boxA, which performs such wasteful operations. In other words, because unnecessary gate operations of quantum gate boxA are suppressed, the total number of quantum gate boxA can be reduced. This shortens the ansatz circuit 33 and reduces the number of parameters θ to be optimized. As a result, VQE calculations can be performed efficiently.

[0078] 7 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 quantum bit pair list creator 120, a quantum circuit generator 130, and a VQE executor 140 to perform quantum chemical calculations.

[0079] The quantum computing manager 110 receives a VQE calculation request from, for example, the terminal device 400. The quantum computing manager 110 transmits molecular information regarding the molecule to be solved, which is indicated in the calculation request, to the quantum bit pair list creator 120 and the quantum circuit generator 130. The quantum computing manager 110 also obtains the VQE results from the VQE execution unit 140 and transmits the calculation results to the terminal device 400.

[0080] The qubit pair list creation unit 120 identifies qubit pairs that are targets for the gate operation of quantum gate boxA based on the molecular information of the molecule to be solved, and creates a qubit pair list that indicates the identified qubit pairs. For example, the qubit pair list creation unit 120 creates a qubit pair list that includes all qubit pairs between qubits corresponding to occupied orbitals and qubits corresponding to unoccupied orbitals in a Hartree-Fock state. The qubit pair list creation unit 120 transmits the created qubit pair list to the quantum circuit generation unit 130.

[0081] The quantum circuit generation unit 130 generates a quantum circuit for calculating a solution to a problem using VQE based on molecular information about the molecule to be solved. For example, the quantum circuit generation unit 130 generates a quantum circuit including an ansatz circuit that performs gate operations on the quantum gate boxA for the quantum bit pairs shown in the quantum bit pair list. The quantum circuit generation unit 130 transmits the generated quantum circuit to the VQE execution unit 140.

[0082] The VQE execution unit 140 executes VQE based on the acquired quantum circuit in cooperation with the quantum computer 200. To execute VQE, the VQE execution unit 140 includes a parameter update unit 141 that optimizes a parameter θ used in VQE.

[0083] For example, the VQE execution unit 140 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 140 obtains an energy expectation value as the execution result of the quantum circuit. Upon obtaining the energy expectation value, the parameter update unit 141 updates the parameter θ so as to decrease the energy expectation value. The VQE execution unit 140 instructs the quantum computer 200 to execute the quantum circuit using the updated parameter θ.

[0084] The VQE execution unit 140 repeats updating the parameter θ and executing the quantum circuit with the updated parameter θ until the energy expectation value converges. When the energy expectation value converges, the VQE execution unit 140 transmits the value of the parameter θ and the energy expectation value at that time to the quantum computation management unit 110 as the VQE calculation result.

[0085] The quantum computer 200 has an energy expectation calculation unit 230. The energy expectation calculation unit 230 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 230 then calculates the energy expectation from the measurement result and transmits the energy expectation to the classical computer 100. Note that the process of calculating the energy expectation from the measurement result may be performed by the VQE execution unit 140 of the classical computer 100.

[0086] The functions of the elements in the classical computer 100 shown in FIG. 7 can be realized, for example, by having the processor 101 execute a program module corresponding to the element.

[0087] 7 executes quantum chemical calculations using VQE while controlling the quantum computer 200. The processing procedure for the quantum chemical calculations will be described below with reference to FIGS.

[0088] 8 is a flowchart showing an example of the procedure for quantum chemical calculations. The process shown in FIG. 8 will be explained below in order of step number. [Step S101] The quantum computing manager 110 acquires molecular information indicating the molecule for which a solution is to be obtained from the terminal device 400. The molecular information includes, for example, the number of orbitals of the molecule for which the ground state energy is to be obtained, the number of electrons possessed by the molecule, a Hamiltonian indicating the energy of the molecule, an active space, and the like.

[0089] [Step S102] The qubit pair list creation unit 120 identifies qubit pairs that are the targets of gate operation by quantum gate boxA in VQE, and creates a qubit pair list that indicates the identified qubit pairs. For example, the qubit pair list creation unit 120 creates a qubit pair list "pairs={(i,j)}" that is a set of all pairs (i,j) where i is the qubit number corresponding to an occupied orbital and j is the qubit number corresponding to an unoccupied orbital.

[0090] Electrons in molecular orbitals can be classified as α spin or β spin depending on the direction of their spin. α spin is also called up spin. β spin is also called down spin. Up to two electrons can fit into one orbital of a molecule, and when two electrons fit, one will be α spin and the other will be β spin. Therefore, one orbital is defined as an orbital for α spin and an orbital for β spin, and each orbital is associated with a quantum bit indicating the presence or absence of an α spin electron and a quantum bit indicating the presence or absence of a β spin electron.

[0091] In many problems of quantum chemical calculations, the number of electrons of α spin and the number of electrons of β spin are maintained. Therefore, the qubit pair list creation unit 120 may limit the qubit pairs to be operated on to pairs of qubits corresponding to α spin or pairs of qubits corresponding to β spin. This prevents the gate operation of quantum gate boxA between the qubit corresponding to α spin and the qubit corresponding to β spin. In other words, the number of quantum gate boxA to be executed is reduced.

[0092] [Step S103] The quantum circuit generation unit 130 generates a quantum circuit C that generates a Hartree-Fock state. [Step S104] The quantum circuit generation unit 130 adds a quantum gate boxA that acts on each of all quantum bit pairs shown in the quantum bit pair list "pairs={(i,j)}" to the quantum circuit C, and creates a quantum circuit C that calculates the expected value of the energy of the state affected by the act.

[0093] [Step S105] The VQE execution unit 140, in cooperation with the quantum computer 200, executes VQE to find a trial state |Ψ(θ)> that minimizes the energy expectation value <Ψ(θ)|H|Ψ(θ)> based on the quantum circuit C. The VQE execution unit 140 calculates the initial value θ of the parameter θ in VQE. initial is set to "0." Details of the VQE execution process will be described later (see FIG. 9). When VQE ends, the VQE execution unit 140 transmits the expected value of the energy obtained from the VQE result to the quantum computation management unit 110.

[0094] [Step S106] The quantum computing manager 110 outputs the energy expectation value E. For example, the quantum computing manager 110 transmits the energy expectation value E to the terminal device 400 as the execution result of the quantum chemistry calculation by VQE.

[0095] Next, the VQE execution process will be described in detail. 9 is a flowchart showing an example of the VQE execution process. The process shown in FIG. 9 will be explained below in order of step number.

[0096] [Step S111] The VQE execution unit 140 sets the parameter θ to the initial value “θ initial The parameter θ exists independently for each quantum circuit of quantum gate boxA. Therefore, the parameter θ is a vector data containing the same number of elements (θ1, θ2, . . .) as the quantum gate boxA. The initial value "θ" indicating the Hartree-Fock state initial " has the value "0" for all elements.

[0097] [Step S112] The VQE execution unit 140 transmits the quantum circuit C to the quantum computer 200 and instructs the quantum computer 200 to perform calculation of the energy expectation value <Ψ(θ)|H|Ψ(θ)> in the trial state.

[0098] [Step S113] The VQE execution unit 140 obtains the expected energy value from the quantum computer 200 as the execution result. [Step S114] The VQE execution unit 140 updates the parameter θ using a gradient method or the like so as to reduce the expected value of the energy. The parameter updating method is not limited to the gradient method.

[0099] [Step S115] The VQE execution unit 140 determines whether the amount of change (update step) before and after updating the parameter θ is equal to or less than a threshold. If the update step is equal to or less than the threshold, the VQE execution unit 140 terminates VQE execution. If the update step exceeds the threshold, the VQE execution unit 140 proceeds to step S112 and repeats the calculation of the energy expectation value using the updated parameter θ.

[0100] By the above-described process, VQE is efficiently performed depending on the number of gate operations of quantum gate box A. Note that, as a termination condition of VQE shown in step S114, for example, a condition that the difference between the last calculated energy expectation value and the energy expectation value calculated immediately before that is equal to or less than a threshold value may be applied.

[0101] Next, we will explain an example of calculating the energy minimum using VQE for a specific molecule. In the following example, we will calculate the ground state energy of the Mg surface system using 14 qubits.

[0102] Figure 10 shows an example of an ansatz circuit for VQE. Ansatz circuit 34 shows gate operations for 14 quantum bits. In ansatz circuit 34, the input state is a Hartree-Fock state. In Figure 10, the quantum gate for generating the Hartree-Fock state is omitted.

[0103] The 14 qubits are divided into groups of 7. The qubits in one group are each associated with seven orbitals that accommodate electrons with alpha spin, while the qubits in the other group are each associated with seven orbitals that accommodate electrons with beta spin.

[0104] Because there are 10 electrons in the active space, in the Hartree-Fock state, the five lowest energy alpha spin orbitals and the five lowest energy beta spin orbitals are occupied orbitals. The other orbitals are unoccupied. Therefore, the initial state of the quantum bit corresponding to the five lowest energy orbitals among orbitals that place alpha spin electrons is |1>. Also, the initial state of the quantum bit corresponding to the five lowest energy orbitals among orbitals that place beta spin electrons is |1>. The initial state of the other quantum bits is |0>.

[0105] In the ansatz circuit 34, quantum circuits that perform gate operations of the quantum gate box A are arranged for all combinations of the quantum bits corresponding to occupied orbitals and the quantum bits corresponding to unoccupied orbitals for the seven quantum bits corresponding to the α spin orbitals. Also in the ansatz circuit 34, quantum gate box A is arranged for all combinations of the quantum bits corresponding to occupied orbitals and the quantum bits corresponding to unoccupied orbitals for the seven quantum bits corresponding to the β spin orbitals.

[0106] In this way, there are 10 quantum gate boxA for the quantum bits corresponding to the α spin orbital, and 10 quantum gate boxA for the quantum bits corresponding to the β spin orbital. If the quantum bits to be operated do not overlap, multiple quantum gate boxA can be executed simultaneously. In the ansatz circuit 34, four quantum gate boxA can be executed simultaneously. In Figure 10, quantum gate boxA that can be executed simultaneously are surrounded by a rectangular dashed line. If the depth of one execution of quantum gate boxA is "1", the depth of the ansatz circuit 34 is "5".

[0107] Figure 11 shows an example of the results of VQE. Figure 11 shows the results of VQE for the ground state energy of the Mg surface system. The number of quantum bits used was 14.

[0108] The comparative VQE execution result 41 is the result of VQE when quantum gate boxA is applied between all adjacent quantum bits. The comparative VQE execution result 41 shows the execution results for each case where the number of stages (number of layers) of the basic layer (see FIG. 5) in which quantum gate boxA is applied between all adjacent quantum bits is different.

[0109] In the comparative VQE execution result 41, when the number of layers is "1," the depth is "2," the number of quantum gate box A is "13," the number of parameters is "26," the number of VQE iterations until energy convergence is "16," the processing time is "1000," and the energy expectation value is "-30.6299." When the number of layers is "2," the depth is "4," the number of quantum gate box A is "26," the number of parameters is "52," the number of VQE iterations until energy expectation value convergence is "24," the processing time is "5000," and the energy expectation value is "-30.7026." When the number of layers is "3," the depth is "6," the number of quantum gate box A is "39," the number of parameters is "78," the number of VQE iterations until energy expectation value convergence is "27," the processing time is "13000," and the energy expectation value is "-30.7029."

[0110] According to the comparative VQE execution result 41, the accuracy of the expected energy value obtained when the number of layers is "1" is insufficient. Therefore, to obtain highly accurate calculation results, the number of layers must be "2" or more.

[0111] Proposed VQE execution result 42 is the execution result of VQE when quantum gate boxA is applied to a qubit pair consisting of a qubit corresponding to an occupied orbital and a qubit corresponding to an unoccupied orbital. In the example shown in proposed VQE execution result 42, quantum gate boxA is not applied between the qubit corresponding to the α spin orbital and the qubit corresponding to the β spin orbital.

[0112] When the proposed VQE is applied, the number of occupied orbitals of the same spin is "5", the number of unoccupied orbitals is "2", the depth is "5", the number of quantum gate boxA is "20", and the number of parameters is "40". According to the execution result of the proposed VQE42, the number of VQE iterations until the energy expectation value converges is "10", the processing time is "2000", and the energy expectation value is "-30.7028".

[0113] The processing time shown in Fig. 11 is calculated by "depth x (number of parameters + 1) x number of VQE iterations." As shown in Fig. 11, the VQE of the proposed method obtains expected energy values ​​with similar accuracy in a shorter processing time than the comparative VQE with the number of layers "2" and "3."

[0114] [Third embodiment] In the third embodiment, a quantum gate box A is applied to a quantum bit pair that is highly effective in reducing the energy expectation value, selected from among quantum bit pairs that combine a quantum bit corresponding to an occupied orbital and a quantum bit corresponding to an unoccupied orbital.

[0115] For example, a classical computer selects qubit pairs one by one. It performs VQE using an ansatz circuit that applies the quantum gate boxA to the selected qubit pairs. From all qubit pairs, the classical computer selects qubit pairs whose energy expectation value obtained by VQE is equal to or exceeds a certain threshold. The classical computer performs VQE using an ansatz circuit that applies the quantum gate boxA to all of the selected qubit pairs.

[0116] Figure 12 shows a first example of an ansatz circuit that applies the quantum gate boxA only to qubit pairs that are highly effective in lowering the energy expectation value. For example, assume that there are five electrons on seven molecular orbitals. In this case, five of the seven qubits are associated with occupied orbitals in the Hartree-Fock state, and two are associated with unoccupied orbitals in the Hartree-Fock state.

[0117] In the third embodiment, in order to identify a qubit pair that is highly effective in lowering the energy expectation value, multiple evaluation ansatz circuits are generated that apply the quantum gate boxA to only one qubit pair. For example, ansatz circuit 51 applies the quantum gate boxA to the first qubit and the sixth qubit. Ansatz circuit 52 applies the quantum gate boxA to the fourth qubit and the sixth qubit. Ansatz circuit 53 applies the quantum gate boxA to the fourth qubit and the seventh qubit. Ansatz circuit 54 applies the quantum gate boxA to the fifth qubit and the sixth qubit. Ansatz circuit 55 applies the quantum gate boxA to the fifth qubit and the seventh qubit.

[0118] By performing VQE using each of these ansatz circuits, the expected energy value for each ansatz circuit is obtained. The expected energy value is then calculated based on the threshold E thres If it is below this, it can be determined that the quantum bit pair to which the quantum gate boxA is applied in the ansatz circuit used to calculate the energy expectation value is highly effective in reducing the energy expectation value.

[0119] In the example of FIG. 12, the quantum bit pair of the first quantum bit and the sixth quantum bit has an energy expectation value E 1,6 is the threshold E thres Therefore, the quantum bit pair of the first quantum bit and the sixth quantum bit is judged to have a low effect of reducing the energy expectation value by applying the quantum gate boxA.

[0120] On the other hand, the qubit pair of the fourth qubit and the sixth qubit has the energy expectation value E 4,6 is the threshold E thresTherefore, the quantum bit pair of the fourth quantum bit and the sixth quantum bit is judged to be highly effective in reducing the energy expectation value by applying the quantum gate boxA.

[0121] Based on the results of this determination, an ansatz circuit 56 is generated that applies the quantum gate boxA only to quantum bit pairs that are determined to have a high effect of lowering the energy expectation value. VQE is then performed using the ansatz circuit 56. This allows the number of quantum gate boxA to be reduced without sacrificing calculation accuracy.

[0122] Fig. 13 is a diagram showing an example of functions for quantum chemical calculation in the third embodiment. Of the elements in Fig. 13, elements having the same functions as those in the second embodiment are given the same reference numerals as those in Fig. 7, and descriptions thereof will be omitted.

[0123] The classical computer 100a includes a quantum computation management unit 110, a quantum bit pair list creation unit 120, a quantum circuit generation unit 130a, a VQE execution unit 140a, and a valid pair selection unit 150. The classical computer 100a according to the third embodiment differs from the second embodiment in the processing of the quantum circuit generation unit 130a and the VQE execution unit 140a with the same names in the second embodiment, and also includes a new valid pair selection unit 150.

[0124] When the quantum circuit generation unit 130a obtains the quantum bit pair list from the quantum bit pair list creation unit 120, it generates an ansatz circuit corresponding to each quantum bit pair in the quantum bit pair list. The generated ansatz circuit is an ansatz circuit that causes the quantum gate boxA to act only on the corresponding quantum bit pair. The quantum circuit generation unit 130a transmits multiple quantum circuits for VQE, including each of the generated ansatz circuits, to the VQE execution unit 140a.

[0125] Furthermore, when the quantum circuit generation unit 130a acquires a list of quantum bit pairs (valid pairs) valid for calculating the energy expectation value from the valid pair selection unit 150, it generates an ansatz circuit that causes the quantum gate boxA to act on the valid pairs. Then, the quantum circuit generation unit 130a transmits the quantum circuit for VQE, including the generated ansatz circuit, to the VQE execution unit 140a.

[0126] The VQE execution unit 140a cooperates with the quantum computer 200 to execute VQE based on the acquired quantum circuit. When the VQE execution unit 140a executes VQE using an ansatz circuit that applies quantum gate boxA to only one quantum bit pair, it transmits the calculation result to the valid pair selection unit 150. When the VQE execution unit 140a executes VQE using an ansatz circuit that applies quantum gate boxA to a valid pair, it transmits the calculation result to the quantum computation management unit 110.

[0127] The valid pair selection unit 150 determines the validity of applying the quantum gate boxA to one quantum bit pair based on the results of VQE using an ansatz circuit that applies the quantum gate boxA to that quantum bit pair. The valid pair selection unit 150 sends a list of quantum bit pairs that it has determined to be valid to the quantum circuit generation unit 130a as valid pairs.

[0128] Next, the processing procedure of the quantum chemical calculation in the third embodiment will be specifically described. 14 is a flowchart showing an example of the procedure of quantum chemical calculation in the third embodiment. The process shown in FIG. 14 will be explained below in order of step number.

[0129] [Step S201] The quantum computing manager 110 acquires molecular information about the molecule for which a solution is to be obtained from the terminal device 400. The molecular information includes, for example, the number of orbitals of the molecule for which the ground state energy is to be obtained, the number of electrons possessed by the molecule, a Hamiltonian indicating the energy of the molecule, an active space, and the like.

[0130] [Step S202] The qubit pair list creation unit 120 identifies qubit pairs that are candidates for gate operation by quantum gate boxA in VQE, and creates a qubit pair list that indicates the identified qubit pairs. For example, the qubit pair list creation unit 120 creates a qubit pair list "pairs={(i,j)}" that is a set of all pairs (i,j) where i is the qubit number corresponding to an occupied orbital and j is the qubit number corresponding to an unoccupied orbital.

[0131] [Step S203] The quantum circuit generation unit 130a and the VQE execution unit 140a cooperate to execute the processes of steps S204 to S207 for each quantum bit pair (i, j) included in the quantum bit pair list.

[0132] [Step S204] The quantum circuit generation unit 130a generates a quantum circuit C that generates a Hartree-Fock state. i,j Create a. [Step S205] The quantum circuit generation unit 130a generates a quantum gate boxA that acts on the quantum bit pair (i, j) to be processed in the quantum circuit C. i,j and calculates the expectation value of the energy of the affected state. i,j Create a.

[0133] [Step S206] The VQE execution unit 140a cooperates with the quantum computer 200 to generate the quantum circuit C i,j The VQE execution unit 140a executes the VQE using the trial state shown in the following. The VQE execution unit 140a executes the VQE using the initial value θ of the parameter θ. initial is set to “0.” When the VQE execution unit 140a finishes executing the VQE, the VQE execution unit 140a transmits the expected value of the energy obtained from the execution result of the VQE to the valid pair selection unit 150.

[0134] [Step S207] The valid pair selection unit 150 calculates the energy expectation value E i,j Get. [Step S208] When the VQE execution unit 140a has completed processing for all quantum bit pairs (i, j) included in the quantum bit pair list, the VQE execution unit 140a proceeds to step S209.

[0135] [Step S209] The valid pair selection unit 150 calculates the expected energy E i,j For example, the effective pair selection unit 150 generates an effective pair list (EffectivePairs) based on the energy expectation value E i,j For each, the energy expectation threshold E thres Then, the valid pair selection unit 150 compares the energy expectation value E i,j is the threshold E thres The following list of qubit pairs is called the effective pair list (EffectivePairs={(i,j)|E i,j ≦E thres}).

[0136] [Step S210] The quantum circuit generation unit 130a generates a quantum circuit C that generates a Hartree-Fock state. final Create a. [Step S211] The quantum circuit generation unit 130a generates a quantum gate boxA that operates on all quantum bit pairs shown in the effective pair list “EffectivePairs={(i,j)}” as a quantum circuit C final and calculates the expectation value of the energy of the affected state. final Create a.

[0137] [Step S212] The VQE execution unit 140a cooperates with the quantum computer 200 to generate the quantum circuit C final The VQE execution unit 140a executes the VQE using the trial state shown in the following. The VQE execution unit 140a executes the VQE using the initial value θ of the parameter θ. initial is set to "0." When the VQE execution is completed, the VQE execution unit 140a transmits to the quantum computation management unit 110 the expected value of the energy obtained from the VQE execution result.

[0138] [Step S213] The quantum computing manager 110 outputs the energy expectation value E. For example, the quantum computing manager 110 transmits the energy expectation value E to the terminal device 400 as the execution result of VQE.

[0139] In this way, VQE can be performed using an ansatz circuit that applies the quantum gate boxA only to qubit pairs that are effective in improving the accuracy of the energy expectation value. As a result, the number of quantum gate boxA can be reduced without reducing the accuracy of the energy expectation value.

[0140] [Fourth embodiment] The fourth embodiment evaluates the energy reduction effect when quantum gate boxA is made to act on one quantum bit pair based on the differential coefficient of the energy expectation value of the ansatz circuit that makes quantum gate boxA act on only that quantum bit pair. For example, the differential coefficient of the energy expectation value at parameter θ=0 of an ansatz circuit that makes quantum gate boxA act on only one quantum bit pair is calculated. The value of parameter θ set in quantum gate boxA that acts on quantum bit pair (i, j) is set as "θ i,j ", then the derivative of the energy expectation value is given by

[0141]

number

[0142] "θ i,j = 0" is the differential coefficient of the energy expectation value at parameter θ = 0. In the fourth embodiment, VQE is performed using an ansatz circuit that applies the quantum gate boxA to all qubit pairs whose obtained differential coefficient is equal to or greater than a threshold.

[0143] Figure 15 shows a second example of an ansatz circuit that applies the quantum gate boxA only to qubit pairs that are highly effective in lowering the energy expectation value. For example, assume that there are five electrons on seven molecular orbitals. In this case, five of the seven qubits are associated with occupied orbitals in the Hartree-Fock state, and two are associated with unoccupied orbitals in the Hartree-Fock state.

[0144] In the fourth embodiment, multiple ansatz circuits for evaluation are generated, each of which applies the quantum gate boxA to only one pair of quantum bits. For example, ansatz circuit 61 applies the quantum gate boxA to the first and sixth quantum bits. Ansatz circuit 62 applies the quantum gate boxA to the fourth and sixth quantum bits. Ansatz circuit 63 applies the quantum gate boxA to the fourth and seventh quantum bits. Ansatz circuit 64 applies the quantum gate boxA to the fifth and sixth quantum bits. Ansatz circuit 65 applies the quantum gate boxA to the fifth and seventh quantum bits.

[0145] Using these ansatz circuits, i,j The derivative of the energy expectation at "=0" is calculated, and the energy expectation for each ansatz circuit is obtained. The obtained energy expectation is then applied to the threshold D thres If this is the case, it can be concluded that the quantum bit pair in which the quantum gate boxA is applied in the ansatz circuit used to calculate the energy expectation value is highly effective in reducing the energy expectation value.

[0146] In the example of FIG. 15, the quantum bit pair of the first quantum bit and the sixth quantum bit has a differential coefficient D of the energy expectation value obtained using the corresponding ansatz circuit 61. 1,6 is the threshold D thres Therefore, the quantum bit pair of the first quantum bit and the sixth quantum bit is judged to have a low effect of reducing the energy expectation value by applying the quantum gate boxA.

[0147] On the other hand, the qubit pair of the fourth qubit and the sixth qubit has the energy expectation value D obtained by VQE using the corresponding ansatz circuit 62. 4,6 is the threshold D thres Therefore, the quantum bit pair of the fourth quantum bit and the sixth quantum bit is judged to be highly effective in reducing the energy expectation value by applying the quantum gate boxA.

[0148] Based on the results of this determination, an ansatz circuit 66 is generated that applies the quantum gate boxA only to the qubit pairs that are determined to have a high effect of lowering the energy expectation value. Then, VQE is performed using the ansatz circuit 66. This allows the number of quantum gate boxA to be reduced without sacrificing calculation accuracy.

[0149] Fig. 16 is a diagram showing an example of functions for quantum chemical calculation in the fourth embodiment. Of the elements in Fig. 16, elements having the same functions as those in the second embodiment are given the same reference numerals as those in Fig. 7, and descriptions thereof will be omitted.

[0150] The classical computer 100b includes a quantum computation management unit 110, a quantum bit pair list creation unit 120, a quantum circuit generation unit 130b, a VQE execution unit 140, a valid pair selection unit 150a, and a derivative calculation unit 160. The classical computer 100b according to the fourth embodiment differs from the second embodiment in the processing of the quantum circuit generation unit 130b with the same name, and also includes a derivative calculation unit 160 and a valid pair selection unit 150a.

[0151] When the quantum circuit generation unit 130b obtains the quantum bit pair list from the quantum bit pair list creation unit 120, it generates an ansatz circuit corresponding to each quantum bit pair in the quantum bit pair list. The generated ansatz circuit is an ansatz circuit that causes the quantum gate boxA to act only on the corresponding quantum bit pair. The quantum circuit generation unit 130b transmits multiple quantum circuits for VQE, including each of the generated ansatz circuits, to the derivative calculation unit 160.

[0152] Furthermore, when the quantum circuit generation unit 130b acquires a list of quantum bit pairs (valid pairs) valid for calculating the energy expectation value from the valid pair selection unit 150a, it generates an ansatz circuit that causes the quantum gate boxA to act on the valid pairs. Then, the quantum circuit generation unit 130b transmits the quantum circuit for VQE, including the generated ansatz circuit, to the VQE execution unit 140.

[0153] The differential coefficient calculation unit 160 acquires the quantum circuit for each quantum bit pair from the quantum circuit generation unit 130b, and causes the quantum computer 200 to execute the quantum circuit using different values ​​of the parameter θ. The differential coefficient calculation unit 160 calculates the differential coefficient of the energy expectation value for each quantum bit pair at parameter θ=0, based on the energy expectation value obtained as a result of executing the quantum circuit. The differential coefficient calculation unit 160 then transmits the differential coefficient of the energy expectation value for each quantum bit pair to the valid pair selection unit 150a.

[0154] The valid pair selection unit 150a determines whether or not applying the quantum gate boxA to a quantum bit pair is effective in improving the accuracy of the energy expectation value, based on the differential coefficient of the energy expectation value corresponding to the quantum bit pair. The valid pair selection unit 150a transmits a list of quantum bit pairs that it has determined to be valid as valid pairs to the quantum circuit generation unit 130b.

[0155] Next, the processing procedure of the quantum chemical calculation in the fourth embodiment will be specifically described. 17 is a flowchart showing an example of the procedure of quantum chemical calculation in the fourth embodiment. The process shown in FIG. 17 will be explained below in order of step number.

[0156] [Step S301] The quantum computing manager 110 acquires molecular information about the molecule for which a solution is to be obtained from the terminal device 400. The molecular information includes, for example, the number of orbitals of the molecule for which the ground state energy is to be obtained, the number of electrons in the molecule, the number of quantum bits used in VQE, and a Hamiltonian indicating the energy of the molecule.

[0157] [Step S302] The qubit pair list creation unit 120 identifies qubit pairs that are candidates for gate operation by quantum gate boxA in VQE, and creates a qubit pair list indicating the identified qubit pairs. For example, the qubit pair list creation unit 120 creates a qubit pair list "pairs={(i,j)}" that is a set of all pairs (i,j) where i is the qubit number corresponding to an occupied orbital and j is the qubit number corresponding to an unoccupied orbital.

[0158] [Step S303] The quantum circuit generation unit 130b and the differential coefficient calculation unit 160 cooperate to execute the processes of steps S304 to S306 for each quantum bit pair (i, j) included in the quantum bit pair list.

[0159] [Step S304] The quantum circuit generation unit 130b generates a quantum circuit C that generates a Hartree-Fock state. i,j Create a. [Step S305] The quantum circuit generation unit 130b generates a quantum gate boxA that acts on the quantum bit pair (i, j) to be processed in the quantum circuit C i,j and calculates the expectation value of the energy of the affected state. i,j Create a.

[0160] [Step S306] The derivative calculation unit 160 executes an energy expectation derivative calculation process in cooperation with the quantum computer 200. The energy expectation derivative calculation process will be described in detail later (see FIG. 18). The calculated energy expectation derivative is sent to the valid pair selection unit 150a.

[0161] [Step S307] If the differential coefficients of the energy expectation values ​​have been calculated for all quantum bit pairs (i, j), the quantum circuit generation unit 130b proceeds to step S308.

[0162] [Step S308] The valid pair selection unit 150a calculates the differential coefficient D i,j For example, the effective pair selection unit 150a generates an effective pair list (EffectivePairs) based on the differential coefficient D of the energy expectation value. i,j For each, the absolute value of the derivative |D i,j | is the threshold D thres The valid pair selection unit 150a then compares the absolute value of the differential coefficient |D i,j | is the threshold D thres The list of qubit pairs that satisfies the above is called the effective pair list (EffectivePairs={(i,j)|abs(dH i,j (θ) / dθ|θ=0)≦D thres}).

[0163] [Step S309] The quantum circuit generation unit 130b generates a quantum circuit C that generates a Hartree-Fock state. final Create a. [Step S310] The quantum circuit generation unit 130b generates quantum gate boxA that operates on all quantum bit pairs shown in the effective pair list “EffectivePairs={(i,j)}” as the quantum circuit C final and calculates the expectation value of the energy of the affected state. final Create a.

[0164] [Step S311] The VQE execution unit 140 cooperates with the quantum computer 200 to generate the quantum circuit C final The VQE execution unit 140 executes the VQE using the trial state shown in initial is set to “0.” When the VQE execution is completed, the VQE execution unit 140 transmits the expected value of the energy obtained from the VQE execution result to the quantum computation management unit 110.

[0165] [Step S312] The quantum computing manager 110 outputs the energy expectation value E. For example, the quantum computing manager 110 transmits the energy expectation value E to the terminal device 400 as the execution result of VQE.

[0166] Next, the energy expectation differential coefficient calculation process will be described in detail. 18 is a flowchart showing an example of the procedure for calculating the energy expected value derivative coefficient. The process shown in FIG. 18 will be described below in order of step number.

[0167] [Step S321] The differential coefficient calculation unit 160 calculates the energy expectation value “H i,j (0)=<Ψ i,j (0)|H|Ψ i,j As a result, the differential coefficient calculation unit 160 obtains the energy expectation value when the parameter θ=0 from the quantum computer 200.

[0168] [Step S322] The differential coefficient calculation unit 160 sends the quantum computer 200 the energy expectation value “H i,j (δ)=<Ψ i,j (δ)|H|Ψ i,j (δ)> (δ is a predetermined real value). As a result, the differential coefficient calculation unit 160 obtains from the quantum computer 200 the energy expectation value when the parameter θ=δ.

[0169] [Step S323] The differential coefficient calculation unit 160 calculates the differential coefficient "dH i,j (θ) / dθ| θ=0 " is calculated. In this way, VQE can be performed using an ansatz circuit that operates the quantum gate boxA only on quantum bit pairs that are effective in improving the accuracy of the energy expectation value. As a result, the number of quantum gate boxA can be reduced without reducing the accuracy of the energy expectation value. Moreover, in the fourth embodiment, the calculation for determining quantum bit pairs that are effective in improving the accuracy of the energy expectation value is easy, and processing efficiency is improved compared to the third embodiment.

[0170] 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. For example, similar functions can be realized using a program product executed on a computer. Also, other optional components or steps can be added. Furthermore, any two or more configurations (features) of the above-described embodiments can be combined. [Explanation of symbols]

[0171] 1. Quantum computers 2 Molecular information 3 Quantum circuit 3a ansatz circuit 4a~4j 2-qubit gates 10. Information processing equipment 11 Storage section 12 Processing section

Claims

1. creating a plurality of quantum bit pairs, each of which is a combination of a first quantum bit corresponding to a first orbital in which an electron exists in an initial configuration and a second quantum bit corresponding to a second orbital in which an electron does not exist in the initial configuration, from among a plurality of quantum bits indicating the presence or absence of an electron occupying each of a plurality of orbitals of the molecule; a quantum circuit that causes a two-qubit gate to generate a superposition state of a first state in which the states of the first qubit and the second qubit are not swapped and a second state in which the states are swapped, according to a parameter value, to act on at least some of the plurality of qubit pairs; and acquiring an energy expectation value in the ground state of the molecule by repeatedly executing the quantum circuit on a quantum computer while updating the parameter values ​​of the two-qubit gate. A quantum computing control program that causes a computer to execute processing.

2. In the process of generating the quantum circuit, an evaluation value relating to the effect of reducing the energy expectation value of the molecule by operating the two-qubit gate is calculated for each of the plurality of qubit pairs, and the qubit pair on which the two-qubit gate is to operate is determined based on the evaluation value. The quantum computing control program according to claim 1.

3. In the process of generating the quantum circuit, each of the plurality of quantum bit pairs is used as an evaluation target, and an evaluation quantum circuit is generated in which the two-qubit gate is applied to the quantum bit pair to be evaluated and the two-qubit gate is not applied to quantum bit pairs that are not the evaluation target, and the evaluation quantum circuit is repeatedly executed by the quantum computer while updating the parameter values ​​of the two-qubit gate, and the evaluation value is set to an expected energy value obtained. The quantum computing control program according to claim 2.

4. In the process of generating the quantum circuit, each of the plurality of quantum bit pairs is evaluated, and an evaluation quantum circuit is generated in which the two-qubit gate acts on the quantum bit pair to be evaluated and the two-qubit gate does not act on quantum bit pairs that are not to be evaluated, and the evaluation quantum circuit is executed on the quantum computer to obtain a differential coefficient of the energy expectation value when the parameter of the two-qubit gate is a predetermined value, and the obtained differential coefficient is used as the evaluation value. The quantum computing control program according to claim 2.

5. In the process of creating the plurality of quantum bit pairs, creation of the quantum bit pair between the first quantum bit corresponding to the first orbital in which electrons of α spin can be arranged and the second quantum bit corresponding to the second orbital in which electrons of β spin can be arranged is suppressed, and creation of the quantum bit pair between the first quantum bit corresponding to the first orbital in which electrons of β spin can be arranged and the second quantum bit corresponding to the second orbital in which electrons of α spin can be arranged is suppressed. The quantum computing control program according to claim 1.

6. creating a plurality of quantum bit pairs, each of which is a combination of a first quantum bit corresponding to a first orbital in which an electron exists in an initial configuration and a second quantum bit corresponding to a second orbital in which an electron does not exist in the initial configuration, from among a plurality of quantum bits indicating the presence or absence of an electron occupying each of a plurality of orbitals of the molecule; a quantum circuit that causes a two-qubit gate to generate a superposition state of a first state in which the states of the first qubit and the second qubit are not swapped and a second state in which the states are swapped, according to a parameter value, to act on at least some of the plurality of qubit pairs; and acquiring an energy expectation value in the ground state of the molecule by repeatedly executing the quantum circuit on a quantum computer while updating the parameter values ​​of the two-qubit gate. A quantum computing control method in which processing is performed by a computer.

7. a processing unit that generates a plurality of quantum bit pairs, each pair combining a first quantum bit corresponding to a first orbital in which an electron exists in an initial configuration and a second quantum bit corresponding to a second orbital in which no electron exists in the initial configuration, among a plurality of quantum bits that indicate the presence or absence of an electron occupying each of a plurality of orbitals of a molecule, and that generates a quantum circuit that causes a two-qubit gate that generates a superposition state, according to a value of a parameter, between a first state in which the states of the first quantum bit and the second quantum bit are not swapped and a second state in which the states are swapped, to act on at least some of the plurality of quantum bit pairs, and that acquires an expected energy value in the ground state of the molecule by repeatedly executing the quantum circuit on a quantum computer while updating the value of the parameter of the two-qubit gate; An information processing device having the above.

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