Quantum computing assistance program, quantum computing assistance method, and information processing apparatus

Abstract

To reduce the effect of VQE errors.SOLUTION: An information processing apparatus 10 classifies a plurality of observables into one of multiple groups that group together observables that can be measured simultaneously. The information processing apparatus 10 generates a first quantum circuit 1 including a first basis conversion circuit 1b for enabling simultaneous measurement of a plurality of first observables belonging to a first group. The information processing apparatus 10 generates a second quantum circuit 2 including a second basis conversion circuit 2b in which a second two-qubit gate 2c that performs the same gate operation as a first two-qubit gate 1c included in the first basis conversion circuit 1b is placed. The information processing apparatus 10 causes a quantum computer 9 to execute the first quantum circuit 1 and the second quantum circuit 2, and performs reinterpretation of the measurement result of the second quantum circuit 2 in accordance with the second two-qubit gate 2c. The information processing apparatus 10 calculates a Hamiltonian using the measurement results.SELECTED DRAWING: Figure 1

Description

[Technical Field]

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

[0002] In the field of quantum computers, there are high hopes for the practical application of NISQ (Noisy Intermediate-Scale Quantum computer). NISQ is a medium-scale quantum computer without error correction capabilities. One of the applications of NISQ is calculations using the Variational Quantum Eigensolver (VQE). VQE is a variational algorithm that finds the ground state of a quantum many-body system. VQE can be used, for example, to perform quantum chemistry calculations on NISQ. Quantum chemistry calculations are calculations that obtain information on molecular states and physical properties by solving the Schrödinger equation. Currently, various research efforts are underway to put VQE-based calculations into practical use.

[0003] One of the problems facing practical use of VQE is that the calculation accuracy deteriorates due to noise from the hardware. NISQ does not have an error correction function, and errors can cause inaccuracies in the calculation results.

[0004] As a countermeasure against errors, systems have been proposed to mitigate errors due to sampling in quantum devices. A system for error reduction through circuit gauge selection has also been proposed. A technique has also been proposed to reduce unitary errors during quantum instruction execution in a system that randomly accesses a set of quantum gates related to any quantum gate included in a quantum instruction set. Furthermore, a device has been proposed that actively mitigates coherent errors by inserting Clifford gate operations at intermediate stages and modifying the original quantum circuit. [Prior art documents] [Patent documents]

[0005] [Patent Document 1] Japanese Patent Publication No. 2023-035941 [Patent Document 2] Special Publication No. 2023-501752 [Patent Document 3] US Patent Application Publication No. 2021 / 0294680 [Patent Document 4] US Patent Application Publication No. 2023 / 0016817 Summary of the Invention [Problem to be solved by the invention]

[0006] In VQE, multiple quantum circuits are executed as part of the algorithm. At this time, the impact of errors on each of the multiple quantum circuits executed varies. If the impact of errors on each quantum circuit differs, the error mitigation function of VQE will not work well, and the impact of errors will remain significant on the final calculation value (basis energy). If the impact of the remaining errors is large, the calculation result will be inaccurate.

[0007] In one aspect, the present invention aims to reduce the impact of errors in VQE. [Means for solving the problem]

[0008] One proposal provides the following quantum computing assistance program: The computer classifies multiple observables used to calculate a Hamiltonian corresponding to a problem to be solved using the variational quantum eigenvalue method into one of multiple groups that group together simultaneously measurable observables. The computer generates a first quantum circuit including a first basis conversion circuit for making multiple first observables belonging to the first group simultaneously measurable. The computer generates a second quantum circuit including a second basis conversion circuit in which a quantum gate for making multiple second observables belonging to a second group simultaneously measurable and a second two-qubit gate that performs the same gate operation as the first two-qubit gate included in the first basis conversion circuit are arranged. The computer acquires measurement results of the multiple first observables by having the quantum computer execute the first quantum circuit. The computer acquires measurement results of the multiple second observables by interpreting the measurement results obtained by having the quantum computer execute the second quantum circuit according to the second two-qubit gate. The computer then calculates a Hamiltonian using measurement results of the plurality of first observables and the plurality of second observables. [Effects of the Invention]

[0009] According to one aspect, the effect of errors in VQE can be reduced. [Brief explanation of the drawings]

[0010] [Figure 1] FIG. 1 is a diagram illustrating an example of a quantum computing assistance method according to a first embodiment. [Figure 2] FIG. 10 illustrates an example of a system configuration according to a second embodiment. [Figure 3] FIG. 1 is a diagram illustrating an example of hardware of a device that constitutes a quantum computing system. [Figure 4] FIG. 1 is a block diagram showing an example of the functions of a classical computer for quantum chemical calculations using VQE. [Figure 5] FIG. 1 is a diagram showing an example of quantum chemistry calculation using VQE. [Figure 6]FIG. 1 is a diagram illustrating an example of a quantum circuit configuration for VQE calculation. [Figure 7] FIG. 10 is a diagram illustrating an example of additional processing of the basis conversion circuit for observables of "pattern 1." [Figure 8] FIG. 10 is a diagram illustrating an example of additional processing of the basis conversion circuit for observables of "pattern 2." [Figure 9] FIG. 10 is a diagram illustrating an example of additional processing of the basis conversion circuit for an observable of "pattern 3." [Figure 10] FIG. 10 is a diagram showing an example of how to interpret measurement results when a CNOT gate is added. [Figure 11] FIG. 10 is a diagram illustrating an example of a quantum circuit for each divided Hamiltonian. [Figure 12] 10 is a flowchart illustrating an example of a procedure for VQE calculation processing. [Figure 13] 10 is a flowchart showing an example of a procedure for generating a basis conversion circuit (common part). [Figure 14] Basis conversion circuit ( <hi>10 is a flowchart illustrating an example of a procedure for generating a unique portion. [Figure 15] <hi>10 is a flowchart illustrating an example of a procedure for an expected value calculation process. [Figure 16] FIG. 1 is a diagram illustrating an example of an Ansatz circuit. [Figure 17] FIG. 10 is a diagram illustrating an example of a common part of a basis conversion circuit. [Figure 18] <h1>FIG. 1 illustrates an example of a quantum circuit for computation. [Figure 19] < / h1> <h2>FIG. 1 illustrates an example of a quantum circuit for computation. DETAILED DESCRIPTION OF THE INVENTION

[0011] 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 computing assistance method that reduces the difference in the effect of errors among multiple quantum circuits executed in the VQE, thereby reducing the effect of errors in the entire VQE.

[0012] Fig. 1 is a diagram illustrating an example of a quantum-assisted computing method according to a first embodiment. Fig. 1 illustrates an information processing device 10 that implements the quantum-assisted computing method. The information processing device 10 can implement the quantum-assisted computing method by, for example, executing a quantum-assisted computing program.

[0013] 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.

[0014] The storage unit 11 stores, for example, a quantum computing support program. The storage unit 11 also stores data on the problem to be solved, intermediate data generated in the process of executing the quantum computing support program, expected values ​​of energy output as execution results, and the like.

[0015] The processing unit 12 uses the quantum computer 9 to calculate a Hamiltonian corresponding to the problem to be solved by VQE. For example, the processing unit 12 classifies multiple observables used in calculating the Hamiltonian into one of multiple groups that group together observables that can be measured simultaneously. In the example of FIG. 1, a first group and a second group are generated. The first group includes observables (XX or YY) calculated using the X-basis measurement results or Y-basis measurement results of the a-th and b-th quantum bits (a and b are natural numbers). The second group includes observables calculated using the Z-basis measurement results for one or more quantum bits.

[0016] The processing unit 12 generates a quantum circuit for each group. For example, the processing unit 12 generates a first quantum circuit 1 that can simultaneously measure observables belonging to a first group. The first quantum circuit 1 includes an Ansatz circuit 1a that represents a wave function and a first basis conversion circuit 1b that enables simultaneous measurement of multiple first observables belonging to the first group. The first basis conversion circuit 1b includes, for example, a first two-qubit gate 1c (CNOT gate) and a one-qubit gate 1d (Hadamard gate).

[0017] Furthermore, the processing unit 12 generates a second quantum circuit 2 capable of simultaneously measuring observables belonging to a second group. The second quantum circuit 2 includes an Ansatz circuit 2a representing a wave function and a second basis conversion circuit 2b for enabling simultaneous measurement of observables belonging to the second group. In addition to a quantum gate for enabling simultaneous measurement of multiple second observables belonging to the second group, the processing unit 12 is also provided with a second two-qubit gate 2c that performs the same gate operation as the first two-qubit gate 1c included in the first basis conversion circuit 1b.

[0018] Processing unit 12 acquires measurement results of a plurality of first observables by having quantum computer 9 execute first quantum circuit 1. Processing unit 12 also acquires measurement results of a plurality of second observables by interpreting measurement results obtained by having quantum computer 9 execute second quantum circuit 2 in accordance with second two-qubit gate 2c.

[0019] The reinterpretation according to the second two-qubit gate 2c is a process of calculating the state that would occur if the second two-qubit gate 2c were not operated, for example, based on the measurement results. For example, if the second two-qubit gate 2c is a CNOT gate, the state of the qubits when the CNOT gate is again applied to the qubit pair that has been acted upon by the second two-qubit gate 2c becomes the reinterpreted state.

[0020] Then, the processing unit 12 calculates a Hamiltonian using measurement results of the plurality of first observables and the plurality of second observables. For example, the processing unit 12 repeats the calculation of the Hamiltonian using the quantum computer 9 while updating the values ​​of the parameters included in the Ansatz circuits 1a and 2a until the value of the Hamiltonian converges. The processing unit 12 outputs the value of the Hamiltonian when the value of the Hamiltonian converges as the expected value of energy in the problem to be solved.

[0021] In this way, the similarity between multiple quantum circuits used in VQE can be increased. In the example of Figure 1, the first quantum circuit 1 and the second quantum circuit 2 have the same two-qubit gate configuration. The difference between the first quantum circuit 1 and the second quantum circuit 2 is the presence or absence of the one-qubit gate 1d. However, the probability of an error occurring in the gate operation of the one-qubit gate 1d is lower than the gate operation of the two-qubit gate. Therefore, it can be said that the impact of errors in the first quantum circuit 1 and the second quantum circuit 2 is equivalent. Furthermore, because the impact of errors in the first quantum circuit 1 and the second quantum circuit 2 is equivalent, the error mitigation function in the VQE can be effectively used, reducing the impact of errors on the VQE calculations.

[0022] Note that a second two-qubit gate 2c that is not required for simultaneous measurement of multiple second observables belonging to the second group is added to second quantum circuit 2. Therefore, although the measurement results of second quantum circuit 2 do not directly represent the multiple second observables, processing unit 12 can obtain the measurement results of the multiple second observables by reinterpreting the measurement results of second quantum circuit 2.

[0023] The processing unit 12 generates a third quantum circuit 3 that indicates a gate operation common to the first quantum circuit 1 and the second quantum circuit 2, and can generate the first quantum circuit 1 and the second quantum circuit 2 based on the third quantum circuit 3. For example, the processing unit 12 generates the third quantum circuit 3 that includes a third basis conversion circuit 3b in which a third two-qubit gate 3c corresponding to any of a plurality of observables is arranged following an Ansatz circuit 3a.

[0024] The processing unit 12 generates the first quantum circuit 1 by adding a quantum gate that is missing in order to enable simultaneous measurement of multiple first observables to the third basis conversion circuit 3b of the third quantum circuit 3. In the example of Fig. 1, a one-qubit gate 1d is added.

[0025] Furthermore, the processing unit 12 generates the second quantum circuit 2 by adding quantum gates that are missing in order to enable simultaneous measurement of multiple second observables to the third basis transformation circuit 3b of the third quantum circuit 3. In the example of Fig. 1, there are no quantum gates that are missing in order to enable simultaneous measurement of multiple second observables, so a second quantum circuit 2 with the same configuration as the third quantum circuit 3 is generated.

[0026] In this way, by generating the first quantum circuit 1 and the second quantum circuit 2 based on the third quantum circuit 3 that exhibits a common gate operation, the first quantum circuit 1 and the second quantum circuit 2 can be generated efficiently.

[0027] The processing unit 12 can generate the third quantum circuit 3, for example, in the following procedure. The processing unit 12 selects each of the multiple observables in turn. Next, if the third two-qubit gate 3c corresponding to the selected observable has not been placed in the third basis conversion circuit 3b, the processing unit 12 places the third two-qubit gate 3c corresponding to the selected observable in the third basis conversion circuit 3b. Note that if the state to be measured by the selected observable is only in the Z basis, the processing unit 12 determines that the corresponding two-qubit gate is unnecessary. In this way, if there is a corresponding two-qubit gate for each of the multiple observables, the corresponding two-qubit gate is placed in the third quantum circuit 3 without any omissions. As a result, the configurations of the first quantum circuit 1 and the second quantum circuit 2 can be shared to the maximum extent possible.

[0028] Furthermore, when a two-qubit gate is placed in the third quantum circuit 3, the processing unit 12 may set the pair of two qubits acting on the two qubits as the target of replacement. For example, the processing unit 12 places in the third basis conversion circuit 3b a third two-qubit gate 3c that acts on a pair of two qubits that are to be measured in the X basis or the Y basis in one first observable among the plurality of first observables. Then, the processing unit 12 sets the pair of qubits that are to be acted on by the third two-qubit gate 3c as the target of replacement.

[0029] The processing unit 12 determines whether the first two-qubit gate 1c, which acts on the pair of two qubits to be measured in the X basis or the Y basis in the first observable, has already been placed in the third basis conversion circuit 3b. If the first two-qubit gate 1c has already been placed, the processing unit 12 excludes the pair of qubits from being subject to reinterpretation (reinterpretation cancellation) for the measurement results obtained by executing the first quantum circuit 1. By canceling the reinterpretation in this way, erroneous reinterpretation of the measurement results is prevented.

[0030] Second Embodiment The second embodiment is a quantum computing system that can reduce the influence of errors on the results of quantum computing when performing quantum chemical calculations by VQE using a quantum computer.

[0031] 2 is a diagram illustrating an example of a system configuration according to the second embodiment. In the second embodiment, a quantum computing system 300 and a terminal device 31 are connected via a network 20. The terminal device 31 transmits a quantum computing request to the quantum computing system 300 in response to an operation by a user.

[0032] The quantum computing system 300 includes a classical computer 100 and a quantum computer 200. The classical computer 100 and the quantum computer 200 are connected via a communication interface. The classical computer 100 is a von Neumann-type computer that performs processes such as generating quantum circuits and optimizing parameters used in quantum circuit calculations. The quantum computer 200 is a computer that performs quantum chemistry calculations by performing operations based on quantum gates on quantum bits. The quantum computer 200 performs quantum chemistry calculations of the VQE algorithm according to the quantum circuits and parameters generated by the classical computer 100.

[0033] 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).

[0034] 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.

[0035] 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.

[0036] 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).

[0037] 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.

[0038] 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.

[0039] 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.

[0040] 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.

[0041] 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.

[0042] 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.

[0043] 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.

[0044] 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.

[0045] Quantum computer 200 includes a control device 210 and a quantum device 220. Control device 210 executes gate operations on quantum bits in the quantum device according to a quantum circuit. Quantum device 220 includes multiple quantum bits. Quantum device 220 is, for example, a quantum processing unit (QPU).

[0046] In the quantum computing system 300, a classical computer 100 and a quantum computer 200 operate in cooperation with each other to perform quantum chemical computations using VQE. 4 is a block diagram showing an example of the functions of a classical computer for quantum chemical calculations using VQE. The classical computer 100 includes a quantum circuit generation unit 110, a quantum calculation management unit 120, a basis energy calculation unit 130, and an optimization calculation unit 140.

[0047] The quantum circuit generation unit 110 generates a quantum circuit for calculating the energy of a quantum many-body system such as a molecule. For example, the quantum circuit generation unit 110 generates a quantum circuit using a VQE algorithm. The quantum circuit generation unit 110 transmits the generated quantum circuit to the quantum computation management unit 120.

[0048] The quantum computation manager 120 instructs the quantum computer 200 to compute an observable based on the generated quantum circuit and to measure the state of the quantum bit. For example, before the first quantum computation, the quantum computation manager 120 sets initial values ​​for the values ​​of multiple parameters θ. The quantum computation manager 120 acquires information indicating the computation results of the observable based on the quantum circuit parameterized by the multiple parameters θ from the quantum computer 200. The quantum computation manager 120 instructs the quantum computer 200 to repeatedly compute the observable until a predetermined number of shots (the number of computations required to obtain a valid observable) is reached.

[0049] The ground state energy calculation unit 130 calculates the ground state energy based on the calculation results of the observables. For example, the ground state energy calculation unit 130 calculates a Hamiltonian based on the values ​​of the observables that are repeatedly measured. If the value of the Hamiltonian has converged, the ground state energy calculation unit 130 outputs the value of the Hamiltonian as the ground state energy. If the value of the Hamiltonian has not converged, the ground state energy calculation unit 130 instructs the optimization calculation unit 140 to optimize the parameters.

[0050] The basis energy calculation unit 130 may determine whether an error has occurred based on information indicating the state of the parity-check quantum bit. If an error has occurred, the basis energy calculation unit 130 discards the measurement values ​​of the observables acquired at the same time. By discarding the measurement values ​​when an error has occurred in this way, the impact of the error is mitigated.

[0051] The optimization calculation unit 140 updates all or part of the values ​​of the parameters θ for each quantum calculation so that the energy value decreases. When the optimization calculation is completed, the optimization calculation unit 140 notifies the quantum calculation management unit 120 of the updated values ​​of the parameters θ.

[0052] The functions of each element in the classical computer 100 shown in FIG. 4 can be realized, for example, by causing the computer to execute a program module corresponding to that element. FIG. 5 is a diagram showing an example of quantum chemistry calculation using VQE. In quantum chemistry calculation using VQE, a quantum computer 200 performs quantum measurement based on the initial value of a parameter θ (a set of circuit variables corresponding to electronic excitations). That is, the quantum computer 200 calculates a plurality of divided Hamiltonians (H1, H2, . . . , H N ) are calculated (N is a natural number). The quantum circuit 30 used for quantum measurement includes an Ansatz circuit. The calculated multiple Hamiltonians are added together in the classical computer 100 to obtain the expected value of the energy of the entire system. Then, the optimization calculation unit 140 in the classical computer 100 optimizes the parameter θ based on the expected value of the energy. In other words, the optimization calculation unit 140 updates the parameter θ in a direction that reduces the expected value of the energy. When the parameter θ is updated, the quantum computer 200 again calculates a Hamiltonian based on the updated parameter θ.

[0053] This calculation of the Hamiltonian and updating of the parameter θ are repeated until the ground state energy is obtained. The energy E required in the ground state calculation of a molecule using VQE is expressed by the following formula (1).

[0054]

number

[0055]

number

[0056] Each decomposed Hamiltonian H i (i=1,2,...) is the sum of real multiples of observables that can be measured by one quantum circuit, "H i =aO i1 +bO i2 +···" (a and b are real numbers). i1 ,O i2 ,··· is an observable of the i-th Hamiltonian. The observable is Z 0, It is expressed as X0Z1X2, where Z0 is the Z-basis measurement result of the 0th qubit. X0Z1X2 is the tensor product of the X-basis measurement result of the 0th qubit, the Z-basis measurement result of the 1st qubit, and the X-basis measurement result of the 2nd qubit.

[0057] The quantum circuits that make up VQE include circuits called Ansatz, which make up the majority of the VQE quantum circuit. Ansatz is a circuit that represents the wave function ψ(θ) parameterized by variables in a quantum circuit.

[0058] In VQE, one quantum bit represents the state indicating whether or not an up-spin electron is present in a certain molecular orbital. Another quantum bit represents the state indicating whether or not a down-spin electron is present in that molecular orbital. Each quantum bit is in a "1" state when an electron with the spin corresponding to the corresponding molecular orbital is present, and in a "0" state when no electron is present. The states indicating the presence or absence of up-spin electrons and the states indicating the presence or absence of down-spin electrons in the molecular orbital are assigned to adjacent quantum bits in the quantum circuit. For example, up-spin electrons are assigned to even-numbered quantum bits (even quantum bits), and down-spin electrons are assigned to odd-numbered quantum bits (odd quantum bits).

[0059] Here, we will explain the influence of errors in VQE calculations using quantum computer 200. Errors that affect calculation results include thermal relaxation errors, gate operation errors, and measurement errors (readout errors). Thermal relaxation errors are errors that cause the quantum state to be lost over time and return to the initial state |0>. Gate operation errors are errors that arise when gate operations are not ideally accurate, causing the quantum bit state to deviate from the intended operation. Measurement errors are errors that occur during measurements after gate processing, and this error can lead to the |0> state being misread as |1>, or the |1> state being misread as |0>.

[0060] These errors can cause errors in the results of quantum computations. This can be fatal for computations on NISQ, which lacks error correction capabilities. Therefore, it is important to mitigate the effects of errors as much as possible.

[0061] The impact of errors in VQE can be reduced by error mitigation functions such as parity checks. However, VQE's algorithm involves running multiple quantum circuits, and the impact of hard errors varies for each quantum circuit. If the impact of errors varies, the error mitigation functions built into VQE may not work properly. If the error mitigation functions do not work correctly, the impact of errors will remain significant in the final calculation value (basis energy).

[0062] Therefore, the quantum computing system 300 reduces the influence of errors without using auxiliary quantum bits in multiple quantum circuits. For example, the quantum computing system 300 unifies the basis conversion circuits of multiple quantum circuits as much as possible.

[0063] The basis conversion circuit is a circuit that converts the output of the Ansatz so that the Z basis (computational basis), X basis (Hadamard basis), or Y basis (circular basis) included as an element in the observable to be calculated can be measured. In the quantum computer 200, only the Z basis can be measured by hardware. Therefore, when measuring the X basis or Y basis, the state of the qubit is converted so that the state of those bases can be projected onto the Z axis, for example, onto the Z basis, and then the Z basis measurement is performed.

[0064] Furthermore, among the multiple observables to be calculated when the VQE Hamiltonian is divided into multiple Hamiltonians, there are observables that can be measured simultaneously using a common quantum circuit. In VQE calculations, if simultaneously measurable observables are measured at the same time using the same quantum circuit, the calculation of the basis energy using VQE becomes efficient. When simultaneously measurable observables are measured using a common quantum circuit, a basis conversion is performed using a two-qubit gate or a one-qubit gate in the basis conversion circuit corresponding to the observable to be measured.

[0065] For example, when the Hamiltonian to be calculated, which is generated under the Jordan-Wigner transformation, is decomposed into observable form, the observables can be divided into the following three patterns.

[0066] [Pattern 1] An observable consisting only of the tensor product of Z and I (I is the identity operator) [Pattern 2] (X or Y) k Z k+1 ···Z l-1 (X or Y) l Z p (X or Y) k Z k+1 ···Z l-1 (X or Y) l (X or Y) k Z k+1 ···Z l-1 (X or Y) l Z p [Pattern 3] (X or Y) k Z k+1 ···Z l-1 (X or Y) l (X or Y) p Z p+1 ···Z q-1 (X or Y) q k, l, p, and q are integers greater than or equal to 0 that indicate the quantum bit numbers in the quantum circuit. k+1 ···Z l-1 " indicates an odd number of consecutive Zs. In other words, in "Pattern 2," if k is even, then l is also even, and if k is odd, then l is also odd.

[0067] For "Pattern 3", "Z k+1 ···Z l-1 " and "Z p+1 ···Z q-1 " indicates an even number of Zs in a row. In other words, in "Pattern 3", if k is even, then p is also even, and l and p are odd. Also, in "Pattern 3", if k is odd, then p is also odd, and l and p are even.

[0068] Of these three patterns of observables, those that are commutative (satisfy the commutation relation) can be measured simultaneously. The commutation relation means that the Pauli matrices corresponding to the qubits with the same qubit number for each of the two observables are "σ i σ j -σ j σ i = 0". σ is the Pauli matrix (σ x If both are the same Pauli matrix, they commute. If one is I, they also commute. If both are X, Y, or Z and have different Pauli matrices, they do not commute.

[0069] "Observables as a whole commit" means that the Pauli matrices for the same numbered qubits are compared to determine whether they are commutative or non-commutative, and there is an even number of non-commutative matrices. For example, when considering "I0Y1X2" and "Z0Z1Z2", "I0Z0=Z0I0" (commutative), "Y1Z1=-Z1Y1" (non-commutative), and "X2Z2=-Z2X2" (non-commutative). In this case, since there are two non-commutative matrices, the overall result is "I0Y1X2Z0Z1Z2=Z0Z1Z2I0Y1X2", which means they are commutative.

[0070] Specifically, the quantum circuit generation unit 110 decomposes the Hamiltonian into groups that can be simultaneously measured as follows. [About Pattern 1] The quantum circuit generation unit 110 treats all observables consisting of only Z as being in the same group.

[0071] [About Pattern 2] Pattern 2 is "(XorY) k Z k+1 ···Z l-1 (X or Y) l "," "Z p (X or Y) k Z k+1 ···Z l-1 (X or Y) l ", "(XorY) k Z k+1 ···Z l-1 (X or Y) l Z p " is an observable that can be expressed either as

[0072] The quantum circuit generation unit 110 groups, among the observables of pattern 2, multiple observables that share a common quantum bit (k, l) that performs an X-basis or Y-basis measurement and whose measurement content is XX or YY. For example, the quantum circuit generation unit 110 groups "X0Z1X2" and "Y0Z1Y2" in the same group. "X0Z1Z2X3" has one of the quantum bits that performs an X-basis or Y-basis measurement that is different from the aforementioned group. Therefore, the quantum circuit generation unit 110 groups "X0Z1Z2X3" separately from the group {X0Z1X2, Y0Z1Y2}.

[0073] Furthermore, quantum circuit generation unit 110 groups together, among the observables of pattern 2, multiple observables that share a common quantum bit (k, l) that performs measurement in the X basis or the Y basis, and whose measurement content is XY or YX.

[0074] [About Pattern 3] Pattern 3 is "(XorY) k Z k+1 ···Z l-1 (X or Y) l (X or Y) p Z p+1 ···Z q-1 (X or Y) q " is an observable expressed as

[0075] The quantum circuit generation unit 110 groups observables of pattern 3 that have the same k, l, p, and q and that commute as a whole into the same group. In order to perform simultaneous measurements of multiple observables, the quantum circuit generation unit 110 adds a basis conversion circuit using a two-qubit gate so that the result of the tensor product of the states of multiple qubits can be measured as the state of a single qubit.

[0076] Figure 6 shows an example of a quantum circuit configuration for VQE calculations. Quantum circuits 41, 42, 43,... are prepared for each Hamiltonian after division. Quantum circuits 41, 42, 43,... include a common Ansatz circuit. Furthermore, each of quantum circuits 41, 42, 43,... has a basis conversion circuit added after the Ansatz circuit that corresponds to the observable being calculated. The basis conversion circuit is divided into a two-qubit gate group section and a one-qubit gate group section.

[0077] 7 is a diagram showing an example of the process of adding a basis conversion circuit for the observable of "Pattern 1." When measuring the observable of "Pattern 1," the observable can be obtained from the measurement results by performing Z measurements on all quantum bits after executing the Ansatz circuit 40a. Therefore, there is no need to add a quantum conversion circuit.

[0078] 8 is a diagram showing an example of additional processing of a basis conversion circuit for an observable of "Pattern 2." For an observable of "Pattern 2," the basis conversion circuit after Ansatz circuit 40a differs depending on whether the measurement target of the quantum bit pair of the kth quantum bit and the lth quantum bit is "XX" or "YY" or whether it is "XY" or "YX."

[0079] When the measurement target of the quantum bit pair is "XX" or "YY," a basis conversion circuit 40b is added. In the basis conversion circuit 40b, a CNOT gate is placed between the kth quantum bit and the lth quantum bit, and a Hadamard gate is placed on the control quantum bit side of the CNOT gate.

[0080] When the basis conversion circuit 40b is added, the measurement result of the qubit on the control qubit side of the CNOT gate becomes "XX," and the measurement result of the qubit on the target qubit side of the CNOT gate becomes "ZZ." "YY" can be calculated using the formula "YY=-(XX)(ZZ)" based on the measurement result of the basis conversion circuit 40b.

[0081] When the measurement target of the quantum bit pair is "XY" or "YX," a basis conversion circuit 40c is added. In the basis conversion circuit 40c, a CNOT gate is placed between the kth quantum bit and the lth quantum bit, and a phase shift gate (S gate) and a Hadamard gate are placed on the control quantum bit side of the CNOT gate.

[0082] When the basis conversion circuit 40c is added, the measurement result of the qubit on the control qubit side of the CNOT gate becomes "XY," and the measurement result of the qubit on the target qubit side of the CNOT gate becomes "ZZ." "YX" can be calculated based on the measurement result of the basis conversion circuit 40c.

[0083] FIG. 9 is a diagram showing an example of the process of adding a basis conversion circuit for a "pattern 3" observable. In the case of a "pattern 3" observable, the kth qubit and the pth qubit are the qubit pair to which a basis conversion circuit is added. Similarly, the lth qubit and the qth qubit are also the qubit pair to which a basis conversion circuit is added. If the measurement target of each qubit pair is "XX" or "YY," a basis conversion circuit 40b is added. If the measurement target of each qubit pair is "XY" or "YX," a basis conversion circuit 40c is added.

[0084] As shown in Figures 7 to 9, in order to simultaneously measure a group of simultaneously measurable observables in a single quantum circuit, a basis conversion circuit including a CNOT gate is added. The one-qubit gate in the basis conversion circuit is less affected by noise than a two-qubit gate such as the CNOT gate. Therefore, if the configuration of the CNOT gate in the basis conversion circuit can be standardized, the influence of noise in the quantum circuits corresponding to each group including the simultaneously measurable observables can be equalized.

[0085] In order to standardize the configuration of the CNOT gates in the basis conversion circuit, the quantum circuit generation unit 110 adds an unnecessary CNOT gate to the quantum circuit of one of the groups. When such a CNOT gate is added, the basis energy calculation unit 130 reinterprets the measurement results for each quantum bit.

[0086] FIG. 10 is a diagram showing an example of how to interpret the measurement results when a CNOT gate is added. For example, the basis conversion circuit of the quantum circuit 41 of one of the two groups of simultaneously measurable observables includes a CNOT gate (CNOT ab ) and the basis conversion circuit of the quantum circuit 42 of the other group does not include a CNOT gate. In this case, the same CNOT gate (CNOT ab ) to quantum circuit 42, the difference in configuration between quantum circuit 41 and quantum circuit 42 is reduced.

[0087] The measurement results for quantum circuit 42a after the addition of the CNOT gate differ from those before the addition of the CNOT gate. Therefore, the basis energy calculation unit 130 reinterprets the measurement results for quantum circuit 42a according to the added CNOT gate. The quantum bit number of the control quantum bit of the added CNOT gate is set to "a", and the quantum bit number of the target quantum bit is set to "b". In this case, if the measurement result for quantum bit number "a" is |0>, the measurement result is used as is. If the measurement result for quantum bit number "a" is |1>, the measurement result |0> for quantum bit number "b" is reinterpreted as |1>, and the measurement result |1> for quantum bit number "b" is reinterpreted as |0>.

[0088] If the measurement result of the quantum bit with quantum bit number "a" is |x> and the measurement result of the quantum bit with quantum bit number "b" is |y>, the state of all quantum bits can be expressed as |···x···y···>. In this case, the interpretation is as follows: |···0···0···> → |···0···0···> |···0···1···> → |···0···1···> |···1···0···> → |···1···1···> |···1···1···> → |···1···0···> The quantum circuit generation unit 110 standardizes the configuration of the two-qubit gate groups of the basis conversion circuit as much as possible. If the two-qubit gate groups of the basis conversion circuit are identical quantum circuits, the effects of errors are considered to be approximately the same. Even if the two-qubit gate groups of the basis conversion circuit are not identical, if they are similar, the difference in the effects of errors will be smaller.

[0089] 11 is a diagram showing an example of a quantum circuit for each divided Hamiltonian. The quantum circuit generation unit 110 divides the Hamiltonian so that simultaneously measurable observables are combined into one Hamiltonian. If no process for reducing the differences in the configurations of the Hamiltonians is performed, quantum circuits 51a, 51b, 51c, 51d, 51e,... are generated for each post-division Hamiltonian. The quantum circuits 51a, 51b, 51c, 51d, 51e,... have the same Ansatz circuit, but differ in both the two-qubit gate group and the one-qubit gate group.

[0090] When the process of reducing the difference in configuration for each Hamiltonian is performed, quantum circuits 52a, 52b, 52c, 52d,..., 52k,... are generated. Quantum circuits 52a, 52b, 52c, 52d,... have the same two-qubit gate groups as the Ansatz circuit. Although quantum circuits 52a, 52b, 52c, 52d,... have different one-qubit gate groups, the impact of errors in one-qubit gates is smaller than that of two-qubit gates.

[0091] The two-qubit gate groups of quantum circuits 52k,... are different from but similar in configuration to quantum circuits 52a, 52b, 52c, 52d,... Therefore, the influence of errors between quantum circuits 52a, 52b, 52c, 52d,... and quantum circuit 52k,... is less than when processing to reduce the differences in configuration is not performed.

[0092] The reason why the influence of errors is reduced as the differences in quantum circuits are reduced can be explained as follows. Consider the case where there is one group after Hamiltonian division. In this case, assume that the wave function |ψ(θ)> has been affected by an error and has become |ψ'(θ')> (θ, θ' are real number parameters). In this case, the energy obtained is "E'(θ') = <ψ'(θ')|H|ψ'(θ')>". Although "|ψ'> ≠ |ψ>", the variational space is almost the same. Therefore, when performing a variational calculation, "E'(θ´) ≒ E(θ)" is obtained.

[0093] Consider the case where there are two groups after Hamiltonian division, and the quantum circuits between the groups are significantly different. The effect of errors differs depending on the quantum circuit, and the wave function |ψ(θ)> becomes "|ψ1'(θ1')>" in the first quantum circuit and "|ψ2'(θ2')>" in the second quantum circuit (θ1', θ2' are real parameters). In this case, "E'(θ')=<ψ1'(θ1')|H1|ψ1'(θ1')>+<ψ2'(θ2')|H2|ψ2'(θ2')>". In this example, there are two types of parameters, θ1' and θ2', making optimization difficult.

[0094] When the quantum circuits between the groups are identical except for the group of one-qubit gates in the basis conversion circuit, |ψ1”(θ1”)> holds for the wave functions of both the first and second quantum circuits. In this case, "E”(θ”)=<ψ1”(θ1”)|H1|ψ1”(θ1”)>+<ψ1”(θ1”)|H2|ψ1”(θ1”)>" (θ1” is a real parameter). Because there is only one parameter, θ1”, both groups can be optimized and successfully led to the minimum value.

[0095] The procedure for calculating VQE with reduced noise effects will be described in detail below. 12 is a flowchart showing an example of the VQE calculation process. The process shown in FIG. 12 will be explained below in order of step number.

[0096] [Step S101] The quantum computing manager 120 acquires a Hamiltonian to be solved from the terminal device 31. The quantum computing manager 120 instructs the quantum circuit generator 110 to generate a quantum circuit for calculating the Hamiltonian.

[0097] [Step S102] The quantum circuit generation unit 110 decomposes the Hamiltonian H as "H = H1 + H2 + ...". For example, the quantum circuit generation unit 110 obtains multiple observables for calculating the Hamiltonian H, and groups observables that can be measured simultaneously. Then, for each group of observables, the quantum circuit generation unit 110 generates a Hamiltonian obtained from the observables.

[0098] [Step S103] The quantum circuit generation unit 110 generates an Ansatz circuit common to all the decomposed Hamiltonians. [Step S104] The quantum circuit generation unit 110 generates a common part of a basis conversion circuit. Details of the process of generating a basis conversion circuit (common part) will be described later (see FIG. 13).

[0099] [Step S105] The quantum circuit generation unit 110 calculates the Hamiltonian of the basis conversion circuit. <H i > Generate the proper part. Basis conversion circuit ( <H i The details of the process for generating the unique part will be described later (see FIG. 14).

[0100] [Step S106] The quantum computation manager 120 executes a quantum circuit for each of the generated Hamiltonians in the quantum computer 200, thereby generating each of the divided Hamiltonians. <H i Calculate the expected value of >. <H i The procedure for calculating the expected value will be described in detail later (see FIG. 15).

[0101] [Step S107] The ground energy calculation unit 130 calculates each Hamiltonian <H i Based on the expected value of <H i Calculate ">". [Step S108] The basis energy calculation unit 130 determines whether the energy E has converged to a minimum value. For example, the basis energy calculation unit 130 determines that the energy E has converged when the difference between the previous energy E value and the most recent energy E value is equal to or less than a predetermined threshold. If the energy E has converged, the basis energy calculation unit 130 proceeds to step S110. If the energy E has not converged, the basis energy calculation unit 130 proceeds to step S109.

[0102] [Step S109] The optimization calculation unit 140 updates the parameter θ so that the expected value of the energy decreases. For example, the optimization calculation unit 140 updates the value of the parameter θ using a method such as a gradient method. After that, the optimization calculation unit 140 proceeds to step S106.

[0103] [Step S110] The quantum computing manager 120 outputs, as the basis energy, the value of the energy E last calculated by the basis energy calculator 130. For example, the quantum computing manager 120 transmits the basis energy to the terminal device 31.

[0104] Next, the process of generating the common part of the basis conversion circuit will be described in detail. 13 is a flowchart showing an example of the procedure for generating a basis conversion circuit (common part). The process shown in FIG. 13 will be explained below in order of step number.

[0105] [Step S201] The quantum circuit generation unit 110 reads an Ansatz circuit. [Step S202] The quantum circuit generation unit 110 executes the processes of steps S203 to S209 for each observable. For example, the quantum circuit generation unit 110 counts up the loop variable i from 1 in order, and generates the ith observable O i Execute the processing for.

[0106] [Step S203] The quantum circuit generation unit 110 generates an observable O i The quantum circuit generation unit 110 determines the configuration of the observable O i If the configuration corresponds to pattern 1, the process proceeds to step S210. i If the configuration corresponds to pattern 2, the process proceeds to step S204. i If the configuration corresponds to pattern 3, the process proceeds to step S206.

[0107] [Step S204] The quantum circuit generation unit 110 generates an observable O i CNOT gate (CNOT) for two qubits "qubit a" and "qubit b" that measure the X or Y basis in ab The quantum circuit generation unit 110 determines whether the CNOT ab If the quantum circuit generation unit 110 has already placed the CNOT, the process proceeds to step S210. ab If not, the process proceeds to step S205.

[0108] [Step S205] The quantum circuit generation unit 110 generates a CNOT with “qubit a” as the control qubit and “qubit b” as the target qubit. ab in the basis conversion circuit. At this time, the quantum circuit generation unit 110 sets "qubit a" and "qubit b" as a quantum bit pair to be converted into measurement results.

[0109] [Step S206] The quantum circuit generation unit 110 generates an observable O i CNOT gate (CNOT) for two odd-numbered qubits "qubit a" and "qubit b" that measure the X or Y basis in ab The quantum circuit generation unit 110 determines whether the CNOT ab If the quantum circuit generation unit 110 has already placed the CNOT, the process proceeds to step S208. ab If not, the process proceeds to step S207.

[0110] [Step S207] The quantum circuit generation unit 110 generates a CNOT with “qubit a” as the control qubit and “qubit b” as the target qubit. ab in the basis conversion circuit. At this time, the quantum circuit generation unit 110 sets "qubit a" and "qubit b" as a quantum bit pair to be converted into measurement results.

[0111] [Step S208] The quantum circuit generation unit 110 generates an observable O i CNOT gate (CNOT) for two even-numbered qubits, "qubit c" and "qubit d", which measure the X or Y basis in cd The quantum circuit generation unit 110 determines whether the CNOT cd If the quantum circuit generation unit 110 has already placed the CNOT, the process proceeds to step S210. cd If not, the process proceeds to step S209.

[0112] [Step S209] The quantum circuit generation unit 110 generates a CNOT with “qubit c” as the control qubit and “qubit d” as the target qubit. cd in the basis conversion circuit. At this time, the quantum circuit generation unit 110 sets "qubit c" and "qubit d" as a quantum bit pair to be converted into the measurement result.

[0113] [Step S210] When the processes of steps S203 to S209 are completed for all observables, the quantum circuit generation unit 110 ends the process of generating a basis conversion circuit (common part).

[0114] Following the common part of the basis conversion circuit thus generated, a process of generating a specific part for each divided Hamiltonian is performed. Figure 14 shows the basis conversion circuit ( <H i 14 is a flowchart showing an example of a procedure for generating a unique portion. The process shown in FIG. 14 will be described below in order of step number.

[0115] [Step S301] The quantum circuit generation unit 110 calculates the post-division Hamiltonian <H i For each of them, execute the processes of steps S302 to S316. [Step S302] The quantum circuit generation unit 110 <H i For example, the quantum circuit generation unit 110 counts up the loop variable i from 1, and generates the i-th Hamiltonian <H i >Perform the processing.

[0116] [Step S303] The quantum circuit generation unit 110 <H i The quantum circuit generation unit 110 determines the configuration of the observable within. If the configuration of the observable corresponds to pattern 1, the quantum circuit generation unit 110 proceeds to step S316. If the configuration of the observable corresponds to pattern 2, the quantum circuit generation unit 110 proceeds to step S304. If the configuration of the observable corresponds to pattern 3, the quantum circuit generation unit 110 proceeds to step S308.

[0117] [Step S304] The quantum circuit generation unit 110 <H i CNOT gate (CNOT) for two qubits "qubit a" and "qubit b" that measure the X or Y basis of the observable in ab ) has been placed at the end of the common part of the basis conversion circuit. ab If the quantum circuit generation unit 110 has already placed the CNOT, the process proceeds to step S306. ab If not, the process proceeds to step S305.

[0118] [Step S305] The quantum circuit generation unit 110 generates a CNOT with “qubit a” as the control qubit and “qubit b” as the target qubit. ab of, <H i >Place it at the end of the basis conversion circuit for.

[0119] [Step S306] The quantum circuit generation unit 110 cancels the setting for reinterpreting the measurement results for the quantum bit pair of quantum bits "qubit a" and "qubit b." [Step S307] The quantum circuit generation unit 110 ab For example, in the case of measuring "XX" or "YY", the quantum circuit generation unit 110 places a 1-qubit gate on the qubits "qubit a" and "qubit b" to be operated on according to the observable to be measured. ab In addition, the quantum circuit generation unit 110 adds a Hadamard gate to the control qubit side of the added CNOT ab An S gate and a Hadamard gate are added to the control qubit side of the quantum circuit generation unit 110. After that, the quantum circuit generation unit 110 proceeds to step S316.

[0120] [Step S308] The quantum circuit generation unit 110 <H i CNOT gates (CNOT) for two odd-numbered qubits, "qubit a" and "qubit b", that measure the X or Y basis of the observables in ab ) has been placed at the end of the common part of the basis conversion circuit. ab If the quantum circuit generation unit 110 has already placed the CNOT, the process proceeds to step S310. ab If not, the process proceeds to step S309.

[0121] [Step S309] The quantum circuit generation unit 110 generates a CNOT with “qubit a” as the control qubit and “qubit b” as the target qubit. ab is placed at the end of the basis conversion circuit.

[0122] [Step S310] The quantum circuit generation unit 110 cancels the setting for reinterpreting the measurement results for the quantum bit pair of quantum bits "qubit a" and "qubit b." [Step S311] The quantum circuit generation unit 110 ab A one-qubit gate corresponding to the observable to be measured is placed on the quantum bits to be operated, ``qubit a'' and ``qubit b.''

[0123] [Step S312] The quantum circuit generation unit 110 <H i CNOT gate (CNOT) for two even-numbered qubits, "qubit c" and "qubit d", which measure the X or Y basis of the observable in cd ) has been placed at the end of the common part of the basis conversion circuit. cd If the quantum circuit generation unit 110 has already placed the CNOT, the process proceeds to step S314. cd If not, the process proceeds to step S313.

[0124] [Step S313] The quantum circuit generation unit 110 generates a CNOT with “qubit c” as the control qubit and “qubit d” as the target qubit. cd is placed at the end of the basis conversion circuit.

[0125] [Step S314] The quantum circuit generation unit 110 cancels the setting for reinterpreting the measurement results for the quantum bit pair of quantum bits "qubit c" and "qubit d." [Step S315] The quantum circuit generation unit 110 cd A one-qubit gate corresponding to the observable to be measured is placed on the qubits to be operated, ``qubit c'' and ``qubit d''.

[0126] [Step S316] The quantum circuit generation unit 110 <H i The quantum circuit for calculation is stored in memory 102 or storage device 103. [Step S317] The quantum circuit generation unit 110 <H i When the processing of steps S302 to S316 is completed, the basis conversion circuit ( <H i >Ends the generation process for the unique part.

[0127] In this way, the Hamiltonian <H i >A quantum circuit (Ansatz circuit + basis transformation circuit) is generated for each Hamiltonian. <H i The expected value of is calculated.

[0128] Figure 15 shows <H i 15 is a flowchart showing an example of the procedure for the expected value calculation process of the above. The process shown in FIG. 15 will be described below in order of step number. [Step S401] The quantum computation manager 120 calculates all Hamiltonians <H i For the above, the processes of steps S402 to S404 are executed.

[0129] [Step S402] The quantum computing manager 120 instructs the quantum computer 200 to <H i The quantum computer 200 executes the quantum circuit in accordance with the instruction and transmits the measurement results to the quantum computation manager 120. The quantum computation manager 120 transmits the acquired measurement results to the basis energy calculator 130.

[0130] [Step S403] The basis energy calculation unit 130 reinterprets the measurement results taking into account the CNOT gate. For example, the basis energy calculation unit 130 reinterprets the measurement results for the quantum bit pairs set as targets for reinterpretation by the CNOT gate.

[0131] [Step S404] The ground energy calculation unit 130 calculates the Hamiltonian <H i For example, the ground state energy calculation unit 130 calculates the expectation value of the Hamiltonian <H i Then, the ground energy calculation unit 130 calculates all observables that can be measured simultaneously based on these observables, <H i Calculate the expected value of >.

[0132] [Step S405] The quantum computation manager 120 calculates all Hamiltonians <H i If the expected value of can be calculated, <H i >Ends the expected value calculation process. In this way, the quantum computing system 300 calculates the Hamiltonian for each group when simultaneously measurable observables are grouped. <H i > can be calculated using a similar quantum circuit. <h>A calculation example of the above will be explained.

[0133] For example, the following Hamiltonian <h>Consider the case where energy E is measured from E= <h>=ΣH i =h0Z0+h1Z1+h2Z2+h3Z3+h4Z0Z1+h5Z0Z2+h6Z0Z3+h7Z1Z2+h8Z1Z3+h9Z2Z3+h 10 X0X1Y2Y3+h 11 X0Y1Y2X3+h 12 Y0X1X2Y3+h 13 Y0Y1X2X3 In this case, the following two groups of simultaneously measurable observables are generated:

[0134] Observables in group 1 ( <h1>used to calculate Z0,Z1,Z2,Z3,Z0Z1,Z0Z2,Z0Z3,Z1Z2,Z1Z3,Z2Z3 Observables in group 2 (< / h1> <h2>used to calculate X0X1Y2Y3,X0Y1Y2X3,Y0X1X2Y3,Y0Y1X2X3 For each of these groups< / h2> <h1>、< / h1> <h2> and summing the individual Hamiltonians gives the energy E.< / h2> <h1>、< / h1> <h2> To calculate< / h2> <h1>、< / h1> <h2>A corresponding quantum circuit is generated for each. To generate the two quantum circuits, a common Ansatz circuit is first generated.

[0135] FIG. 16 is a diagram showing an example of an Ansatz circuit. In the example of FIG. 16, a calculation is performed using four quantum bits. A quantum circuit 60 shows the procedure for operating a quantum gate on the four quantum bits. In the quantum circuit 60, an Ansatz circuit 61 is first set up to generate a wave function for the problem to be solved.

[0136] Next, a common part of the basis conversion circuit is added to the quantum circuit 60. 17 is a diagram showing an example of a common part of a basis conversion circuit. The placement of CNOT gates in the common part of the basis conversion circuit is determined for each observable. All observables belonging to group 1 are Z (determined as "pattern 1" in step S203 of FIG. 13). Therefore, no CNOT gates corresponding to these observables are added.

[0137] Among the observables in group 2, first, the placement process of the corresponding CNOT gates is performed for X0X1Y2Y3. In X0X1Y2Y3, the odd-numbered qubits ("1", "3") are X and Y, and the even-numbered qubits ("0", "2") are X and Y (determined as "Pattern 3" in step S203 of FIG. 13). Therefore, the CNOT gate (CNOT 02 ) and the CNOT gate (CNOT 13 ) is placed next to the Ansatz circuit 61 in the quantum circuit 60.

[0138] After that, CNOT gate placement processing is performed for the other observables X0Y1Y2X3, Y0X1X2Y3, and Y0Y1X2X3 in group 2. These observables are also determined to be "Pattern 3," but the corresponding CNOT gates have already been placed ("YES" is determined in steps S206 and S208 in FIG. 13). Therefore, no new CNOT gates are placed.

[0139] As a result, the CNOT gate added as a common part of the basis conversion circuit 62 is 02 and CNOT 13 Based on the quantum circuit 60 to which the common part of the basis conversion circuit 62 is added, a quantum circuit is generated for each divided Hamiltonian.

[0140] Figure 18 shows< / h2> <h1> FIG. 1 illustrates an example of a quantum circuit for computation.< / h1> <h1> All observables contained in are composed of only Z (determined as "Pattern 1" in step S303 of Figure 14). Therefore, no CNOT gate or 1-qubit gate is added. As a result,< / h1> <h1>The basis conversion circuit 62a of the quantum circuit 60a for calculation has the same configuration as the common part of the basis conversion circuit 62 of the quantum circuit 60 shown in Fig. 17. Therefore, the quantum circuit 60a as a whole also has the same configuration as the quantum circuit 60.

[0141] Figure 19 shows< / h1> <h2> FIG. 1 illustrates an example of a quantum circuit for computation.< / h2> <h2>The CNOT gates to be added in the observables included in 02 and CNOT 13 For the odd-numbered quantum bit pair of "1" and "3", a CNOT is added to the end of the common part of the basis conversion circuit 62b. 13 has already been placed (determined as "YES" in step S308 of FIG. 14).< / h2> <h2>As an inherent part of the basis conversion circuit 62b, a new CNOT 13 No additions will be made.< / h2> <h2>The reading of the measurement results for the quantum bit pair "1" and "3" in the calculation is canceled.

[0142] CNOT 13 The control qubit, qubit “1”, is provided with the following as an intrinsic part of the basis conversion circuit 62b:< / h2> <h2>The S gate and the H gate, which are one-qubit gates in the intrinsic part, are set.

[0143] For the even-numbered quantum bit pair of "0" and "2", a CNOT is added to the end of the common part of the basis conversion circuit 62b. 02 has already been placed (determined as "YES" in step S312 of FIG. 14).< / h2> <h2>As an inherent part of the basis conversion circuit 62b, a new CNOT 02 No additions will be made.< / h2> <h2>The reading of the measurement results for the quantum bit pair "0" and "2" in the calculation is canceled.

[0144] CNOT 02 The control quantum bit, qubit “0”, is provided with the following as an inherent part of the basis conversion circuit 62b:< / h2> <h2>The S gate and the H gate, which are one-qubit gates in the intrinsic part, are set.

[0145] the result,< / h2> <h2>The quantum circuit 60b for calculation has the same configuration as the quantum circuit 60 shown in FIG. 17, but with the addition of a one-qubit gate. As shown in Figures 18 and 19, the two Hamiltonians after division are< / h2> <h1>,< / h1> <h2>The corresponding quantum circuits 60a and 60b are identical except for the specific parts of the basis conversion circuits 62a and 62b. Because the quantum circuits 60a and 60b have a high degree of commonality, the effects of errors when calculating the quantum circuits 60a and 60b in the VQE calculation are also similar. Similarity in the effects of errors allows for appropriate parameter optimization in the VQE, facilitating the calculation of the expected energy value. In other words, the effects of gate operation errors are mitigated.

[0146] 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. 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]

[0147] 1 The first quantum circuit 1a,2a,3a Ansatz circuit 1b First basis conversion circuit 1c First two-qubit gate 1d 1-qubit gate 2. The second quantum circuit 2b Second base conversion circuit 2c Second two-qubit gate 3 The third quantum circuit 3b Third basis conversion circuit 3c Third two-qubit gate 9. Quantum Computers 10. Information processing equipment 11 Storage section 12 Processing section< / h2> < / h> < / h> < / h> < / h2> < / hi> < / hi>

Claims

1. Classifying multiple observables used in calculating a Hamiltonian corresponding to a problem to be solved by the variational quantum eigenvalue method into one of multiple groups that group together simultaneously measurable observables; generating a first quantum circuit including a first basis conversion circuit for enabling simultaneous measurement of a plurality of first observables belonging to a first group; generating a second quantum circuit including a second basis conversion circuit in which a quantum gate for enabling simultaneous measurement of a plurality of second observables belonging to a second group and a second two-qubit gate that performs the same gate operation as the first two-qubit gate included in the first basis conversion circuit are arranged; acquiring measurement results of the plurality of first observables by executing the first quantum circuit on a quantum computer; and acquiring measurement results of the plurality of second observables by performing a conversion according to the second two-qubit gate on measurement results obtained by executing the second quantum circuit on the quantum computer; calculating the Hamiltonian using measurements of the plurality of first observables and the plurality of second observables; Quantum computing support program.

2. generating a third quantum circuit including a third basis conversion circuit in which a third two-qubit gate corresponding to any one of the plurality of observables is arranged, following an Ansatz circuit representing the wave function; In the process of generating the first quantum circuit, the first quantum circuit is generated by adding a quantum gate that is missing in order to enable simultaneous measurement of the plurality of first observables to the third basis conversion circuit of the third quantum circuit; In the process of generating the second quantum circuit, the second quantum circuit is generated by adding a quantum gate that is missing in order to enable simultaneous measurement of the plurality of second observables to the third basis conversion circuit of the third quantum circuit. The quantum computing support program according to claim 1.

3. In the process of generating the third quantum circuit, each of the plurality of observables is selected in order, and if the third two-qubit gate corresponding to the selected observable has not been placed in the third basis conversion circuit, the third two-qubit gate corresponding to the selected observable is placed in the third basis conversion circuit. The quantum computing support program according to claim 2.

4. In the process of generating the third quantum circuit, the third two-qubit gate that acts on a pair of two qubits to be measured in the X basis or the Y basis in one first observable among the plurality of first observables is placed in the third basis conversion circuit, and the pair of qubits on which the third two-qubit gate acts is set as a conversion target; In the process of generating the first quantum circuit, when the first two-qubit gate that acts on a pair of two qubits to be measured in the X basis or the Y basis in the first observable has already been placed in the third basis conversion circuit, the pair of qubits that act on the first two-qubit gate is excluded from the object of conversion for the measurement result obtained by executing the first quantum circuit. The quantum computing support program according to claim 2.

5. Classifying multiple observables used in calculating a Hamiltonian corresponding to a problem to be solved by the variational quantum eigenvalue method into one of multiple groups that group together simultaneously measurable observables; generating a first quantum circuit including a first basis conversion circuit for enabling simultaneous measurement of a plurality of first observables belonging to a first group; generating a second quantum circuit including a second basis conversion circuit in which a quantum gate for enabling simultaneous measurement of a plurality of second observables belonging to a second group and a second two-qubit gate that performs the same gate operation as the first two-qubit gate included in the first basis conversion circuit are arranged; acquiring measurement results of the plurality of first observables by executing the first quantum circuit on a quantum computer; and acquiring measurement results of the plurality of second observables by performing a conversion according to the second two-qubit gate on measurement results obtained by executing the second quantum circuit on the quantum computer; calculating the Hamiltonian using measurements of the plurality of first observables and the plurality of second observables; Quantum computing support method.

6. a processing unit that classifies a plurality of observables used in calculating a Hamiltonian corresponding to a problem to be solved by the variational quantum eigenvalue method into one of a plurality of groups that group together simultaneously measurable observables, generates a first quantum circuit including a first basis conversion circuit for making a plurality of first observables belonging to a first group simultaneously measurable, generates a second quantum circuit including a second basis conversion circuit in which a quantum gate for making a plurality of second observables belonging to a second group simultaneously measurable and a second two-qubit gate that performs the same gate operation as the first two-qubit gate included in the first basis conversion circuit are arranged, executes the first quantum circuit on a quantum computer to obtain measurement results of the plurality of first observables, executes the second quantum circuit on the quantum computer to perform a conversion according to the second two-qubit gate to obtain measurement results of the plurality of second observables, and calculates the Hamiltonian using the measurement results of the plurality of first observables and the plurality of second observables; An information processing device having the above.

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