Quantum circuit learning system, quantum circuit learning method, quantum circuit learning program, quantum inference system and quantum circuit

Abstract

To accomplish a high inference precision at low calculation costs.SOLUTION: A quantum circuit includes a first block circuit and a second block circuit coupled to each other. The first block circuit includes: a gate operation layer including an encode gate to which a first encode parameter is given, the first encode parameter encoding input information, and establishing a first Hartree-Fock state, and a conversion gate to which a learning parameter for converting the first Hartree-Fock state into a first quantum state is given; and a measurement layer that measures the first quantum state. The second block circuit includes: a gate operation layer including an encode gate to which a second encode parameter is given, the second encode gate encoding a measured value, and establishing a second Hartree-Fock state, and a conversion gate to which a learning parameter for converting the second Hartree-Fock state into a second quantum state is given; and an output layer that outputs the second quantum state.SELECTED DRAWING: Figure 2

Description

[Technical Field]

[0001] Embodiments of the present invention include a quantum circuit learning system, a quantum circuit learning method, a quantum circuit learning program, and a quantum inference system. and Quantum rotation on the road To relate to. [Background technology]

[0002] In recent years, the development of gate-type quantum computers has made remarkable progress, enabling small-scale quantum computation using quantum properties in various ways. These quantum computers are called NISQ (Noisy Intermediate Scale Quantum devices) and are considered an important first step towards future quantum computers with error correction. Research utilizing NISQ is currently thriving, and in particular, the Variational Quantum Eigensolver (VQE) algorithm (see Non-Patent Literature 1) is expected to be applied to quantum chemical calculations as a hybrid method of utilizing quantum computers and classical computers. However, there are many challenges in implementing VQE for practical problems such as drug discovery and materials development. Specifically, obtaining high-precision results with VQE requires a huge number of measurement samples that repeatedly switch between the NISQ device and the classical computer. Therefore, various proposals are currently being made to reduce computational costs by reducing the number of measurements and improving error mitigation. [Prior art documents] [Patent Documents]

[0003] [Patent Document 1] International Publication No. 2019 / 163866 [Non-patent literature]

[0004] [Non-Patent Document 1] A. Peruzzo, J. McClean, P. Shadbolt, M.-H. Yung, X.-Q. Zhou, PJ Love, A. Aspuru-Guzik and JLO'Brien, “A variational eigenvalue solver on a photonic quantum processor,” Nature Communications,5, article number: 4213, 2014. [Non-Patent Document 2] R. Xia and S. Kais, “Hybrid Quantum-Classical Neural Network for Calculating Ground State Energies of Molecules” Entropy 22, 828 (2020) [Overview of the project] [Problems that the invention aims to solve]

[0005] In a series of studies aimed at reducing the computational cost of VQE, Xia & Kais et al. proposed in 2020 a quantum-classical hybrid neural network, disclosed in Non-Patent Document 2, which can accurately estimate the potential energy surface (PES) of the ground state of small molecules. Their method is a construction method for a VQE surrogate model that replaces the conventional VQE computation procedure with a neural network using quantum circuits. Following their proposed method, variational optimization at each molecular structure, which was previously required in PES calculations using VQE, becomes unnecessary. Therefore, computational costs can be reduced, and highly accurate PES estimates can be obtained on NISQ devices. However, the method disclosed in Non-Patent Document 2 uses parameterized quantum circuits that have too high expressive power to solve the task of quantum chemical calculation. Therefore, although it has been reported that highly accurate inference is possible with the simple two-molecule system disclosed in Non-Patent Document 2, the inference accuracy decreases when the number of molecules or qubits increases. To improve the accuracy of energy inference for H3 molecules using the method described in Non-Patent Document 2, it is necessary to sufficiently reduce the cost function. However, this requires many iterative calculations, resulting in an inefficient computational method that is difficult to apply to practical molecules.

[0006] The problem that this invention aims to solve is to provide a quantum circuit learning system, a quantum circuit learning method, a quantum circuit learning program, a quantum inference system, a quantum circuit, and a quantum-classical hybrid neural network that achieve high inference accuracy with low computational cost. [Means for solving the problem]

[0007] The quantum circuit learning system according to the embodiment includes a quantum computing unit and a learning control unit. The quantum computing unit applies input information to a quantum circuit that performs quantum gate operations on a plurality of qubits, and obtains output information corresponding to the input information. The learning control unit updates the learning parameters of the quantum circuit based on the difference between the output information and the teacher information. The quantum circuit has a connected first block circuit and second block circuit. The first block circuit includes a first encoding gate, which is a quantum gate for encoding the input information and attached with first encoding parameters for constructing a first Hartree-Fock state, and a first conversion gate, which is a quantum gate attached with the learning parameters for converting the first Hartree-Fock state into a first quantum state, and a first gate operation layer having the first conversion gate, and a measurement layer for outputting a measurement value of the first quantum state. The second block circuit includes a second encoding gate, which is a quantum gate for encoding the measurement value and attached with second encoding parameters for constructing a second Hartree-Fock state, and a second conversion gate, which is a quantum gate attached with the learning parameters for converting the second Hartree-Fock state into a second quantum state, and a second gate operation layer having the second conversion gate, and an output layer for outputting the second quantum state as the output information.

Brief Description of Drawings

[0008] [Figure 1] Block diagram showing a configuration example of a quantum circuit learning system [Figure 2] Block diagram showing a configuration example of a quantum circuit [Figure 3] Schematic diagram of the circuit configuration of a quantum circuit [Figure 4] Schematic diagram of the circuit configuration of SYMP in FIG. 3 [Figure 5] Schematic diagram of the circuit configuration of SYMP in the quantum gate notation of FIG. 4 [Figure 6] Diagram showing the processing procedure of the quantum circuit learning process by the quantum circuit learning system [Figure 7] Block diagram showing a configuration example of a quantum inference system [Figure 8]A diagram illustrating the processing steps of quantum inference using a quantum inference system. [Figure 9] Schematic diagram of the circuit configuration of the quantum circuit in quantum gate notation according to Example 1 [Figure 10] Figure showing a graph representing the numerical simulation results for Example 1. [Figure 11] Figure showing other graphs representing the numerical simulation results related to Example 1. [Figure 12] This figure shows a graph representing the numerical simulation results of the H2O molecule in Example 2. [Figure 13] This figure shows a graph representing the numerical simulation results of the NH3 molecule in Example 2. [Figure 14] Figure 12 shows a graph illustrating the error between the numerical simulation results of the H2O molecule using CASCI and the numerical simulation results using HQCNN. [Figure 15] Figure 13 shows a graph illustrating the error between the numerical simulation results of the NH3 molecule using CASCI and the numerical simulation results using HQCNN. [Figure 16] This figure shows a graph representing the numerical simulation results of the H3 molecule in the comparative example of Example 3. [Figure 17] This figure shows a graph representing the numerical simulation results of the H3 molecule in Example 3. [Modes for carrying out the invention]

[0009] The following describes the quantum circuit learning system, quantum circuit learning method, quantum circuit learning program, quantum inference system, quantum circuit, and quantum-classical hybrid neural network related to this embodiment, with reference to the drawings.

[0010] (Quantum circuit learning system) Figure 1 is a block diagram showing one example configuration of the quantum circuit learning system 1 according to this embodiment. As shown in Figure 1, the quantum circuit learning system 1 includes a classical computer 100 and a quantum computer 200. The classical computer 100 and the quantum computer 200 are connected to each other via wired or wireless means so that they can communicate with each other.

[0011] Classical computer 100 is a computer that processes binary classical bits. Classical computer 100 is a computer that has a processing circuit 110, a storage device 120, an input device 130, a communication device 140, and a display device 150. Information communication between the processing circuit 110, storage device 120, input device 130, communication device 140, and display device 150 is performed via a bus. Note that the storage device 120, input device 130, communication device 140, and display device 150 are not essential components and can be omitted as appropriate.

[0012] The processing circuit 110 includes a processor such as a CPU (Central Processing Unit) and memory such as RAM (Random Access Memory). The processing circuit 110 also includes a learning control unit 111 and a display control unit 112. The processing circuit 110 realizes the functions of each of the above parts 111 to 112 by executing a quantum circuit learning program. The quantum circuit learning program is stored in a non-temporary computer-readable recording medium such as a storage device 120. The quantum circuit learning program may be implemented as a single program describing all the functions of each of the above parts 111 to 112, or it may be implemented as multiple modules divided into several functional units. Furthermore, each of the above parts 111 to 112 may be implemented using integrated circuits such as Application Specific Integrated Circuits (ASICs) or Field Programmable Gate Arrays (FPGAs). In this case, they may be implemented in a single integrated circuit or individually in multiple integrated circuits.

[0013] The learning control unit 111 controls quantum circuit learning for the quantum circuit 210 implemented in the quantum computer 200. Specifically, the learning control unit 111 acquires learning information. The learning information includes multiple learning samples. Each learning sample includes input information and teacher information corresponding to that input information. The learning control unit 111 provides the input information to the quantum circuit 210. The input information is converted into output information by the quantum circuit 210. The learning control unit 111 updates the circuit parameters of the quantum circuit 210 based on the difference between the output information and the teacher information. The learning control unit 111 executes the above update process until the termination condition is satisfied. When the termination condition is satisfied, the learning control unit 111 finalizes the circuit parameters. This completes the quantum circuit 210. Note that the circuit parameters are an example of parameters that control the quantum gates included in the quantum circuit 210. In this embodiment, the circuit parameters to be updated are referred to as learning parameters.

[0014] The display control unit 112 displays various information on the display device 150. For example, the display control unit 112 displays input information, output information, teacher information, etc.

[0015] The storage device 120 consists of ROM (Read Only Memory), HDD (Hard Disk Drive), SSD (Solid State Drive), integrated circuit storage, etc. The storage device 120 stores quantum circuit learning programs, etc.

[0016] The input device 130 receives various commands from the operator. The input device 130 can include a keyboard, mouse, various switches, a touchpad, a touch panel display, etc. The output signals from the input device 130 are supplied to the processing circuit 110. Note that the various commands from the operator may be input not only through the input device 130 installed in the classical computer 100, but also through input devices on other classical computers connected via the communication device 140.

[0017] The communication device 140 is an interface for communicating information with external devices such as a quantum computer 200 that is connected to the classical computer 100 via wired or wireless means.

[0018] The display device 150 displays various information under the control of the display control unit 112. The display device 150 can be a CRT (Cathode-Ray Tube) display, a liquid crystal display, an organic EL (Electro-Luminescence) display, an LED (Light-Emitting Diode) display, a plasma display, or any other display known in the art. Alternatively, the display device 150 may be a projector.

[0019] The quantum computer 200 is a computer equipped with a quantum circuit 210 that performs quantum gate operations on multiple qubits and uses the quantum circuit 210 to perform quantum computations. The implementation method for qubits and quantum gates by the quantum circuit 210 may be any method, such as a superconducting circuit method, an ion trap method, a quantum dot method, an optical lattice method, or any other method. The quantum computer 200 is assumed to have various hardware to realize an environment corresponding to the implementation method of qubits and quantum gates. Although not shown in Figure 1, the quantum computer 200 may also have a processing circuit for performing various information processing using classical bits, as well as a memory device, input devices, communication devices, and display devices. The quantum computer 200 is an example of a quantum computing unit.

[0020] The quantum computer 200 receives input information from the classical computer 100 and inputs this information into a quantum circuit 210 that performs quantum gate operations on multiple qubits. The quantum circuit 210 converts the input information into output information. The quantum computer 200 obtains the output information from the quantum circuit 210. The quantum computer 200 transmits the obtained output information to the classical computer 100.

[0021] Figure 2 is a block diagram showing one example configuration of the quantum circuit 210. The quantum circuit 210 is a parameterized quantum circuit (parameterized quantum circuit) that includes a sequence of quantum gates controlled by learning parameters. Since the learning parameters of a parameterized quantum circuit are trained by quantum circuit learning, a parameterized quantum circuit is also called a quantum neural network. The quantum circuit 210 according to this embodiment performs quantum computation using quantum gates and classical measurement operations, so it can also be called a quantum-classical hybrid neural network.

[0022] As shown in Figure 2, the quantum circuit 210 is equipped with n (where n is a natural number greater than or equal to 3) qubits. n can be appropriately set according to the scale of the target molecule, such as the number of molecules, atoms, electrons, or electron orbitals. The quantum circuit 210 performs quantum computation on the n qubits to construct output information 250 from input information 240. The type of input information 240 can be arbitrarily selected according to the task of the quantum circuit 210. In this embodiment, the task of the quantum circuit 210 is quantum chemical calculation, and the input information 240 is assumed to be molecular structure parameters, which are parameters that define the molecular structure of the target molecule. Examples of molecular structure parameters include the coordinates of each atom constituting the target molecule, the distance between atoms (bond length), and the angle between bonds (bond angle).

[0023] The quantum circuit 210 can be described as a quantum-classical hybrid neural network characterized by a repeating block circuit structure in which quantum information is processed in the order of Hartree-Fock state, parameterized quantum circuit, and measurement layer. Specifically, as shown in Figure 2, the quantum circuit 210 includes a connected first block circuit 220 and a second block circuit 230. The first block circuit 220 includes a first gate operation layer 221 and a measurement layer 222. The first gate operation layer 221 has a sequence of first encoding gates 223 and a sequence of first transformation gates 224. The first encoding gate 223 is a quantum gate to which input information 240 is encoded and to which a first encoding parameter 225 is attached for constructing a first Hartree-Fock state. The first encoding parameter 225 is a circuit parameter but is not subject to update by quantum circuit learning. The first encoding parameter 225 is set to a value corresponding to the input information 240. A Hartree-Fock state represents a quantum state when electrons are filled sequentially from the lowest energy electron orbitals. A quantum state is represented by n qubits. The first conversion gate 224 is a quantum gate with a first learning parameter 226 for converting the first Hartree-Fock state to the first quantum state. The measurement layer 222 outputs a measurement value 260 of the first quantum state. The measurement value 260 outputs the expected value of the observable represented by the first quantum state.

[0024] The second block circuit 230 includes a second gate operation layer 231 and an output layer 232. The second gate operation layer 231 has a sequence of second encoding gates 233 and a sequence of second transformation gates 234. The second encoding gate 233 is a quantum gate to which the measured value 260 output by the measurement layer 222 is encoded and to which a second encoding parameter 235 is attached for constructing a second Hartree-Fock state. The second encoding parameter 235 is a circuit parameter but is not subject to update by quantum circuit learning. The second encoding parameter 235 is set to a value corresponding to the measured value 260. The second transformation gate 234 is a quantum gate to which a second learning parameter 236 is attached for transforming a second Hartree-Fock state into a second quantum state. The output layer 232 outputs the second quantum state as output information 250. The trial wave function represented by the second quantum state is output as output information 250. The first gate operation layer 221 and the second gate operation layer 231 may have the same quantum gate configuration or they may have different quantum gate configurations.

[0025] As described above, the first block circuit 220 and the second block circuit 230 are connected via the measurement value 260 obtained by the measurement layer 222. With this configuration, the second encoding gate 233 can encode the quantum state (Hartree-Fock state) represented by the measurement value 260 into a qubit. The first gate operation layer 221 and the second gate operation layer 231 are each realized by a particle number conservation circuit called an A gate. The particle number conservation circuit is an ansatz that conserves the particle number between the input quantum state and the output quantum state. That is, the first gate operation layer 221 and the second gate operation layer 231 each conserve the particle number for the input Hartree-Fock state while performing quantum gate operations with a transformation gate controlled by the learning parameter.

[0026] By adopting this configuration, the quantum circuit 210 can adopt a circuit configuration specifically suited for quantum chemical calculations using Hartree-Fock states as initial input, compared to the more general-purpose Non-Patent Document 2. This enables improved convergence in systems with a large number of atoms, application to practical systems, reduction of the number of circuit parameters, and consequently, reduction of the computational cost of quantum circuit learning.

[0027] Next, we will explain the details of the quantum circuit 210.

[0028] Figure 3 is a schematic diagram of the circuit configuration of quantum circuit 210. The quantum circuit 210 in Figure 3 is, as an example, a qubit qr with 4 (n=4) qubits. k This is a quantum-classical hybrid neural network that performs quantum computation on (k=0,1,2,3). As described above, the quantum circuit 210 has a first block circuit 220 and a second block circuit 230.

[0029] The first block circuit 220 includes a parameterized quantum circuit (SYMP) 221 and a measurement layer 222. The SYMP 221 includes a sequence of quantum gates that construct a first Hartree-Fock state and a sequence of transformation gates that convert the first Hartree-Fock state into a first quantum state. The encoding gate and transformation gate are realized by rotation gates that perform quantum gate operations that rotate the quantum state by an angle θ around a predetermined axis. The rotation gate is controlled by a rotation angle parameter θ, which is an example of a circuit parameter.

[0030] In the example in Figure 3, the rotation angle parameters θ included in SYMP221 are assumed to be six types, for example, θ[0] to θ[5]. As described above, the rotation angle parameter θ that controls the encode gate is the encode parameter, and the rotation angle parameter θ that controls the transform gate is the learning parameter θ. The measurement layer 222 is provided after SYMP221 and has four qubits qr k At least one qubit is measured. In the example in Figure 3, the measurement layer 222 measures the first qubit qr0.

[0031] The second block circuit 230 is located after the first block circuit 220, with the initialization layer 270 in between. The initialization layer 270 initializes all qubits qr k It includes a quantum gate that initializes the quantum state |0>. The second block circuit 230 is connected via the first qubit qr0, which is measured by the measurement layer 222, in the example of Figure 3.

[0032] The second block circuit 230 has a parameterized quantum circuit (SYMP) 231 and an output layer. SYMP231 has a sequence of quantum gates that construct a second Hartree-Fock state and a sequence of transformation gates that convert the second Hartree-Fock state into a second quantum state. The encoding gate and transformation gate are controlled by a rotation angle parameter θ. In the example in Figure 3, the rotation angle parameters θ included in SYMP231 are assumed to be six types, θ[6] to θ

[11] . The output layer, although not shown in Figure 3, is provided after SYMP231 and contains a qubit qr k The quantum state represented by is output as a trial wave function. Unlike the measurement layer 222, the output layer does not perform any measurement operations.

[0033] Hereafter, unless there is a specific distinction between SYMP221 and SYMP231, they will simply be referred to as SYMP.

[0034] Figure 4 is a schematic diagram of the circuit configuration of SYMP in Figure 3. Figure 5 is a schematic diagram of the circuit configuration of SYMP in Figure 4 using quantum gate notation. SYMP consists of particle number conservation circuits 281, 282, and 283, also known as A gates. Particle number conservation circuits 281, 282, and 283 perform computational processing that spans two qubits. For example, particle number conservation circuit 281 spans the first and second qubits, particle number conservation circuit 282 spans the third and fourth qubits, and particle number conservation circuit 283 spans the second and third qubits. Particle number conservation circuits 281, 282, and 283 are composed of a sequence of multiple rotation gates. Particle number conservation circuits 281, 282, and 283 include at least one rotation angle parameter θ, and if the computation target to be performed satisfies time-reversal symmetry, only one rotation angle parameter is sufficient. As an example, the particle number conservation circuit 281 is assigned a rotation angle parameter θ[0], the particle number conservation circuit 282 is assigned a rotation angle parameter θ[1], and the particle number conservation circuit 283 is assigned a rotation angle parameter θ[2].

[0035] Figure 5 is a schematic diagram of the circuit configuration of the SYMP in Figure 4 in quantum gate notation. The SYMP in Figures 4 and 5 has 4 qubits and contains 3 types of rotation angle parameters θ[0] to θ[2]. The SYMP in Figure 3 is constructed by repeating m blocks containing the particle number conservation circuits 281, 282, and 283 shown in Figures 4 and 5. In this case, the number of rotation angle parameters θ contained in each SYMP is 3m. Since the SYMP in Figure 3 contains 6 types of rotation angle parameters θ[0] to θ[5], m=2.

[0036] More generally, when n qubits are provided, the number of parameters included in each SYMP1 block is (n-1)m. Generally, SYMP, which is constructed by providing n qubits and repeating the particle number conservation circuit 281, 282, 283 in Figure 4 m times, can be expressed mathematically as shown in equation (1) below.

[0037]

number

[0038] At least one encoding parameter included in SYMP is the rotation angle parameter θ0~θ, expressed by equation (1). n-1 These are some of the parameters. For example, the encoding parameter can be θ0 in A(θ0) of equation (1) above. The remaining rotation angle parameters such as θ1 and θ2 are set as learning parameters. Note that the above n rotation angle parameters θ0~θ n-1 The selection of which rotation angle parameter to use as the encoding parameter is arbitrary, and the number of encoding parameters can also be changed according to the degrees of freedom of the computation target. The total number of remaining rotation angle parameters No included in SYMP is given by No = (n-1)m - Ne, where Ne is the number of encoding parameters. In other words, No is the number of learning parameters included in SYMP for constructing a quantum state from a Hartree-Fock state.

[0039] As shown in Figure 5, the particle number conservation circuit 281 has a rotation gate Ry with -1.0*θ[0] as the encoding parameter and a rotation gate Ry with θ[0] as the encoding parameter. The particle number conservation circuit 282 has a rotation gate Ry with -1.0*θ[1] as the learning parameter and a rotation gate Ry with θ[1] as the learning parameter. The particle number conservation circuit 283 has a rotation gate Ry with -1.0*θ[2] as the learning parameter and a rotation gate Ry with θ[2] as the learning parameter.

[0040] In both the first block circuit 220 and the second block circuit 230, each rotation angle parameter included in SYMP (gate operation layer) is allocated to an encoding parameter and a learning parameter according to the above rule. The values ​​of the rotation angle parameters are determined by quantum circuit learning. The encoding parameter of the first block circuit 220 is set to the molecular structure parameter itself, which is the input information, or a value based on that molecular structure parameter. The encoding parameter of the second block circuit 230 is set to the measured value itself, which is measured by the measurement layer 222, or a value based on that measured value.

[0041] In the measurement layer 222, measurements are performed on Ne encoding parameters. The measurement layer 222 is performed using a quantum state converted from a Hartree-Fock state, and outputs the expected value of an observable constructed by an arbitrary tensor product of the n-qubit Pauli operations I,X,Y,Z as the measured value. For example, in the case of Ne=1 in Figure 3, the measurement layer 222 is performed as a measurement of the expected value of the Z basis Pauli operator of the first qubit. Measurements may also be performed on the second, third, or fourth qubit.

[0042] Quantum circuit 210 calculates the ground state energy for any system under computation based on learned information from a subset of the systems being computed. The following explains the prerequisites.

[0043] A quantum computer performs quantum computations based on a quantum circuit U(θ) consisting of unitary operators. The parameter θ is a generally N-dimensional vector that represents the quantum circuit. In the case of n qubits, the quantum circuit U(θ) and the quantum state ψ(θ) are related by equation (2) below.

[0044]

number

[0045] Given the Hamiltonian H to be calculated, the expectation value E(θ) can be calculated using the quantum state |ψ(θ)> according to equation (3) below.

[0046]

number

[0047] VQE in Non-Patent Document 1 is an algorithm that minimizes the expected value E(θ) obtained using a quantum computer with respect to θ.

[0048] The quantum-classical hybrid neural network is a surrogate model of VQE. A part of the calculation target and its Hamiltonian are prepared as D = {X i , H i} (the subscript i represents the number of the training sample), and an algorithm is implemented to minimize the cost function f represented by the following formula (4) using D as the training sample.

[0049]

Equation

[0050] The Hamiltonian H is given in the second quantization representation that regards the state "0" of the qubit as the unoccupied orbital and the state "1" of the qubit as the occupied orbital, and represents the quantum state by the occupancy state of the spin orbit. However, the Hamiltonian of the second quantization cannot be calculated on the quantum circuit, and it is converted to the qubit Hamiltonian by rewriting the creation and annihilation operators as a linear combination of Pauli operators. As a typical conversion method, there is the Jordan-Wigner transformation [Jordan and Wigner (1928)], and several other conversion methods [Bravi and Kitaev (2005); Seeley and Love (2012)] are also known. By using these conversion methods, the Hamiltonian is given by the tensor product of weighted arbitrary Pauli operators represented by the following (5).

[0051]

Equation

[0052] In the formula (5), σ l ∈{I, X, Y, Z}, which are the identity operator and the Pauli operators of the X, Y, Z components. When training the quantum-classical hybrid neural network, the input value X i of the training sample D = {X i} is classical data, and similar to the Hamiltonian represented by (5), it needs to be encoded into a quantum state that can be processed by a quantum circuit.​​

[0053] Classical data: Input value X i The encoding of a qubit can generally be represented by the gate operation shown in equation (6) below for n qubits, where i is the qubit number and f i g is an arbitrary classical function acting on the i-th qubit. i is f i This is an arbitrary single-qubit gate whose parameter is the result output from [the source].

[0054]

number

[0055] By preparing the initial state and performing the encoding shown in equation (4), the initial quantum state function |ψ shown in equation (7) below is obtained. encoded > can be constructed.

[0056]

number

[0057] The quantum state is determined by the initial quantum state function |ψ of the quantum circuit U(θ) encoded By applying this to |ψ(θ)>=U(θ)|ψ encoded >This is what you get.

[0058] Using the above procedures with equations (5) and (6), the learning sample D = {X i ,H i The cost function f, expressed by equation (4), can be calculated from}.

[0059] In quantum classical hybrid neural networks applied to diatomic molecular systems, such as hydrogen molecules, f i =I and g i =R y H is used, X i The bond distance between two atoms is used as the coefficient. In such a quantum-classical hybrid neural network, R is used for the quantum circuit U(θ). yIt uses a Real Amplitude 2-local type consisting of gates and CNOT gates, and further constructs a quantum circuit with a measurement layer in between to introduce nonlinearity to the quantum circuit consisting of unitary operators.

[0060] In the quantum-classical hybrid neural network described above, the expectation value of the Pauli operator of the Z component obtained using the quantum state ψ(θ) is measured, and the measured value is given by equation (6) X i Substituting these values ​​into the equation yields G', and a new initial quantum state |ψ´ is obtained from the quantum state ψ(θ). encoded >=G'|ψ(θ)> is constructed, and further |ψ' encoded > and U(θ') form a newly constructed quantum state |ψ'(θ')>=U(θ')|ψ' encoded By constructing |ψ´(θ´)> and calculating the cost function f expressed by equation (4) using |ψ´(θ´)>, a quantum circuit with a measurement layer is constructed.

[0061] For example, in a quantum-classical hybrid neural network applied to diatomic molecular systems such as hydrogen molecules, the training sample D = {X i ,H i By preparing} and constructing U(θ) and U(θ') and ψ(θ) and ψ(θ') using the above procedure, and performing learning to minimize the cost function f expressed by equation (4) for θ and θ', the energy at any interatomic distance and the potential energy surface of the hydrogen molecule are estimated and calculated.

[0062] Next, we will explain the quantum circuit learning process using the quantum circuit learning system 1.

[0063] Figure 6 shows the processing procedure for quantum circuit learning by the quantum circuit learning system 1. As shown in Figure 6, the classical computer 100 provides input information to the quantum computer 200 (step S601). In step S601, input information for multiple learning samples from a plurality of learning samples used for quantum circuit learning is provided.

[0064] When step S601 is performed, the quantum computer 200 applies the input information provided in step S601 to the quantum circuit 210 and outputs output information (step S602). The first encoding parameter that controls the first encoding gate of the first block circuit included in the quantum circuit 210 is set to a value based on the input information provided in step S601. The first learning parameter and the second learning parameter that control the first and second transformation gates of the first and second block circuits included in the quantum circuit 210 are set to arbitrary initial values. The first gate operation layer encodes the input information into a qubit by performing a quantum gate operation on the qubit using the first encoding gate with the first encoding parameter attached, thereby constructing a first Hartree-Fock state. The first gate operation layer constructs a first quantum state by performing a quantum gate operation on the first Hartree-Fock state using the first transformation gate with the first learning parameter attached. The measurement layer outputs the expected value of the observable for the first quantum state as a measured value. As an example of the expected value of the observable, the expected value of the Hamiltonian is measured.

[0065] The quantum computer 200 sets the measured value output from the measurement layer to the value of a second encoding parameter that controls the second encoding gate of the second block circuit. The second gate operation layer encodes the measured value into a qubit initialized by the initialization layer by performing a quantum gate operation on the qubit using the second encoding gate with the second encoding parameter attached, thereby constructing a second Hartree-Fock state. The second gate operation layer constructs a second quantum state by performing a quantum gate operation on the second Hartree-Fock state using the second transformation gate with the second learning parameter attached. The output layer outputs the second quantum state as a trial wave function. This trial wave function is output as output information.

[0066] When step S602 is performed, the classical computer 100 updates the learning parameters of the quantum circuit 210 based on the difference between the output information output in step S602 and the teacher information corresponding to the input information provided in step S601 (step S603). Specifically, in step S603, the learning control unit 111 updates the learning parameters using a cost function that evaluates the difference between the output information and the teacher information. Specifically, the learning control unit 111 calculates the cost function based on the output information and the teacher information. The cost function is defined by the sum of the expectation values ​​of the Hamiltonian for the second quantum state over the number of samples of the input information. The learning control unit 111 updates the learning parameters according to a predetermined optimization method so that the cost function becomes smaller. As a result, the first learning parameter 226 and the second learning parameter 236 are updated so that the quantum circuit 210 constructs accurate output information (trial wave function) 250 from the input information (molecular structure parameters) 240.

[0067] As optimization methods, the Nelder-Mead method, Powell method, CG method, Newton method, BFGS method, L-BFGS-B method, TNC method, COBYLA method and / or SLSQP method, or any other arbitrary optimization method can be used. The training information is high-precision output information calculated based on the corresponding input information. As an example, as training information, it is preferable to use exact solutions calculated by a classical computer based on the input information according to any high-precision algorithm such as the FCI (Full Configuration Interaction Method) method or the CASCI (Complete Active Space CI) method. Alternatively, experimental results for the input information may be used as training information.

[0068] When step S603 is performed, the classical computer 100 determines whether or not to terminate the learning parameter update process (step S604). Specifically, the learning control unit 111 of the classical computer 100 determines whether or not the conditions for stopping the update process are met. The stopping conditions can be set to any conditions, such as when the number of iterations of steps S601 to S604 reaches a predetermined number or when the function value of the cost function reaches a threshold. If it is determined that the stopping conditions are not met, that is, when it is determined that the update process should not be terminated (step S604: NO), steps S601 to S604 are repeated for the other samples.

[0069] Then, if it is determined that the termination condition has been met, that is, if it is determined that the learning parameter update process should be terminated (step S604: YES), the classical computer 100 finalizes the learning parameters (step S605). The quantum circuit 210 with the finalized learning parameters set is implemented as a trained quantum circuit in the quantum inference system described later.

[0070] With this, the quantum circuit learning process by the quantum circuit learning system 1 is completed.

[0071] The quantum circuit learning system 1 described above is an example, and can be modified, added to, and / or deleted as appropriate, as long as it does not depart from the spirit of the invention. As an example, as shown in Figure 1, the quantum circuit learning system 1 has a classical computer 100 and a quantum computer 200. However, this embodiment is not limited thereto, and the classical computer 100 may be incorporated into the quantum computer 200, or the quantum computer 200 may be incorporated into the classical computer 100.

[0072] As another example, in Figure 3, the measurement layer 222 is shown to perform a measurement on any one of the first, second, third, and fourth qubits, but it may also perform a measurement on any combination of two or three qubits, or it may perform a measurement on all of the first, second, third, and fourth qubits. As yet another example, in Figure 2, the quantum circuit 210 has a second block circuit 220 which includes a second gate operation layer 231 and an output layer 232, but one or more blocks of measurement layer 222 and second gate operation layer 231 may be connected between the second gate operation layer 231 and the output layer 232. In this case, the multiple second gate operation layers 231 are connected via the measured value of the preceding measurement layer 222. In other words, the first encoding parameter of each second gate operation layer 231 is set to the measured value of the preceding measurement layer 222. This makes it possible to handle complex quantum chemical calculations.

[0073] (Quantum inference system) Figure 7 shows an example configuration of the quantum inference system 7 according to this embodiment. As shown in Figure 7, the quantum inference system 7 includes a classical computer 300 and a quantum computer 400. The classical computer 300 and the quantum computer 400 are connected to each other via wired or wireless means so that they can communicate with each other.

[0074] The classical computer 300 is a computer that processes binary classical bits. The classical computer 300 is a computer that has a processing circuit 310, a storage device 320, an input device 330, a communication device 340, and a display device 350. Information communication between the processing circuit 310, the storage device 320, the input device 330, the communication device 340, and the display device 350 is performed via a bus.

[0075] The processing circuit 310 includes a processor such as a CPU and memory such as RAM. The processing circuit 310 also includes an inference unit 311 and a display control unit 312. The processing circuit 310 realizes the functions of each of the above units 311 to 312 by executing a quantum inference program. The quantum inference program is stored in a non-temporary computer-readable recording medium such as a memory device 320. The quantum circuit learning program may be implemented as a single program describing all the functions of each of the above units 311 to 312, or it may be implemented as multiple modules divided into several functional units. Furthermore, each of the above units 311 to 312 may be implemented using integrated circuits such as ASICs or FPGAs. In this case, they may be implemented in a single integrated circuit or individually in multiple integrated circuits.

[0076] The inference unit 311 controls the quantum inference process using the trained quantum circuit 410 implemented in the quantum computer 400. Specifically, the inference unit 311 acquires the input information to be processed. The inference unit 311 provides the input information to the trained quantum circuit 410. The input information is converted into inference result information by the trained quantum circuit 410. The inference result information is the output information constructed by the trained quantum circuit 410.

[0077] The display control unit 312 displays various information on the display device 350. For example, the display control unit 312 displays input information, inference result information, etc.

[0078] The storage device 320 is composed of ROM, HDD, SSD, integrated circuit storage, etc. The storage device 320 stores quantum inference programs, etc.

[0079] The input device 330 receives various commands from the operator. The input device 330 can include a keyboard, mouse, various switches, a touchpad, a touch panel display, etc. The output signals from the input device 330 are supplied to the processing circuit 310. Note that the various commands from the operator may be input not only through the input device 330 installed in the classical computer 300, but also through input devices on other classical computers connected via the communication device 340.

[0080] The communication device 340 is an interface for communicating information with external devices such as a quantum computer 400 that is connected to the classical computer 300 via wired or wireless means.

[0081] The display device 350 displays various information under the control of the display control unit 312. The display device 350 can be a CRT display, liquid crystal display, organic EL display, LED display, plasma display, or any other display known in the art. Alternatively, the display device 350 may be a projector.

[0082] The quantum computer 400 is a computer that is equipped with a trained quantum circuit 410 that performs quantum gate operations on multiple qubits and uses the trained quantum circuit 410 to perform quantum computations. The trained quantum circuit 410 is the quantum circuit 210 trained by the quantum circuit learning system 1. That is, the trained quantum circuit 410 is set with the learning parameters determined in step S605 of Figure 6.

[0083] The quantum computer 400 receives input information to be processed from the classical computer 300 and inputs this information to a trained quantum circuit 410 that performs quantum gate operations on multiple qubits. The trained quantum circuit 410 converts the input information into inference result information. The quantum computer 400 retrieves the inference result information from the trained quantum circuit 410. The quantum computer 400 transmits the retrieved inference result information to the classical computer 300. The hardware configuration of the quantum computer 400 is the same as that of the quantum computer 200 in the quantum circuit learning system 1.

[0084] Figure 8 shows the processing procedure for quantum inference by the quantum inference system 7. As shown in Figure 8, the classical computer 300 provides input information to be processed to the quantum computer 400 (step S801). The input information provided is the molecular structure parameters of the molecule to be processed.

[0085] When step S801 is performed, the quantum computer 400 applies the input information provided in step S801 to the trained quantum circuit 410 and outputs inference result information (step S802). The first encoding parameter that controls the first encoding gate of the first block circuit included in the trained quantum circuit 410 is set to a value based on the input information provided in step S801. The first and second learning parameters that control the first and second transformation gates of the first and second block circuits included in the trained quantum circuit 410 are set to the first learning parameter (hereinafter referred to as the first definitive parameter) and the second learning parameter (hereinafter referred to as the second definitive parameter), respectively, which were determined in step S605. The first gate operation layer encodes the qubit into input information and constructs a first Hartree-Fock state by performing a quantum gate operation on the qubit using the first encoding gate to which the first encoding parameter is attached. The first gate operation layer constructs a first quantum state by performing quantum gate operations on a first Hartree-Fock state using a first transformation gate with a first deterministic parameter. The measurement layer outputs the expected value of the observable for the first quantum state as a measured value.

[0086] The quantum computer 400 sets the measured value output from the measurement layer to the value of a second encoding parameter that controls the second encoding gate of the second block circuit. The second gate operation layer encodes the measured value into a qubit initialized by the initialization layer by performing a quantum gate operation on the qubit using the second encoding gate with the second encoding parameter attached, thereby constructing a second Hartree-Fock state. The second gate operation layer constructs a second quantum state by performing a quantum gate operation on the second Hartree-Fock state using the second transformation gate with the second deterministic parameter attached. The output layer outputs the second quantum state as a trial wave function. This trial wave function is output as inference result information.

[0087] When step S802 is performed, the classical computer 300 displays the inference result information (step S803). The classical computer 300 may also calculate secondary information such as potential energy and Hermann-Feynman force based on the inference result information. The inference result information and secondary information are displayed on the display device 350 in a predetermined layout.

[0088] With this, the quantum inference process by quantum inference system 7 is completed.

[0089] The quantum inference system 7 described above is an example and can be modified, added to, and / or deleted as appropriate, as long as it does not depart from the spirit of the invention. As an example, as shown in Figure 7, the quantum inference system 7 has a classical computer 300 and a quantum computer 400. However, this embodiment is not limited thereto, and the classical computer 300 may be incorporated into the quantum computer 400, or the quantum computer 400 may be incorporated into the classical computer 300.

[0090] The following describes an example of quantum chemical calculation according to this embodiment.

[0091] (Example 1) The molecule to be treated in Example 1 is the H2 molecule. Numerical simulations were performed using the electron Hamiltonian of the H2 molecule. In Example 1, the existing open-source library PySCF (see Reference 1 (Q. Sun, TC Berkelbach, NS Blunt, GH Booth, S. Guo, Z. Li, J. Liu, JD McClain, ER Sayfutyarova, S. Sharma, S. Wouters, and GK Chan, Wiley Interdisciplinary Reviews: Computational Molecular Science 8, e1340 (2017))) and OpenFermion (see Reference 2 (JR McClean, KJ Sung, ID Kivlichan, Y. Cao, C. Dai, ES Fried, C. Gidney, B. Gimby, P. Gokhale, T. Hner, T. Hardikar, V. Havlek, O. Higgott, C. Huang, J. Izaac, Z. Jiang, X. Liu, S. McArdle, M. Neeley, T. O'Brien, B. The Hamiltonian was calculated using O'Gorman, I. Ozdan, MD Radin, J. Romero, N. Rubin, NPD Sawaya, K. Setia, S. Sim, DS Steiger, M. Steudtner, Q. Sun, W. Sun, D. Wang, F. Zhang, and R. Babbush, (2017), arXiv:1710.07629. Quantum circuit simulations were performed using Qiskit (see Reference 3 (G. Aleksandrowicz, T. Alexander, P. Barkoutsos, L. Bello, Y. Ben-Haim, D. Bucher, F. Jose Cabrera-Hernandez, J. Carballo-Franquis, A. Chen, C. Chen, J. Chow, A. Corcoles-Gonzales)).A. Cross, A. Cross, J. Cruz-Benito, C. Culver, S. Gonzalez, E. Torre, D, Ding, E. Dumitrescu, I.Duran, P. Eendebak, M. Everitt, I. Sertage, A. Frisch, A. Fuhrer, J. Gambetta, B. Gago, J. Gomez-Mosque, D. Hamura, I. Hamura. V. Havlicek, J. Hellmers, L. Herok, H. Horii, S. Hu, T. Imamichi, T. Itoko, A. Javadi-Abhari, N. Kanazawa, A. Karazeev, K. Krsulich, P. Liu, Y. Luh, Y. Maeng, M. Marques, F. Martin-Fernandez, D. McClure, D. McKay, D. McKay, S. McKay, N. Kanazawa. Mezzacapo, N. Moll, D. Rodriguez, G. Nannicini, P. Nation, P. Ollitrault, L. O'Riordan, H. Paik, J. Perez, A. Phan, M. Pistoia, V. Prutyanov, M. Reuter, J. Rice, A. Davila, R. Rudy, M. Ryu, N. Rye, C. Schoutha, E. Schoutha, E. K. Setia, Y. Shi, A. Silva, Y. Siraichi, S. Sivarajah, J. Smolin, M. Soeken, H. Takahashi, I. Tavernelli, J. Taylor, P. Taylour, K. Trabing, M. Treinish, W. Turner, D. Vogt-Lee, C. Vuillot, J. Wild, Wilson, J. Winston, C. Winston, C. Wood, H. Takahashi, I. Tavernelli. Wood, S. Worner, I. Akhalwaya, J. Zoufalhttps. https: / / doi.org / 10.This was done using 5281 / zenodo.2562111, (2019) An Open-source Framework for Quantum Computing (see reference).

[0092] Figure 9 is a schematic diagram of the circuit configuration of the quantum circuit according to Example 1 (hereinafter referred to as quantum circuit QC1) in quantum gate notation. Quantum circuit QC1 has a configuration in which quantum gate operations are performed on four qubits, and the SYMC blocks shown in Figures 4 and 5 are connected to the first block circuit and the second block circuit, respectively. In Figure 9, "Ry" represents a y-axis rotation gate, and the gate spanning two qubits is a CNOT gate.

[0093] Figure 10 shows a graph representing the numerical simulation results for Example 1. In the graph shown in Figure 10, the vertical axis is defined by potential energy E [Hr] and the horizontal axis is defined by bond length [Å]. In Example 1, the bond length (interatomic distance) between hydrogen molecules was used as the encoding parameter, and the learning parameters of the quantum circuit QC1 were updated to construct a trained quantum circuit QC1. Subsequently, the potential energy for each of the multiple bond lengths, which are the encoding parameters, was inferred using the trained quantum circuit QC1. The potential energy is calculated by the inference unit 311 of the classical computer 300 based on the trial wave function output from the trained quantum circuit QC1. The surface formed by the potential energy for each bond length is called the potential energy surface (PES).

[0094] In Figure 10, HF (Hartree-Fock), MP2 (Moller-Plesset 2), and FCI represent the potential energy surfaces obtained using the Hartree-Fock approximation, the MP2 method (perturbation method), and the Full-CI method, respectively. HF, MP2, and FCI were calculated based on trial wave functions derived using a classical computer, without using the quantum circuit QC1. FCI yields the exact solution with the highest computational accuracy. HQCNN is the result of the potential energy surface calculated using the quantum circuit QC1. As shown in Figure 10, HQCNN can be seen to infer the result of the exact solution FCI obtained using a classical computer with high accuracy.

[0095] Figure 11 shows another graph representing the numerical simulation results for Example 1. In the graph shown in Figure 11, the vertical axis is defined by the Hermann-Feynmanck force (HF Force) [Hr / Å], and the horizontal axis is defined by the bond length between hydrogen atoms (bond length between H2) [Å]. The Hermann-Feynman force is the force acting on a hydrogen atom, determined from the coordinate differential of energy based on the Hermann-Feynman theorem. The HQCNN prediction shown in Figure 11 is the result inferred based on the trial wave function obtained by the quantum circuit QC1. The exact solution is the exact solution calculated based on the trial wave function calculated by a classical computer without using the quantum circuit QC1. As shown in Figure 11, it can be seen that the HQCNN prediction is able to infer the Hermann-Feynman force with good accuracy.

[0096] Thus, by using the quantum circuit QC1 according to this embodiment, it is possible to infer energy and the forces acting on atoms with high accuracy, making it applicable to simulation techniques that perform molecular dynamics calculations, such as molecular dynamics.

[0097] (Example 2) The molecules to be treated in Example 2 are H2O molecules and NH3 molecules. In Example 2, a 4-qubit calculation was performed using a fully active space cas(2e,2o) model. Numerical simulations in Example 2 were performed using the same open-source library as in Example 1.

[0098] Figure 12 shows a graph representing the numerical simulation results of an H2O molecule according to Example 2. In the graph shown in Figure 12, the vertical axis is defined by the potential energy E [Hr] and the horizontal axis is defined by the bond angle θ [degree]. The bond angle θ represents the angle ∠HOH between the two hydrogen atoms and oxygen atoms of the H2O molecule. In Example 2, the bond angle was used as an encoding parameter, the learning parameters of the quantum circuit QC1 were updated, and a trained quantum circuit QC1 was constructed. Subsequently, the potential energy for each of the multiple bond angles, which are the encoding parameters, was inferred using the trained quantum circuit QC1. The potential energy is calculated by the inference unit 311 of the classical computer 300 based on the trial wave function output from the trained quantum circuit QC1. The surface formed by the potential energy for each bond angle is called the potential energy surface (PES).

[0099] Figure 13 shows a graph representing the numerical simulation results of the NH3 molecule according to Example 2. In the graph shown in Figure 13, the vertical axis is defined by the potential energy E [Hr], and the horizontal axis is defined by the improved dihedral angle φ [degree] of the NH3 molecule. In Example 2, the bond angle was used as an encoding parameter, the learning parameters of the quantum circuit QC1 were updated, and a trained quantum circuit QC1 was constructed. Subsequently, the potential energy for each of the multiple bond angles, which are the encoding parameters, was inferred using the trained quantum circuit QC1. The potential energy is calculated by the inference unit 311 of the classical computer 300 based on the trial wave function output from the trained quantum circuit QC1.

[0100] Figures 12 and 13 show the CASCI results obtained using a classical computer with a fully active space cas(2e,2o) model. HQCNN is the result of the potential energy surface from Example 2. Figures 12 and 13 show the results of the CASCI obtained using a classical computer with a fully active space cas(2e,2o) model and the result of the potential energy surface obtained using HQCNN from Example 2.

[0101] Figure 14 is a graph showing the absolute error between the numerical simulation results of the H2O molecule using CASCI and the numerical simulation results using HQCNN, as shown in Figure 12. Figure 15 is a graph showing the absolute error between the numerical simulation results of the NH3 molecule using CASCI and the numerical simulation results using HQCNN, as shown in Figure 13. The dotted line represents chemical accuracy, where 1 kcal / mol ≈ 1.593 × 10⁻¹⁰. -3 The value of Hr is shown, and it is desirable that the error be below chemical precision. It can be seen that HQCNN is able to infer the results of the exact CASCI solution performed on a classical computer with high accuracy.

[0102] (Example 3) The molecule to be processed in Example 3 is the H3 molecule. In Example 3, a quantum circuit (hereinafter referred to as quantum circuit QC3) that performs quantum gate operations on 6 qubits was used. Quantum circuit QC3 is an extension of quantum circuit QC1 shown in Figure 9, with the number of qubits increased from 4 to 6. Numerical simulations for Example 3 were performed using the same open-source library as in Example 1.

[0103] Figure 16 is a graph showing the numerical simulation results of an H3 molecule related to a comparative example of Example 3. Figure 17 is a graph showing the numerical simulation results of an H3 molecule related to Example 3. In the graphs shown in Figures 16 and 17, the vertical axis is defined by potential energy E [Hr] and the horizontal axis is defined by bond length [Å]. In Example 3, the bond length between hydrogen molecules (interatomic distance) was used as an encoding parameter, the learning parameters of the quantum circuit QC3 were updated, and a trained quantum circuit QC3 was constructed. Subsequently, the potential energy for each of the multiple bond lengths, which are the encoding parameters, was inferred using the trained quantum circuit QC3. Specifically, the coordinates of the first, second, and third hydrogen atoms were defined as [0,0,0], [xa0,0,0], and [4a0,0,0], respectively, and the bond length was changed by varying the variable x between 1.0 and 3.0 at predetermined distance intervals. a0 is the Bohr radius (=0.529 Å). The potential energy is calculated by the inference unit 311 of the classical computer 300 based on the trial wave function output from the trained quantum circuit QC3.

[0104] The HQCNN in Figure 16 is the potential energy surface calculated using the quantum-classical hybrid neural network described in Non-Patent Literature 2. The New HQCNN in Figure 17 is the potential energy surface calculated using the trained quantum circuit QC3 according to Example 3. As shown in Figures 16 and 17, the New HQCNN can infer the exact solution FCI result from a classical computer with higher accuracy than the HQCNN in Non-Patent Literature 2.

[0105] Thus, according to this embodiment, it is possible to provide a quantum circuit learning system, a quantum circuit learning method, a quantum circuit learning program, a quantum inference system, a quantum circuit, and a quantum-classical hybrid neural network that achieve high inference accuracy with low computational cost.

[0106] While several embodiments of the present invention have been described, these embodiments are presented as examples only and are not intended to limit the scope of the invention. These novel embodiments can be carried out in a variety of other forms, and various omissions, substitutions, and modifications can be made without departing from the spirit of the invention. These embodiments and their variations are included in the scope and spirit of the invention, as well as in the claims of the invention and its equivalents.

[0107] The inventions disclosed in the specification and claims of this application at the time of filing are listed below. [1] A quantum computing unit that applies input information to a quantum circuit that performs quantum gate operations on multiple qubits and obtains output information corresponding to the input information, The system comprises a learning control unit that updates the learning parameters of the quantum circuit based on the difference between the output information and the teacher information, The quantum circuit has a connected first block circuit and a second block circuit, The first block circuit comprises a first gate operation layer having a first encoding gate which is a quantum gate to which the input information is encoded and to which a first encoding parameter is attached for constructing a first Hartree-Fock state, and a first conversion gate which is a quantum gate to which the learning parameter is attached for converting the first Hartree-Fock state to a first quantum state, and a measurement layer which outputs a measurement value of the first quantum state, The second block circuit comprises a second gate operation layer having a second encoding gate to encode the measured value and to which a second encoding parameter is attached for constructing a second Hartree-Fock state, and a second conversion gate to which the learning parameter is attached for converting the second Hartree-Fock state to a second quantum state, and an output layer that outputs the second quantum state as output information. Quantum circuit learning system. [2] The measurement layer outputs the expected value of the observable for the first quantum state as the measured value. The quantum computing unit sets the measured value to the second encoding parameter having the second encoding gate. [1] The quantum circuit learning system described in [1]. [3] The quantum circuit learning system according to [2], wherein the output layer outputs the second quantum state as a trial wave function. [4] The quantum circuit learning system according to [2] or [3], wherein the first block circuit and / or the second block circuit store the number of particles represented by the plurality of qubits. [5] The quantum circuit learning system according to any one of [1] to [4], wherein the learning control unit updates the learning parameters using a cost function that evaluates the difference. [6] The quantum circuit learning system according to [5], wherein the cost function is defined by the sum of the expectation values ​​of the Hamiltonian for the second quantum state over the number of samples of the input information. [7] The quantum circuit learning system according to any one of [1] to [6], wherein the learning control unit updates the learning parameters according to the Nelder-Mead method, Powell method, CG method, Newton method, BFGS method, L-BFGS-B method, TNC method, COBYLA method, or SLSQP method. [8] The quantum circuit learning system according to any one of [1] to [7], wherein the learning parameter is a rotation angle parameter representing the rotation angle of the rotation gate among the first and second transformation gates. [9] The quantum circuit learning system according to any one of [1] to [8], wherein the first gate operation layer and the second gate operation layer have different quantum gate configurations.

[10] The aforementioned input information consists of molecular structure parameters that define the molecular structure of the target molecule. The output information is the trial wave function. A quantum circuit learning system as described in any of [1] through [9].

[11] Input information is applied to a quantum circuit that performs quantum gate operations on multiple qubits, and output information corresponding to the input information is obtained. The learning parameters of the quantum circuit are updated based on the difference between the output information and the teacher information, and the system is equipped with The quantum circuit has a connected first block circuit and a second block circuit, The first block circuit comprises a first gate operation layer having a first encoding gate which is a quantum gate to which the input information is encoded and to which a first encoding parameter is attached for constructing a first Hartree-Fock state, and a first conversion gate which is a quantum gate to which the learning parameter is attached for converting the first Hartree-Fock state to a first quantum state, and a measurement layer which outputs a measurement value of the first quantum state, The second block circuit comprises a second gate operation layer having a second encoding gate to encode the measured value and to which a second encoding parameter is attached for constructing a second Hartree-Fock state, and a second conversion gate to which the learning parameter is attached for converting the second Hartree-Fock state to a second quantum state, and an output layer that outputs the second quantum state as output information. A method for learning quantum circuits. The inventions described in [2] to

[10] above can be applied to the quantum circuit learning method.

[12] On the computer, A function that applies input information to a quantum circuit that performs quantum gate operations on multiple qubits and obtains output information corresponding to the input information, A program that implements a function to update the learning parameters of the quantum circuit based on the difference between the output information and the teacher information, The quantum circuit has a connected first block circuit and a second block circuit, The first block circuit comprises a first gate operation layer having a first encoding gate which is a quantum gate to which the input information is encoded and to which a first encoding parameter is attached for constructing a first Hartree-Fock state, and a first conversion gate which is a quantum gate to which the learning parameter is attached for converting the first Hartree-Fock state to a first quantum state, and a measurement layer which outputs a measurement value of the first quantum state, The second block circuit comprises a second gate operation layer having a second encoding gate to encode the measured value and to which a second encoding parameter is attached for constructing a second Hartree-Fock state, and a second conversion gate to which the learning parameter is attached for converting the second Hartree-Fock state to a second quantum state, and an output layer that outputs the second quantum state as output information. A quantum circuit learning program. The inventions described in [2] to

[10] above are applicable to the quantum circuit learning program.

[13] The system includes a quantum computing unit that applies input information to a quantum circuit that performs quantum gate operations on multiple qubits and obtains output information corresponding to the input information. The quantum circuit has a connected first block circuit and a second block circuit, The first block circuit comprises a first gate operation layer having a first encoding gate which is a quantum gate on which the input information is encoded and which is fitted with a first encoding parameter for constructing a first Hartree-Fock state, and a first conversion gate which is a quantum gate fitted with a learning parameter for converting the first Hartree-Fock state to a first quantum state, and a measurement layer which outputs a measurement value of the first quantum state, The second block circuit comprises a second gate operation layer having a second encoding gate to encode the measured value and to which a second encoding parameter is attached for constructing a second Hartree-Fock state, and a second conversion gate to which the learning parameter is attached for converting the second Hartree-Fock state to a second quantum state, and an output layer that outputs the second quantum state as output information. Quantum inference system. The inventions described in [2] to

[10] above are applicable to the quantum inference system.

[14] It comprises a first block circuit and a second block circuit that are connected, The first block circuit comprises a first gate operation layer having a first encoding gate which is a quantum gate to which input information is encoded and to which a first encoding parameter is attached for constructing a first Hartree-Fock state, and a first conversion gate which is a quantum gate to which the learning parameter is attached for converting the first Hartree-Fock state to a first quantum state, and a measurement layer which outputs a measurement value of the first quantum state, The second block circuit comprises a second gate operation layer having a second encoding gate to encode the measured value and to which a second encoding parameter is attached for constructing a second Hartree-Fock state, and a second conversion gate to which the learning parameter is attached for converting the second Hartree-Fock state to a second quantum state, and an output layer that outputs the second quantum state as output information. quantum circuit. The inventions described in [2] to

[10] above are applicable to the quantum circuit in question.

[15] A quantum classical hybrid neural network characterized by a repeating block circuit structure in which quantum information is processed in the following order: Hartree-Fock state, parameterized quantum circuit, and measurement layer. The inventions described in [2] to

[10] above are applicable to the quantum-classical hybrid neural network. [Explanation of symbols]

[0108] 1...Quantum circuit learning system, 7...Quantum inference system, 100...Classical computer, 110...Processing circuit, 111...Learning control unit, 112...Display control unit, 120...Memory device, 130...Input device, 140...Communication device, 150...Display device, 200...Quantum computer, 210...Quantum circuit, 220...First block circuit, 221...First gate operation layer, 221...Parameterized quantum circuit (SYMP), 222...Measurement layer, 223...First encoding gate, 224...First transformation gate, 225...First encoding parameter, 226...First learning parameter, 230...Second block circuit, 23 1…Second gate operation layer, 231…Parameterized quantum circuit (SYMP), 232…Output layer, 233…Second encoding gate, 234…Second transformation gate, 235…Second encoding parameter, 236…Second learning parameter, 240…Input information, 250…Output information, 260…Measured value, 270…Initialization layer, 281,282,283…Particle number conservation circuit, 300…Classical computer, 310…Processing circuit, 311…Inference unit, 312…Display control unit, 320…Memory device, 330…Input device, 340…Communication device, 350…Display device, 400…Classical computer, 410…Trained quantum circuit,

Claims

1. A quantum computing unit that applies input information to a quantum circuit that performs quantum gate operations on multiple qubits and obtains output information corresponding to the input information, The system comprises a learning control unit that updates the learning parameters of the quantum circuit based on the difference between the output information and the teacher information, The quantum circuit has a connected first block circuit and a second block circuit, The first block circuit comprises a first gate operation layer having a first encoding gate which is a quantum gate to which the input information is encoded and to which a first encoding parameter is attached for constructing a first Hartree-Fock state, and a first conversion gate which is a quantum gate to which the learning parameter is attached for converting the first Hartree-Fock state to a first quantum state, and a measurement layer which outputs a measurement value of the first quantum state, The second block circuit comprises a second gate operation layer having a second encoding gate to which the measured value is encoded and to which a second encoding parameter is attached for constructing a second Hartree-Fock state, and a second conversion gate to which the learning parameter is attached for converting the second Hartree-Fock state to a second quantum state, and an output layer that outputs the second quantum state as output information. Quantum circuit learning system.

2. The measurement layer outputs the expected value of the observable for the first quantum state as the measured value. The quantum computing unit sets the measured value to the second encoding parameter having the second encoding gate. The quantum circuit learning system according to claim 1.

3. The quantum circuit learning system according to claim 2, wherein the output layer outputs the second quantum state as a trial wave function.

4. The quantum circuit learning system according to claim 1, wherein the first block circuit and / or the second block circuit store the number of particles represented by the plurality of qubits.

5. The quantum circuit learning system according to claim 1, wherein the learning control unit updates the learning parameters using a cost function that evaluates the difference.

6. The quantum circuit learning system according to claim 5, wherein the cost function is defined by the sum of the expectation values ​​of the Hamiltonian for the second quantum state over the number of samples of the input information.

7. The quantum circuit learning system according to claim 1, wherein the learning control unit updates the learning parameters according to the Nelder-Mead method, Powell method, CG method, Newton method, BFGS method, L-BFGS-B method, TNC method, COBYLA method, or SLSQP method.

8. The quantum circuit learning system according to claim 1, wherein the learning parameter is a rotation angle parameter representing the rotation angle of the rotation gate among the first and second transformation gates.

9. The quantum circuit learning system according to claim 1, wherein the first gate operation layer and the second gate operation layer have different quantum gate configurations.

10. The aforementioned input information consists of molecular structure parameters that define the molecular structure of the target molecule. The output information is the trial wave function. The quantum circuit learning system according to claim 1.

11. Input information is applied to a quantum circuit that performs quantum gate operations on multiple qubits, and output information corresponding to the input information is obtained. The system includes updating the learning parameters of the quantum circuit based on the difference between the output information and the training information, The quantum circuit has a connected first block circuit and a second block circuit, The first block circuit comprises a first gate operation layer having a first encoding gate which is a quantum gate to which the input information is encoded and to which a first encoding parameter is attached for constructing a first Hartree-Fock state, and a first conversion gate which is a quantum gate to which the learning parameter is attached for converting the first Hartree-Fock state to a first quantum state, and a measurement layer which outputs a measurement value of the first quantum state, The second block circuit comprises a second gate operation layer having a second encoding gate to which the measured value is encoded and to which a second encoding parameter is attached for constructing a second Hartree-Fock state, and a second conversion gate to which the learning parameter is attached for converting the second Hartree-Fock state to a second quantum state, and an output layer that outputs the second quantum state as output information. A method for learning quantum circuits.

12. On the computer, A function that applies input information to a quantum circuit that performs quantum gate operations on multiple qubits and obtains output information corresponding to the input information, A program that implements a function to update the learning parameters of the quantum circuit based on the difference between the output information and the teacher information, The quantum circuit has a connected first block circuit and a second block circuit, The first block circuit comprises a first gate operation layer having a first encoding gate which is a quantum gate to which the input information is encoded and to which a first encoding parameter is attached for constructing a first Hartree-Fock state, and a first conversion gate which is a quantum gate to which the learning parameter is attached for converting the first Hartree-Fock state to a first quantum state, and a measurement layer which outputs a measurement value of the first quantum state, The second block circuit comprises a second gate operation layer having a second encoding gate to which the measured value is encoded and to which a second encoding parameter is attached for constructing a second Hartree-Fock state, and a second conversion gate to which the learning parameter is attached for converting the second Hartree-Fock state to a second quantum state, and an output layer that outputs the second quantum state as output information. A quantum circuit learning program.

13. The system includes a quantum computing unit that applies input information to a quantum circuit that performs quantum gate operations on multiple qubits and obtains output information corresponding to the input information. The quantum circuit has a connected first block circuit and a second block circuit, The first block circuit includes a first gate operation layer having a first encoding gate which is a quantum gate on which the input information is encoded and which is fitted with a first encoding parameter for constructing a first Hartree-Fock state, and a first conversion gate which is a quantum gate fitted with a learning parameter for converting the first Hartree-Fock state to a first quantum state, and a measurement layer which outputs a measured value of the first quantum state. The second block circuit comprises a second gate operation layer having a second encoding gate to which the measured value is encoded and to which a second encoding parameter is attached for constructing a second Hartree-Fock state, and a second conversion gate to which the learning parameter is attached for converting the second Hartree-Fock state to a second quantum state, and an output layer that outputs the second quantum state as output information. Quantum inference system.

14. It comprises a first block circuit and a second block circuit connected together, The first block circuit comprises a first gate operation layer having a first encoding gate which is a quantum gate on which input information is encoded and which is fitted with a first encoding parameter for constructing a first Hartree-Fock state, and a first conversion gate which is a quantum gate fitted with a learning parameter for converting the first Hartree-Fock state to a first quantum state, and a measurement layer which outputs a measured value of the first quantum state, The second block circuit comprises a second gate operation layer having a second encoding gate to which the measured value is encoded and to which a second encoding parameter is attached for constructing a second Hartree-Fock state, and a second conversion gate to which the learning parameter is attached for converting the second Hartree-Fock state to a second quantum state, and an output layer that outputs the second quantum state as output information. quantum circuit.

Images