Quantum circuit learning method, quantum circuit learning system, and quantum-classical hybrid neural network

Abstract

To provide a quantum circuit learning method, a quantum circuit learning system, and a quantum classical hybrid neural network which reduce a calculation cost required for training.SOLUTION: The quantum circuit learning method includes a reading step, a transfer step, and a training step. In the reading step, an optimized first parameter assigned to a first feature extraction circuit included in a trained first quantum circuit for a first task is read. The first quantum circuit is trained based on a first dataset related to first classical data being an explanatory variable. In the transfer step, the first parameter is transferred to a second feature extraction circuit included in a second quantum circuit for a second task. In the training step, the second quantum circuit is trained based on a second dataset related to second classical data while fixing the first parameter transferred to the second feature extraction circuit, and a second parameter of a task-specific circuit included in the second quantum circuit is optimized.SELECTED DRAWING: Figure 3

Description

[Technical Field]

[0001] Embodiments of the present invention relate to a quantum circuit learning method, a quantum circuit learning system, and a quantum-classical hybrid neural network. [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 computing devices 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 devices is currently thriving. In particular, the Variational Quantum Eigensolver (VQE) algorithm, which hybridizes quantum and classical computers, is expected to be applied to quantum chemical calculations. 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 vast number of measurement samples that repeatedly switch between the NISQ device and the classical computer. Conventionally, it has been proposed to remove a portion of the final layer of a quantum circuit, including the measurement layer, and use the remaining circuit for transfer learning. This is quantum machine learning within the realm of linear operations where measurements are performed in the final layer. However, this method had a high learning cost to obtain high-precision results. [Prior art documents] [Patent Documents]

[0003] [Non-Patent Document 1] A. Peruzzo, J. McClean, P. Shadbolt, M.-H. Yung, X.-Q. Zhou, P. J. Love, A. Aspuru-Guzik and J. L.O’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 Neutral Network for Calculating Ground State Energies of Molecules ”Entropy 22, 828 (2020) Non-Patent Document 3 A. Mari, T. R. Bromley, J. Izaac, M. Schuld, and N. Killoran, “Tranfer learning in hybrid classical-quantum neural networks” Quantum 4, 340 (2020) Summary of the Invention Problems to be Solved by the Invention

[0004] In a series of studies aimed at reducing the computational cost of VQE, Xia & Kais et al. proposed a Hybrid Quantum-Classical Neural Network (HQCNN) in 2020 that can accurately estimate the potential energy surface (PES) of the ground state of small molecules. This HQCNN is a method for constructing a surrogate model of VQE that replaces the conventional VQE computation procedure with a neural network using quantum circuits, and is characterized by the inclusion of an intermediate measurement layer. Specifically, by applying this HQCNN to quantum chemical calculations for chemical reaction analysis, variational optimization for each molecular structure, which was required in conventional PES calculations using VQE, becomes unnecessary, and highly accurate PES inference can be performed at low cost. However, this HQCNN has a high training cost because of the large number of quantum circuit parameters that need to be optimized during training.

[0005] The problem that this invention aims to solve is to provide a quantum circuit learning method, a quantum circuit learning system, and a quantum-classical hybrid neural network that can reduce the computational cost required for training. [Means for solving the problem]

[0006] A quantum circuit learning method according to an embodiment comprises a readout step, a transfer step, and a training step. The readout step is a step of reading an optimized first parameter assigned to a first feature extraction circuit included in a first quantum circuit that has been trained for a first task, wherein the first quantum circuit is trained on a first dataset of first classical data which are explanatory variables, and the first feature extraction circuit includes a parameterized quantum circuit having an encode gate for encoding the first classical data and a quantum operation gate for performing quantum operations on qubits according to the first parameter, and a measurement layer that outputs first measurement data of qubits. The transfer step is a step of transferring the first parameter to a second feature extraction circuit included in a second quantum circuit for a second task, wherein the second feature extraction circuit includes a parameterized quantum circuit having an encode gate for encoding second classical data which represent explanatory variables common to the first classical data and a quantum operation gate for performing quantum operations on qubits according to the first parameter, and a measurement layer that outputs second measurement data of qubits. The training step is to train the second quantum circuit based on a second dataset relating to the second classical data, while fixing the first parameters transferred to the second feature extraction circuit, and to optimize the second parameters of a task-specific circuit in the second quantum circuit that follows the second feature extraction circuit, wherein the task-specific circuit includes a parameterized quantum circuit having an encoding gate for encoding the second measurement data and a quantum operation gate for performing quantum operations on qubits according to the second parameters. [Brief explanation of the drawing]

[0007] [Figure 1] Block diagram showing one example configuration of a quantum circuit learning system. [Figure 2] Diagram showing an example of HQCNN circuit configuration. [Figure 3] A diagram illustrating an example of the processing procedure for quantum circuit learning. [Figure 4] Figure 3 schematically illustrates the training process of the first HQCNN performed in step S1. [Figure 5] This figure shows an example configuration of a parameterized quantum circuit layer U(θ) when the number of qubits n=4. [Figure 6] This figure shows an example configuration of a parameterized quantum circuit layer U(θ) when the number of qubits n=5. [Figure 7] Figure 3 schematically illustrates the transfer process performed in step S4 and the training process of the second HQCNN performed in step S5. [Figure 8] This figure shows a graph representing the numerical simulation results of the H2 molecule in Example 1. [Figure 9] This figure shows a graph representing the numerical simulation results of the LiH molecule in Example 1. [Figure 10] Figure 9 shows a graph representing the numerical simulation results for the comparative example corresponding to Figure 9. [Figure 11] Figure showing a graph representing the numerical simulation results for Example 2. [Figure 12] Figure 11 shows a graph representing the numerical simulation results of HQCNN related to the comparative example. [Figure 13] Figure showing a graph representing the numerical simulation results for Example 3. [Figure 14] Figure showing graphs representing other numerical simulation results related to Example 3. [Modes for carrying out the invention]

[0008] The quantum circuit learning method, quantum circuit learning system, and quantum-classical hybrid neural network according to this embodiment will be described below with reference to the drawings.

[0009] 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.

[0010] 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.

[0011] The processing circuit 110 has a processor such as a CPU (Central Processing Unit) and memory such as RAM (Random Access Memory). The processing circuit 110 comprehensively controls the classical computer 100. The processing circuit 110 has a training unit 111 and a display control unit 112. The processing circuit 110 realizes each of the above units 111 to 112 by executing a quantum circuit learning program. The quantum circuit learning program is stored in a non-temporary computer-readable storage medium realized by a storage device 120 or the like. The quantum circuit learning program may be implemented as a single program that describes all the functions of the above units 111 to 112, or it may be implemented as multiple modules divided into several functional units. Furthermore, the above units 111 to 112 may be implemented by 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.

[0012] The training unit 111 performs quantum circuit learning on the quantum classical hybrid neural network (HQCNN) 210, which is implemented on the quantum computer 200. The HQCNN 210 consists of a first HQCNN 210-1 for the first task and a second HQCNN 210-2 for the second task. Hereafter, when the first HQCNN 210-1 and the second HQCNN 210-2 are not distinguished, they will be referred to as HQCNN 210. For quantum circuit learning, the training unit 111 obtains a training dataset. The training dataset contains multiple training samples. Each training sample contains classical data, which is the input data, and corresponding training data. The training unit 111 provides the classical data to the HQCNN 210. The classical data is converted into output data by the HQCNN 210. The training unit 111 trains the HQCNN 210 based on the difference between the output data and the training data and optimizes the parameters of the HQCNN 210.

[0013] The display control unit 112 displays various information on the display device 150. For example, the display control unit 112 displays classical data, output data, training data, etc.

[0014] The storage device 120 is composed 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.

[0015] 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.

[0016] 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.

[0017] 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.

[0018] The quantum computer 200 is equipped with a quantum-classical hybrid neural network (HQCNN) 210 that performs quantum gate operations on multiple qubits, and is a computer that performs quantum computations using the HQCNN 210. The implementation method for qubits and quantum gates by the HQCNN 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.

[0019] Quantum computer 200 receives classical data, which is input data, from classical computer 100, and inputs the classical data into HQCNN210, which performs quantum gate operations on multiple qubits. HQCNN210 converts the classical data into output data. Quantum computer 200 retrieves the output data from HQCNN210. Quantum computer 200 transmits the retrieved output data to classical computer 100.

[0020] The first HQCNN210-1 is a quantum-classical hybrid neural network trainable for a first task, comprising: a feature extraction circuit assigned an optimizable parameter θ for the first task; and a task-specific circuit following the feature extraction circuit, assigned an optimizable parameter Θ for the first task. The feature extraction circuit includes a parameterized quantum circuit having an encode gate for encoding first classical data which are explanatory variables and a quantum operation gate for performing quantum operations on qubits according to parameter θ; and a measurement layer that outputs measured data of qubits. The task-specific circuit includes a parameterized quantum circuit having an encode gate for encoding measured data and a quantum operation gate for performing quantum operations on qubits according to parameter Θ; and an output layer that outputs output data representing the quantum state of qubits.

[0021] The second HQCNN210-2 is a quantum-classical hybrid neural network trainable for a second task different from the first task, and is trained for the first task, with parameters θ extracted from the first HQCNN210-1 which was trained for the first task and optimized for the first task. * The system comprises a feature extraction circuit to which a parameter θ is assigned, and a task-specific circuit that follows the feature extraction circuit and is assigned a parameter Φ that can be optimized for a second task. The feature extraction circuit includes an encoding gate and a parameter θ for encoding the second classical data, which is an explanatory variable. * The parameterized quantum circuit includes a quantum operation gate for performing quantum operations on a qubit according to a parameter Φ, and a measurement layer that outputs measurement data of the qubit. The task-specific circuit includes a parameterized quantum circuit having an encoding gate for encoding the measurement data and a quantum operation gate for performing quantum operations on a qubit according to a parameter Φ, and an output layer that outputs output data representing the quantum state of the qubit.

[0022] In this embodiment, the training unit 111 performs a training step for a first HQCNN210-1 for a first task (hereinafter referred to as the first training) and a training step for a second quantum circuit for a second task (hereinafter referred to as the second training). In the first training step, the training unit 111 optimizes the parameters θ of the feature extraction circuit 220 and the parameters Θ of the task-specific circuit 230 included in the HQCNN210-1.

[0023] In the second training process, the training unit 111 trains the second HQCNN210-2 by quantum transfer learning using the trained first HQCNN210-1. Specifically, the second training process includes a readout process, a transfer process, and a training process. In the readout process, the training unit 111 assigns optimized parameters θ to the feature extraction circuit included in the trained first HQCNN210-1 for the first task. * The data is read out. In the transfer process, the training unit 111 reads the optimized parameter θ. * The optimized parameters θ, which have been transferred to the feature extraction circuit included in the second HQCNN210-2 for the second task, are then transferred to the feature extraction circuit included in the second HQCNN210-2 by the training unit 111 during the training process. * While keeping the parameters fixed, a second HQCNN210-2 is trained based on a second dataset of second classical data, and the parameters Φ of the task-specific circuit that follows the feature extraction circuit in the second HQCNN210-2 are optimized.

[0024] In the first or second training process, the training unit 111 uses a classical computer to optimize the parameter θ or parameter Φ using the Nelder-Mead method, Powell method, CG method, Newton method, BFGS method, L-BFGS-B method, TNC method, COBYLA method and / or SLSQP method.

[0025] Next, with reference to Figure 2, the circuit configurations of the first HQCNN210-1 and the second HQCNN210-2 will be explained in detail. Since the circuit configurations of the first HQCNN210-1 and the second HQCNN210-2 are substantially the same, they will not be distinguished, and Figure 2 will use HQCNN210 as an example.

[0026] Figure 2 shows an example of the circuit configuration of HQCNN210. HQCNN210 is a sequence of quantum circuits that includes a sequence of quantum gates controlled by circuit parameters. As shown in Figure 2, HQCNN210 has n (where n is a natural number greater than or equal to 2) qubits. n can be appropriately set according to the scale of the target molecule, such as the number of atoms, electrons, or spin orbits. HQCNN210 constructs an initial quantum state by applying quantum operations corresponding to classical data 240 to the n qubits, constructs an output quantum state by applying quantum operations corresponding to the circuit parameters to the initial quantum state, and outputs output data 250 corresponding to the output quantum state.

[0027] As shown in Figure 2, the HQCNN210 includes a feature extraction circuit 220 and a task-specific circuit 230 that follows the feature extraction circuit 220. The feature extraction circuit 220 is a quantum circuit that includes a parameterized quantum circuit 221 and a measurement layer 222 that follows the parameterized quantum circuit 221. The parameterized quantum circuit 221 has a sequence of encoding gates 223 and a sequence of quantum manipulation gates 224. The encoding gate 223 is a quantum gate to which an encoding parameter 225 is assigned for encoding classical data 240. The encoding parameter 225 is a type of circuit parameter, but it is not subject to optimization by quantum circuit learning. The encoding parameter 225 is set to a value corresponding to the classical data 240. The quantum manipulation gate 224 is a quantum gate to which a rotation angle parameter 226 is assigned for performing a quantum rotation operation on a qubit. The measurement layer 222 outputs measurement data 260 that represents the quantum states corresponding to n qubits. The rotation angle parameter 226 controls the rotation angle of the quantum gate performing the quantum rotation operation.

[0028] The feature extraction circuit 221 having the above configuration performs quantum operations on n qubits using an encoding gate 223 to which encoding parameters 225 corresponding to classical data 240 are assigned, thereby constructing a first initial quantum state. The quantum operation gate 224 to which rotation angle parameters 226 are assigned converts the first initial quantum state into an intermediate quantum state. The measurement layer 222 outputs the expected value of the observable defined by the arbitrary tensor product of Pauli operators for the intermediate quantum state constructed by the parameterized quantum circuit 221 as measurement data 260.

[0029] The task-specific circuit 230 is a quantum circuit that includes a parameterized quantum circuit 231 and an output layer 232 that follows the parameterized quantum circuit 231. The parameterized quantum circuit 231 has a sequence of encoding gates 233 and a sequence of quantum manipulation gates 234. The encoding gate 233 is a quantum gate to which an encoding parameter 235 is assigned for encoding the measurement data 260 output by the measurement layer 222. The encoding parameter 235 is a circuit parameter, but it is not subject to optimization by quantum circuit learning. The encoding parameter 235 is set to a value corresponding to the measurement data 260. The quantum manipulation gate 234 is a quantum gate to which a rotation angle parameter 236 is assigned for performing a quantum rotation operation on a qubit. The output layer 232 outputs output data 250 that represents the quantum state corresponding to n qubits. The rotation angle parameter 236 controls the rotation angle of the quantum gate that performs the quantum rotation operation.

[0030] The task-specific circuit 230 having the above configuration performs quantum operations on n qubits using an encoding gate 233 to which encoding parameters 235 corresponding to the measurement data 260 are assigned, thereby constructing a second initial quantum state. The quantum operation gate 234 to which rotation angle parameters 236 are assigned converts the second initial quantum state into an output quantum state, and the output layer 232 outputs output data 250 representing the output quantum state. The output data 250 is the trial wave function represented by the output quantum state.

[0031] Parameterized quantum circuits 221 and 231 are each realized by a Real Amplitude type quantum circuit or a particle number conservation circuit called an A gate. A particle number conservation circuit is an ansatz that conserves the number of particles between the input quantum state and the output quantum state. In a particle number conservation circuit, a Hartree-Fock state is used as the input quantum state. A Hartree-Fock state refers to a quantum state when electrons are filled sequentially from the lowest energy electron orbital. That is, parameterized quantum circuits 221 and 231 each perform quantum gate operations on the input Hartree-Fock state using a quantum operation gate controlled by a rotation angle parameter, while conserving the number of particles. By employing a particle number conservation circuit, HQCNN210 can adopt a circuit configuration specialized for quantum chemical calculations using a Hartree-Fock state as the initial input, compared to the more general Non-Patent Document 2. This will enable improved convergence in systems with a large number of atoms, application to practical systems, reduction of the number of circuit parameters, and consequently, a reduction in the computational cost of quantum circuit learning.

[0032] The feature extraction circuit 220 and the task-specific circuit 230 may have the same quantum gate configuration or they may have different quantum gate configurations. Furthermore, the arrangement of the encode gate 223 and the quantum manipulation gate 224 in the parameterized quantum circuit 221 relative to the flow of qubits may be in series or in parallel. Also, the repeating structure of the encode gate 223 and the quantum manipulation gate 224 may be a single repeating structure as illustrated in Figure 2, or a structure with two or more repeating structures. The parameterized quantum circuit 221 may have a circuit configuration in which the encode gate 223 and the quantum manipulation gate 224 are repeated in series two or more times. Note that "in series" means that two or more block circuits of the encode gate 223 and the quantum manipulation gate 224 are repeated from upstream to downstream of the qubits. The parameterized quantum circuit 221 may have a circuit configuration in which the encode gate 223 and the quantum manipulation gate 224 are repeated in series two or more times.

[0033] Next, we will describe an example of quantum circuit learning for the first HQCNN210-1 and the second HQCNN210-2 using the quantum circuit learning system 1. In the following description, the first task of the first HQCNN is to calculate the ground state energy of a hydrogen molecule, and the second task of the second HQCNN is to calculate the ground state energy of a lithium hydride molecule. Both the hydrogen molecule and the lithium hydride molecule are diatomic molecules, with 2 electrons and 4 spin orbitals.

[0034] The first and second tasks are quantum chemical calculations using the variational quantum eigenvalue method (VQE), specifically, tasks to estimate the ground state potential energy surface (PES) of the target molecule. In this case, the classical data used are molecular structure parameters, which are explanatory variables that define the molecular structure of the target molecule. These 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). The number of atoms, electrons, and spin orbitals in the molecular structure of the target molecule can be set arbitrarily. The first and second tasks are set as the same type of task.

[0035] Figure 3 shows an example of the processing procedure for quantum circuit learning according to this embodiment. As shown in Figure 3, first, the training unit 111 trains a first HQCNN based on a dataset DS1 which includes classical data b1 (step S1). The classical data b1 is assumed to be an arbitrary interatomic distance of hydrogen atoms in a hydrogen molecule. The dataset DS1 includes the interatomic distance of hydrogen atoms which is the classical data b1, and the energy value of the ground state corresponding to the said interatomic distance which is the training data.

[0036] FIG. 4 is a diagram schematically showing the training process of the first HQCNN210-1 executed in step S1. As shown in FIG. 4, the number of qubits of the first HQCNN210-1 is 4. The first HQCNN210-1 has a feature extraction circuit 220A and a task-specific circuit 230A. The feature extraction circuit 220A is applied with |0> as an initial quantum state. The feature extraction circuit 220A has a parameterized quantum circuit 221A and a measurement layer 222A, and the parameterized quantum circuit 221A has a data encoding layer G0(b1) and a parameterized quantum circuit layer U(θ). The data encoding layer G0(b1) is a part where the encoding gates of the parameterized quantum circuit 221A are implemented, and the parameterized quantum circuit layer U(θ) is a part where the quantum operation gates of the parameterized quantum circuit 221A are implemented.

[0037] The data encoding layer G0(b1) has an encoding gate for encoding classical data b1 into the feature extraction circuit 220A. The mathematical expression of the encoding gate is represented by the following equation (1) for an n-qubit system.

[0038]

Equation

[0039] Here, g i represents a quantum gate (encoding gate) for a single qubit, {b i} represents general classical data, and f i is a classical function that converts classical data {b i} into the parameters of the quantum gate g i . The quantum gate g i is represented by Ry({b i})H, for example, as shown in the following equation (2).

[0040]

Equation

[0041] The parameterized quantum circuit layer U(θ) applies quantum rotation operations to qubits according to the rotation angle parameter θ. The parameterized quantum circuit layer U(θ) consists of a 1-qubit gate and a 2-qubit gate that entangles qubits, such as a CNOT. The parameterized quantum circuit layer U(θ) plays a crucial role in the expressive power of the first HQCNN210-1, and the performance of the first HQCNN210-1 heavily depends on the structure of the parameterized quantum circuit layer U(θ). A representative example of the first HQCNN210-1 is the CX gate and R y There is a Real Amplitude type quantum circuit that alternately operates a gate. For n qubits, the Real Amplitude type parameterized quantum circuit layer U(θ) is expressed as shown in equation (3) below when n is odd, and as shown in equation (4) below when n is even.

[0042]

number

[0043] Figure 5 shows an example configuration of a parameterized quantum circuit layer U(θ) when the number of qubits n=4, and Figure 6 shows an example configuration of a parameterized quantum circuit layer U(θ) when the number of qubits n=5. As an example, the block circuit in Figure 5 (the block circuit enclosed in parentheses in the figure) has three CNOT gates and four Y-axis rotation gates that perform θ rotations around the Y axis. The block circuit in Figure 6 (the block circuit enclosed in parentheses in the figure) has four CNOT gates and five Y-axis rotation gates that perform θ rotations around the Y axis. In Figures 5 and 6, D represents the circuit depth, which means the number of iterations based on the block circuit in the figure. The number of circuit parameters included in the parameterized quantum circuit layer U(θ) at n qubits and depth D is nD.

[0044] As shown in Figure 4, the measurement layer 222 is sandwiched between the parameterized quantum circuit U(θ) of the feature extraction circuit 220A and the parameterized quantum circuit U(Θ) of the task-specific circuit 230A. The measurement layer 222 corresponds to the activation function in a classical neural network. In the measurement layer 222, the first intermediate quantum state output from the preceding parameterized quantum circuit is used to determine the expected value <σ of the Pauli-Z matrix of each qubit. i z > Measure.

[0045] The task-specific circuit 230A has a parameterized quantum circuit 231A and a measurement layer 232A, and the parameterized quantum circuit 231A has a data encoding layer G({b1'}) and a parameterized quantum circuit layer U(Θ). The task-specific circuit 230A is subjected to |0> as its initial quantum state.

[0046] The data encoding layer G({b1'}) has an encoding gate that encodes the measurement data {b1'} from the measurement layer 222 into the task-specific circuit 230A. More specifically, the expected value <σ measured by the measurement layer 222 i z > is multiplied by π and {b1'} = π < σ i z > is substituted as a parameter for the data encoding layer G({b1'}). The mathematical expression for the encode gate of the data encoding layer G({b1'}) is obtained by replacing (b) in equation (1) with {b1'}.

[0047] The parameterized quantum circuit layer U(Θ) applies a quantum rotation operation to a qubit according to the rotation angle parameter Θ. The parameterized quantum circuit layer U(Θ), like the parameterized quantum circuit layer U(Θ), consists of a 1-qubit gate and a 2-qubit gate that entangles the qubit, such as a CNOT. The mathematical expression of the parameterized quantum circuit layer U(Θ) can be obtained by replacing θ with Θ in equations (3) and (4).

[0048] The output layer 232 is a trial wave function of the output quantum state constructed by the parameterized quantum circuit layer U(Θ). <H H2 > will be output as output data.

[0049] The first HQCNN210-1 shown in Figure 4 represents the interatomic distance of hydrogen atoms in a hydrogen molecule {b i Given {b}, the quantum state corresponding to the rotation angle parameter θ in the preceding parameterized quantum circuit U(θ) and the rotation angle parameter Θ in the subsequent parameterized quantum circuit U(Θ) is calculated, and the expected value of the quantum state is output. The Hamiltonian of a hydrogen molecule is the interatomic distance {b}. i Given}, it can be transformed into the qubit-Hamiltonian H, defined by the tensor product of Pauli matrices, as shown in equation (5) below, using the Jordan-Wigner transformation [Jordan and Wigner (1928)] or several transformation methods [Bravi and Kitaev (2005); Seeley and Love (2012)].

[0050]

number

[0051] The energy of a hydrogen molecule can be calculated by applying the qubit Hamiltonian to the output quantum state obtained from the first HQCNN210-1. At this time, the interatomic distance of hydrogen {b i The energy of a hydrogen molecule at {b} is expressed as a function of the rotation angle parameters θ and Θ. Therefore, the rotation angle parameters θ and Θ are expressed as the interatomic distance between each hydrogen atom {b}. i By variational optimization with respect to}, any hydrogen interatomic distance {b i We can obtain the first HQCNN210-1 which estimates the ground state energy and quantum state of}.

[0052] The training unit 111 optimizes the rotation angle parameters θ and Θ of the first HQCNN210A based on the difference between the output data from the output layer 232 and the training data corresponding to the classical data b1. Specifically, the training unit 111 calculates a loss function that evaluates the difference between the output data and the training data, and updates the rotation angle parameters θ and Θ according to a predetermined optimization method to minimize the loss function.

[0053] The loss function is defined by the sum of the Hamiltonian expectation values ​​for the output quantum state over the number of input data samples. Let α be the number of interatomic distance samples, {b} i}={b0,b1,···b α-1 In that case, specifically, the loss function <l>This is defined by equation (6) below.

[0054]

number

[0055] 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. As training data, high-precision energy expectation values ​​calculated based on the corresponding classical data are used. As an example, as training data, exact solutions calculated by a classical computer based on the classical data according to any high-precision algorithm such as the FCI (Full Configuration Interaction Method) method or CASCI (Complete Active Space CI) method may be used. Alternatively, experimental results for the input data may be used as training data.

[0056] When the rotation angle parameter is updated, the training unit 111 determines whether or not to terminate the optimization of the rotation angle parameter. For example, the training unit 111 determines whether or not the optimization termination condition is met. The termination condition can be set to any condition, such as the number of updates reaching a predetermined number or the function value of the loss function reaching a threshold. If it is determined that the termination condition is not met, that is, if it is determined that the optimization should not be terminated, the update process is repeated for other samples. Then, if it is determined that the termination condition is met, that is, if it is determined that the optimization of the rotation angle parameter should be terminated, the training unit 111 optimizes the rotation angle parameter θ set at the current stage. * and Θ * This is confirmed.

[0057] For the first HQCNN210-1 with n qubits and depth D, the number of rotation angle parameters to optimize is 2nD, and the input {b i α expected value calculations are required, corresponding to the number of samples in}.

[0058] When step S1 is performed, the storage device 120 stores the rotation angle parameter θ assigned to the first HQCNN. * and Θ * Save the set (step S2). Rotation angle parameter θ * and Θ * Each may be associated with a label that represents the hydrogen molecule, which is the molecule to be studied.

[0059] When step S2 is performed, the training unit 111 uses the rotation angle parameter θ saved in step S2. * and Θ * From this set, select the rotation angle parameter θ of the feature extraction circuit 220A. * The data is read (step S3). Step S3 may be disclosed by an instruction to start quantum transfer learning. This instruction may be input by the operator via input device 130, for example. Alternatively, step S3 may be started automatically when step S1 or S2 is completed.

[0060] When step S3 is performed, the training unit 111 reads out the rotation angle parameter θ in step S3. * This is then transferred to the feature extraction circuit included in the second HQCNN210-2 (step S4). Once step S4 is performed, the training unit 111 trains the second HQCNN210-2 based on the dataset DS2, which includes the classical data b2 (step S5).

[0061] Figure 7 schematically shows the transfer process performed in step S4 and the training process of the second HQCNN performed in step S5. As shown in the upper part of Figure 7, in step S1, the optimized rotation angle parameter θ is set for the feature extraction circuit included in the first HQCNN210-1. * However, the rotation angle parameter Θ is optimized for task-specific circuits. * This has been obtained.

[0062] As shown in the lower part of Figure 7, a second HQCNN210-2 is prepared in the quantum computer 200. The second HQCNN210-2 also has the same circuit configuration as the first HQCNN210-1, that is, it has a feature extraction circuit and a task-specific circuit. In step S4, the training unit 111 optimizes the rotation angle parameter θ of the feature extraction circuit included in the first HQCNN210-1. * This is then transferred to the feature extraction circuit included in the second HQCNN210-2. In other words, the feature extraction circuit 220A included in the first HQCNN210-1 is transferred to the second HQCNN210-2.

[0063] The second HQCNN210-2 will learn the lithium hydride molecule (LiH) as an example. The lithium hydride molecule is similar to the hydrogen atom in that it is a diatomic molecule, but one of its constituent atoms is different. Since the feature extraction circuit 220B is represented by 4 qubits, the qubit Hamiltonian for the lithium hydride molecule uses a 2-electron, 2-orbital model. Classical data b2 will be used as input data for the second HQCNN210-2. Classical data b2 represents the interatomic distance of the lithium hydride molecule, i.e., the distance between the hydrogen atom and the lithium atom.

[0064] The second feature extraction circuit F({b2},θ) of HQCNN210-2 * ) constructs a second initial quantum state by applying an encoded gate to the qubit into which classical data b2 has been substituted, and the rotation angle parameter θ * The assigned quantum operation gate is applied to the second initial quantum state to transform it into a second intermediate quantum state, and the measured value of the second intermediate quantum state (second measurement data) b2´ is output. Then, the task-specific circuit G({b2´})U(Φ) constructs the second initial quantum state by applying the data encoding layer G({b2´}), which has an encoding gate into which the measurement data b2´ has been substituted, to the qubit, and then applies the parameterized quantum circuit layer U(Φ), which has a quantum operation gate assigned the rotation angle parameter Φ, to the second initial quantum state to transform it into a second output quantum state, and outputs the qubit Hamiltonian (second output data) corresponding to the second output quantum state.

[0065] In step S5, the training unit 111 trains a second HQCNN210-2 based on the dataset DS2, which includes classical data b2. Specifically, the training unit 111 trains a feature extraction circuit F({b2},θ * ) Optimized rotation angle parameter θ * While fixing the first HQCNN210-2, the second HQCNN210-2 is trained, and the rotation angle parameter Φ of the task-specific circuit G({b2´})U(Φ) is optimized based on the difference between the second output data and the training data corresponding to the classical data b2. Here, the training unit 111 calculates a loss function that evaluates the difference between the output data and the training data, and updates the rotation angle parameter Φ according to the optimization method described above to minimize the loss function. The loss function is obtained by replacing Θ with Φ in equation (6) above and changing θ to θ * This can be obtained by replacing it with θ. Note that in the training of the second HQCNN210-2, θ * It will be fixed in place.

[0066] When the rotation angle parameter Φ is updated, the training unit 111 determines whether or not to terminate the optimization of the rotation angle parameter Φ. For example, the training unit 111 determines whether or not the optimization termination conditions are met. The termination conditions can be set to any conditions, such as the number of updates reaching a predetermined number or the function value of the loss function reaching a threshold. If it is determined that the termination conditions are not met, that is, if it is determined that the optimization should not be terminated, the above update process is repeated for other samples. Then, if it is determined that the termination conditions are met, that is, if it is determined that the optimization of the rotation angle parameter Φ should be terminated, the training unit 111 sets the rotation angle parameter set at the current stage to the optimized parameter Φ. * This is confirmed. This completes the optimized second HQCNN210-2.

[0067] The optimized second HQCNN210-2 is a quantum-classical hybrid neural network trained for the second task, with parameters θ optimized for the first task, extracted from the first HQCNN210-1, which was trained for a first task different from the second task. * A feature extraction circuit to which is assigned, and a parameter Φ optimized for a second task that follows the feature extraction circuit. * The feature extraction circuit has a task-specific circuit assigned to it, and a parameter θ for encoding the classical data which is the explanatory variable. * The system includes a parameterized quantum circuit having a quantum operation gate for performing quantum operations on a qubit according to Φ, and a measurement layer for outputting measurement data of the qubit. The task-specific circuit has an encoding gate for encoding the measurement data and a parameter Φ * The system includes a parameterized quantum circuit having a quantum operation gate for performing quantum operations on a qubit according to a given formula, and an output layer that outputs output data representing the quantum state of the qubit.

[0068] When step S5 is performed, the storage device 120 stores the rotation angle parameter θ assigned to the second HQCNN210-2. * and Φ * Save the set (step S6). Rotation angle parameter θ * and Φ * Each may be associated with a label that represents the lithium hydride molecule, which is the molecule to be studied.

[0069] With the above steps, quantum circuit learning for the first HQCNN210-1 and the second HQCNN210-2 by the quantum circuit learning system 1 is complete.

[0070] When the feature extractor F in the above quantum transfer learning is applied to quantum chemical calculations as shown in Figure 3, the classical input information (classical data) is the interatomic distance of hydrogen atoms {b i It can be considered a quantum circuit that extracts the characteristics of the molecular structure from}. For a second HQCNN210-2 with n qubits and depth D, the number of parameters to be optimized can be reduced from 2nD to nD by using the quantum circuit learning method according to this embodiment.

[0071] The quantum transfer learning according to this embodiment can be used between different tasks where the data structure of the classical input data is similar. The feature extractor F can extract the structure of the target molecule, given as classical data, as abstracted information. Therefore, in the above embodiment, the feature extractor F is generated based on classical data of H2, a diatomic molecule, for the first HQCNN210-1, but this embodiment is not limited to this and may be generated based on other diatomic molecules. Furthermore, by generating the feature extractor F based on classical data of polyatomic molecules with two or more atoms, the feature extractor F becomes capable of extracting features of more complex structures. In this embodiment, the feature extractor F obtained in this way can be transferred to an HQCNN whose task is quantum chemical calculation of molecules with similar molecular structures. In addition to quantum chemical calculations, it can also be applied to materials informatics, where the classical input information is similar.

[0072] The quantum circuit learning method according to this embodiment targets HQCNNs that not only perform measurements in the final layer but also insert measurement layers between parameterized quantum circuits, and uses block circuits including intermediate measurement layers as transfer learning. This enables transfer learning of quantum circuits that realize nonlinear operations beyond the realm of linear operations, and thus enables the realization of highly accurate quantum machine learning models, particularly in quantum chemical calculations.

[0073] 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.

[0074] As another example, in Figure 2, the task-specific circuit 220 is shown to have a parameterized quantum circuit 231 and an output layer 232. However, one or more blocks of parameterized quantum circuits and measurement layers may be connected between the parameterized quantum circuit 231 and the output layer 232. In this case, the multiple parameterized quantum circuits would be connected via the measurement values ​​of the preceding measurement layer 222. This makes it possible to handle complex quantum chemical calculations.

[0075] The following describes an example of quantum chemical calculation according to this embodiment.

[0076] (Example 1) The molecules treated in Example 1 were H2 molecules, LiH molecules, and HF molecules. Numerical simulations were performed using the electron Hamiltonians of these molecules. 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.Durán, P. Eendebak, M. Everitt, I. Sertage, A. Frisch, A. Fuhrer, J. Gambetta, B. Gambetta, J. Gomez, D. Gomez, D. Gomez. Greenberg, I. Hamamura, 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, Martin-Fernand, D. McCrell, D. McCrell. McKay, S. Meesala, A. 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. Davi Rice, A. R. Rudy, N. Rudy, M. Ryu, Ryu, Ryu. C. Schnabel, E. Schoute, K. Setia, Y. Shi, A. Silva, Y. Siraichi, S. Sivarajah, J. Smolin, M. Soeken, H. Takahashi, I. Tavernelli, C. Taylor, P. Taylour, K. Trabing, M. Treinish, W. Turner, D. C. Vogt-Lee, J. Wilson, J. Wilstrom, J. Wilstrom, H. Takahashi. E. Winston, J. Wood, S. Wood, S. Worner, I. Akhalwaya, J. Zoufalhttps.This was done using https: / / doi.org / 10.5281 / zenodo.2562111 (see (2019) An Open-source Framework for Quantum Computing).

[0077] Figure 8 shows a graph representing the numerical simulation results of the H2 molecule according to Example 1. In the graph on the left of Figure 8, the vertical axis is defined by the potential energy E [hartree] of the ground state of the H2 molecule, and the horizontal axis is defined by the bond length [Å] between hydrogen atoms. In the graph on the right of Figure 8, the vertical axis is defined by the absolute error ΔE [hartree] of the ground state of the H2 molecule, and the horizontal axis is defined by the bond length [Å] between hydrogen atoms. The square plots represent the numerical simulation results of the ground state of the H2 molecule using the first HQCNN set to n=4 and D=4. The number of variational optimization iterations is 1000. The number of parameters to be optimized is 2nD=32. The solid line represents the exact solution, FCI (Full Configuration Interaction Method). As shown in Figure 8, the inference error is below the chemical accuracy across the entire specified interatomic distance range, indicating sufficient accuracy.

[0078] Figure 9 shows a graph representing the numerical simulation results of the LiH molecule according to Example 1. In the graph on the left of Figure 9, the vertical axis is defined by the potential energy E [hartree] of the ground state of the LiH molecule, and the horizontal axis is defined by the bond length [Å] between the lithium atom and the hydrogen atom. In the graph on the right of Figure 8, the vertical axis is defined by the absolute error ΔE [hartree] of the ground state of the LiH molecule, and the horizontal axis is defined by the bond length [Å] between the lithium atom and the hydrogen atom. The circular plots represent the numerical simulation results obtained by the second HQCNN (denoted as F-HQCNN in the figure) obtained by transfer learning according to this embodiment. The number of iterations of variational optimization was 10. F-HQCNN has n=4 and D=4, and the feature extraction circuit F extracted from the HQCNN obtained in Figure 8 was used as its feature extraction circuit. Note that the number of iterations is not particularly limited and can be changed as appropriate. For example, the number of iterations can be set in advance or adaptively according to the degree of convergence of the calculation error, the calculation time, etc. In this embodiment, it is preferable to perform the procedure about 10 times.

[0079] Figure 10 is a graph showing the numerical simulation results for the comparative example corresponding to Figure 9. The square plots in Figure 10 represent the numerical simulation results using HQCNN described in Non-Patent Literature 2, which does not perform transfer learning. The number of variational optimization iterations is 10. As can be seen from the comparison of Figure 9 and Figure 10, the HQCNN in the comparative example has a large error with CASCI, which is the exact solution for the 2-electron 2-orbital model, and the F-HQCNN according to this embodiment matches the CASCI solution with better accuracy. Furthermore, in order to perform training using the HQCNN in the comparative example to achieve the same level of accuracy as the F-HQCNN according to this embodiment, more than 100 variational optimizations are required. Therefore, the F-HQCNN according to this embodiment can reduce the number of variational optimizations by about an order of magnitude, thereby reducing the training cost. In addition, since the number of parameters to be optimized in F-HQCNN is nD=16, the computational cost per optimization can also be reduced compared to HQCNN.

[0080] (Example 2) The molecule to be treated in Example 2 is hydrogen fluoride molecule (HF molecule).

[0081] Figure 11 shows graphs representing the numerical simulation results for Example 2. In the graph on the left of Figure 11, the vertical axis is defined by the potential energy E [hartree] of the ground state of the HF molecule, and the horizontal axis is defined by the bond length [Å] between the fluorine atom and the hydrogen atom. In the graph on the right of Figure 11, the vertical axis is defined by the absolute error ΔE [hartree] of the ground state of the HF molecule, and the horizontal axis is defined by the bond length [Å] between the fluorine atom and the hydrogen atom. The circle plots show the numerical simulation results using F-HQCNN set to n=4 and D=6. The number of iterations of variational optimization was 100. Here, F-HQCNN is a second HQCNN obtained by transferring the feature extractor obtained for the hydrogen molecule described in Example 1. The solid line in the graph on the left represents the exact solution, the CASCI solution, and the dotted line in the graph on the right represents the chemical precision.

[0082] Figure 12 is a graph showing the numerical simulation results of the HQCNN for the comparative example corresponding to Figure 11. The square plots in Figure 12 show the numerical simulation results using the HQCNN for the comparative example when n=4 and D=6. The number of variational optimization iterations is 100. As can be seen from the comparison of Figure 11 and Figure 12, the HQCNN for the comparative example shown in Figure 12 has regions of interatomic distance where the error with the CASCI solution is large, while the F-HQCNN according to this embodiment shown in Figure 11 can be seen to perform accurate inference over the entire interatomic distance range. Unlike hydrogen molecules, HF molecules have strong ionic bonding and a different bonding mode than hydrogen molecules, but it can be seen that a quantum machine learning model that accurately infers the PES of HF molecules can be created by repurposing the quantum circuit information optimized for hydrogen molecules. As described above, it can be seen that a quantum machine learning model that predicts the properties of polyatomic molecular systems and molecular systems with different bonding modes can be created using the information of the simplest quantum circuit using hydrogen molecules. Conventional transfer learning using classical data is used when it is necessary to learn another special system at low cost by using a part of a model that has been trained using a large amount of data. The quantum transfer learning according to this embodiment differs from conventional transfer learning in that it can learn another special system using a special system.

[0083] (Example 3) In Example 3, in order to further reduce the computational cost required for learning, the circuit depth D of the parameterized quantum circuit of the feature extraction circuit in the first HQCNN (hereinafter referred to as pre-HQCNN) that learns hydrogen molecules was reduced. F The value was reduced from 4 to 2. The circuit depth of the parameterized quantum circuit for the task-specific circuit is D=4.

[0084] Figure 13 is a graph showing the numerical simulation results for Example 3. In the graph on the left of Figure 13, the vertical axis is defined by the potential energy E [hartree] of the ground state of the H2 molecule, and the horizontal axis is defined by the bond length between hydrogen atoms [Å]. In the graph on the right of Figure 8, the vertical axis is defined by the absolute error ΔE [hartree] of the ground state of the H2 molecule, and the horizontal axis is defined by the bond length between hydrogen atoms [Å]. The square plots shown in Figure 13 are D F =2, D=4 and n M This shows the numerical simulation results of HQCNN with =4 set. F By reducing from 4 to 2, the number of parameters to be optimized decreases from 32 to 24. Comparing Figure 13 and Figure 8, D F Example 3 of =2 is D F Compared to Example 1 with =4, the accuracy is slightly lower, but it can be seen that learning and inference are possible with relatively good accuracy across the entire interatomic distance range. Therefore, the circuit depth of the parameterized quantum circuit included in the feature extraction circuit can be reduced depending on the required accuracy.

[0085] Figure 14 shows graphs representing other numerical simulation results related to Example 3. In the graph on the left of Figure 14, the vertical axis is defined by the potential energy E [hartree] of the ground state of the H2 molecule, and the horizontal axis is defined by the bond length between hydrogen atoms [Å]. In the graph on the right of Figure 14, the vertical axis is defined by the absolute error ΔE [hartree] of the ground state of the H2 molecule, and the horizontal axis is defined by the bond length between hydrogen atoms [Å]. The square plots shown in Figure 14 represent the number of qubits n in the measurement layer of the feature extraction circuit. M 4 qubits (n M =4) to 1 qubit (n M This shows the numerical simulation results when reduced to =1). Comparing Figure 14 and Figure 8, n M Example 3, where =1, is n M Compared to Example 1 with =4, the accuracy is slightly lower, but it can be seen that learning and inference are possible with relatively good accuracy across the entire interatomic distance range. Therefore, the number of qubits n constituting the feature extraction circuit M This can be reduced depending on the required precision.

[0086] Thus, it becomes possible to provide a quantum circuit learning method, a quantum circuit learning system, and a quantum-classical hybrid neural network that can reduce the computational cost required for training.

[0087] 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 and their equivalents. [Explanation of symbols]

[0088] 1...Quantum circuit learning system, 100...Classical computer, 110...Processing circuit, 111...Training unit, 112...Display control unit, 120...Storage device, 130...Input device, 140...Communication device, 150...Display device, 200...Quantum computer, 210...HQCNN, 210-1...First HQCNN, 210-2...Second HQCNN, 220...Feature extraction circuit, 221...Parameterized quantum circuit, 222...Measurement layer, 223...Encode gate, 224...Quantum manipulation gate, 225...Encode parameter, 226...Rotation angle parameter, 230...Task-specific circuit, 231...Parameterized quantum circuit, 232...Output layer, 233...Encode gate, 234...Quantum manipulation gate, 235...Encode parameter, 236...Rotation angle parameter, 240...Classical data, 250...Output data, 260...Measurement data.< / l>

Claims

1. A reading step of reading optimized first parameters assigned to a first feature extraction circuit included in a first quantum circuit trained for a first task, wherein the first quantum circuit is trained on a first dataset of first classical data which are explanatory variables, and the first feature extraction circuit includes a parameterized quantum circuit having an encoding gate for encoding the first classical data and a quantum operation gate for performing quantum operations on qubits according to the first parameters, and a measurement layer for outputting first measurement data of qubits, A transfer step of transferring the first parameter to a second feature extraction circuit included in a second quantum circuit for a second task, wherein the second feature extraction circuit includes a parameterized quantum circuit having an encoding gate for encoding second classical data representing explanatory variables common to the first classical data and a quantum operation gate for performing quantum operations on a qubit according to the first parameter, and a measurement layer that outputs second measurement data of a qubit, A training step comprising: fixing the first parameters transferred to the second feature extraction circuit, training the second quantum circuit based on a second dataset relating to the second classical data, and optimizing the second parameters of a task-specific circuit that follows the second feature extraction circuit within the second quantum circuit, wherein the task-specific circuit includes a parameterized quantum circuit having an encoding gate for encoding the second measurement data and a quantum operation gate for performing quantum operations on qubits according to the second parameters; A quantum circuit learning method that includes the following features.

2. The quantum circuit learning method according to claim 1, further comprising a pre-training step of training the first quantum circuit based on the first dataset relating to the first classical data and optimizing the first parameters assigned to the first feature extraction circuit included in the first quantum circuit.

3. The quantum circuit learning method according to claim 1, wherein the parameterized quantum circuit is a Real Amplitude type quantum circuit or a quantum circuit that conserves the number of particles.

4. The quantum circuit learning method according to claim 3, wherein the quantum circuit that stores the number of particles performs quantum operations on the Hartree-Fock state.

5. The quantum circuit learning method according to claim 1, wherein the first parameter and / or the second parameter control the rotation angle of a quantum gate that performs a quantum rotation operation.

6. The quantum circuit learning method according to claim 1, wherein the second feature extraction circuit and the task-specific circuit have different quantum gate configurations.

7. The quantum circuit learning method according to claim 1, wherein the measurement layer included in the first feature extraction circuit and / or the second feature extraction circuit outputs the expectation value of an observable defined by an arbitrary tensor product of Pauli operators for a quantum state constructed by the parameterized quantum circuit as the first measurement data and / or the second measurement data.

8. The quantum circuit learning method according to claim 1, wherein the training step optimizes the second parameter using a classical computer with the Nelder-Mead method, Powell method, CG method, Newton method, BFGS method, L-BFGS-B method, TNC method, COBYLA method and / or SLSQP method.

9. The quantum circuit learning method according to claim 1, wherein the parameterized quantum circuit has a circuit configuration in which the encoding gate and the quantum manipulation gate are repeated in series two or more times.

10. A quantum computing unit that applies classical data representing explanatory variables to a first quantum circuit and outputs output data corresponding to the classical data, wherein the first quantum circuit comprises a feature extraction circuit to which optimized first parameters are assigned, and a task-specific circuit following the feature extraction circuit and to which optimizeable second parameters are assigned, the feature extraction circuit includes a parameterized quantum circuit having an encoding gate for encoding the classical data and a quantum operation gate for performing quantum operations on a qubit according to the first parameters, and a measurement layer for outputting measurement data of a qubit, the task-specific circuit includes a parameterized quantum circuit having an encoding gate for encoding the measurement data and a quantum operation gate for performing quantum operations on a qubit according to the second parameters, and an output layer for outputting output data representing the quantum state of a qubit, A training unit that fixes the first parameter of the feature extraction circuit, trains the first quantum circuit based on the difference between the output data and the training data corresponding to the classical data, and optimizes the second parameter of the task-specific circuit. A quantum circuit learning system equipped with [the following features].

11. A quantum-classical hybrid neural network that can be trained for a target task, The system comprises: a feature extraction circuit with first parameters assigned that are optimized for other tasks, extracted from other quantum-classical hybrid neural networks trained for tasks different from the aforementioned target task; and a task-specific circuit that follows the feature extraction circuit and has second parameters assigned that are optimized for the aforementioned target task. The feature extraction circuit includes a parameterized quantum circuit having an encoding gate for encoding first classical data which is an explanatory variable and a quantum operation gate for performing quantum operations on a qubit according to the first parameter, and a measurement layer that outputs measurement data of the qubit. The task-specific circuit includes a parameterized quantum circuit having an encoding gate for encoding the measurement data and a quantum operation gate for performing a quantum operation on a qubit according to the second parameter, and an output layer that outputs output data representing the quantum state of the qubit. Quantum-classical hybrid neural network.

12. A quantum-classical hybrid neural network trained for the target task, The system comprises: a feature extraction circuit assigned a first parameter optimized for the other task, extracted from another quantum-classical hybrid neural network trained for a task different from the aforementioned target task; and a task-specific circuit following the feature extraction circuit, assigned a second parameter optimized for the aforementioned target task. The feature extraction circuit includes a parameterized quantum circuit having an encoding gate for encoding classical data which are explanatory variables and a quantum operation gate for performing quantum operations on qubits according to the first parameter, and a measurement layer that outputs measurement data of qubits. The task-specific circuit includes a parameterized quantum circuit having an encoding gate for encoding the measurement data and a quantum operation gate for performing a quantum operation on a qubit according to the second parameter, and an output layer that outputs output data representing the quantum state of the qubit. Quantum-classical hybrid neural network.

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