Machine learning program, machine learning method, and information processing apparatus

Abstract

To generate a highly accurate quantum auto-encoder using short-term machine learning.SOLUTION: An information processing apparatus performs first machine learning on a quantum auto-encoder using first input data and second input data in which the states of each quantum bit are the same. The information processing apparatus performs second machine learning on the quantum auto-encoder learned by the first machine learning, using third input data and fourth input data in which the states of each quantum bit are different from each other.SELECTED DRAWING: Figure 6

Description

[Technical Field]

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

[0002] Quantum circuits are used, which combine quantum gates that perform operations on one or more qubits. Quantum circuits are created by combining gates that change the state of a single qubit or gates that create entanglement between two qubits, and classical information is extracted from the quantum circuit using a process called measurement. Such quantum circuits are divided into parameterless fixed quantum circuits and parameterized variational quantum circuits.

[0003] Furthermore, quantum circuit-based machine learning models, which apply the principles of quantum computing to machine learning, are being used in areas where calculations are difficult using classical computers, the general-purpose computers currently in use. For example, one example of a quantum circuit-based machine learning model is the quantum autoencoder, which uses quantum circuits to implement an autoencoder, an architecture widely used in the fields of deep learning and neural networks. Quantum autoencoders are an adaptation of the autoencoder idea to quantum computing, realizing the process of encoding and decoding data on quantum bits, thereby enabling feature extraction and compression of data with quantum properties.

[0004] In recent years, Ansatsu quantum circuits, which implement quantum autoencoders, have been used as quantum machine learning techniques to remove noise from variational quantum algorithms. [Prior art documents] [Patent documents]

[0005] [Patent Document 1] Japanese Patent Application Publication No. 2022-176899 [Patent Document 2] Patent Publication No. 2021-193615 [Patent Document 3] US Patent Application Publication No. 2020 / 0169396 [Patent Document 4] US Patent Application Publication No. 2019 / 0164034 Summary of the Invention [Problem to be solved by the invention]

[0006] However, for example, in machine learning for noise removal using variational quantum algorithms, it becomes difficult to find local solutions or solutions, which results in a long learning time for the quantum autoencoder and a deterioration in the accuracy of the machine-learned quantum autoencoder. For example, in the machine learning of the above quantum autoencoder, as the problem size increases, it takes time to optimize many variational parameters, making it difficult to achieve high accuracy in designing the quantum circuit structure and initializing parameters.

[0007] In one aspect, an object of the present invention is to provide a machine learning program, a machine learning method, and an information processing device that can generate a highly accurate quantum autoencoder through machine learning in a short period of time. [Means for solving the problem]

[0008] In the first proposal, the machine learning program is characterized by causing a computer to perform the following processes: performing first machine learning on a quantum autoencoder using first input data and second input data in which the states of each quantum bit are the same; and performing second machine learning on the quantum autoencoder trained by the first machine learning using third input data and fourth input data in which the states of each quantum bit are different. [Effects of the Invention]

[0009] According to one embodiment, a highly accurate quantum autoencoder can be generated through short-term machine learning. [Brief explanation of the drawings]

[0010] [Figure 1] Figure 1 is a diagram explaining machine learning of quantum circuits. [Figure 2] FIG. 2 is a diagram illustrating the variational quantum algorithm. [Figure 3] FIG. 3 is a diagram illustrating the quantum circuit of a quantum autoencoder. [Figure 4] Figure 4 is a diagram explaining machine learning of a quantum autoencoder that removes noise. [Figure 5] Figure 5 is a diagram explaining machine learning of a quantum autoencoder that performs noise removal for VQE. [Figure 6] FIG. 6 is a diagram illustrating machine learning of a quantum autoencoder performed by the information processing device according to the first embodiment. [Figure 7] FIG. 7 is a functional block diagram of the information processing apparatus according to the first embodiment. [Figure 8] FIG. 8 is a diagram illustrating generation of learning data for subtask learning. [Figure 9] FIG. 9 is a diagram illustrating subtask learning in QAE. [Figure 10] FIG. 10 is a diagram illustrating the generation of learning data for main task learning. [Figure 11] FIG. 11 is a diagram illustrating main task learning in QAE. [Figure 12] FIG. 12 is a diagram illustrating noise removal using the QAE after learning. [Figure 13] FIG. 13 is a flowchart showing the flow of the QAE learning process. [Figure 14] FIG. 14 is a diagram illustrating the effect of subtask learning. [Figure 15] FIG. 15 is a diagram illustrating the learning of step-by-step effects. [Figure 16] FIG. 16 is a diagram for explaining the determination of the QAE circuit. [Figure 17] FIG. 17 is a diagram illustrating an example of a hardware configuration. DETAILED DESCRIPTION OF THE INVENTION

[0011] Hereinafter, embodiments of the machine learning program, the machine learning method, and the information processing device disclosed in the present application will be described in detail with reference to the accompanying drawings. However, the present invention is not limited to these embodiments. [Example]

[0012] <Introduction> In this example, we will explain an example of machine learning of a quantum autoencoder (QAE) in which an encoder and decoder capable of quantum noise removal are constructed using variational quantum circuits, and generate a highly accurate QAE (hereinafter, sometimes referred to as a QAE circuit) through short-term learning. Note that a quantum autoencoder that performs noise removal may be referred to as a noise-removing QAE.

[0013] Before explaining noise reduction QAEs, we will first explain quantum circuits, variational quantum algorithms, and general QAEs, which are related to noise reduction QAEs. Figure 1 is a diagram explaining machine learning for quantum circuits. As shown in Figure 1, quantum machine learning applies the principles of quantum computing to machine learning (pattern recognition and generation). For example, a quantum feature map is created using a fixed quantum circuit with embedded data information. Next, the output of the quantum feature map is applied to a variational quantum circuit. After that, the information obtained through measurement is used for learning, and data classification and generation can be performed by adjusting the parameters of the variational circuit.

[0014] (Explanation of variational quantum circuits) Next, we will explain the variational quantum circuit used to generate the quantum feature map. A variational quantum circuit is a quantum circuit constructed using a variational quantum algorithm. Figure 2 is a diagram explaining the variational quantum algorithm. Figure 2 (A) shows VQA (Variational Quantum Algorithm), which is one of the algorithms that uses a hybrid of quantum and classical computers. VQA has attracted attention as a means of utilizing current noisy intermediate-scale quantum (NISQ) computers for problems that are difficult to solve using classical computers alone.

[0015] Here, we will explain the components of VQA. As shown in Figure 2(A), first, a quantum state is prepared (see Figure 2(A)(1)), and then a specific quantum computation is performed based on the parameter-dependent quantum state (see Figure 2(A)(2)). Specifically, a parameter-dependent quantum state is prepared on a quantum computer. This state is obtained by operating a quantum circuit (variational quantum circuit) that depends on externally given parameters.

[0016] Next, quantum measurements are performed (see (3) of (A) in Figure 2), classical optimization is performed (see (4) of (A) in Figure 2), and then processing based on the interaction between classical and quantum is performed (see (5) of (A) in Figure 2). Specifically, the quantum state after a specific quantum calculation is measured and the classical value is obtained. Next, the results of the above quantum calculations and measurements are evaluated on a classical computer, and new parameters are proposed to search for the minimum value of a target function (e.g., an energy function).

[0017] Such VQA requires repeated interactions between classical and quantum computers, using new parameters to prepare the quantum state, compute, measure, and repeat until a classical optimization algorithm finds the minimum of the desired function.

[0018] Next, we will explain the Variational Quantum Eigensolver (VQE), a variational quantum algorithm for efficiently solving eigenvalue problems using quantum computers. VQE (hereafter sometimes referred to as VQE circuit) is particularly suited to finding the smallest eigenvalue (usually corresponding to the ground-state energy) of a large Hamiltonian matrix. This VQE is extremely useful in quantum chemistry calculations and simulations of some physical systems. The advantage of VQE is that it can be computed efficiently using shallow quantum circuits, which makes it expected to be used for practical tasks even on current NISQ devices.

[0019] Here, we will explain the components of VQE. As shown in Figure 2(B), first, a setup based on the principles of variational calculus is performed (see Figure 2(B)(1)), and then a parameterized quantum circuit (ansatz) is set up (see Figure 2(B)(2)). Specifically, classical variational calculus is a technique that adjusts the parameters of a trial function (ansatz) to minimize the expected energy, and VQE applies this concept to quantum systems. VQE then uses a parameterized quantum circuit (variational quantum circuit) as the part that corresponds to the trial function of variational calculus. Adjusting the parameters of this circuit changes the quantum state.

[0020] Next, a specific quantum calculation is performed (see (3) in Figure 2(B)), a quantum measurement is performed (see (4) in Figure 2(B)), and classical optimization is performed (see (5) in Figure 2(B)). After that, processing based on the interaction between classical and quantum is performed (see (6) in Figure 2(A)). Specifically, a specific quantum calculation is performed based on the parameter-dependent quantum state described above, and measurements are taken in the quantum state after the calculation to obtain the expectation value (energy value) of the state with respect to the Hamiltonian. Then, after calculating the energy value on the quantum computer, this value is fed back to an optimization algorithm (such as gradient descent) on a classical computer to update the parameters of the Ansatz circuit.

[0021] Such VQE requires repeated interactions between classical and quantum computers, where the quantum computer is used to calculate the expected value and the classical computer is used to perform optimization using the resulting data.

[0022] (Quantum Autoencoder) Next, we will explain quantum autoencoders (QAEs), which perform noise removal on data generated by VQE, etc. First, we will explain a general QAE. Figure 3 is a diagram explaining the quantum circuit of a quantum autoencoder.

[0023] As shown in Figure 3(A), a quantum autoencoder is an adaptation of the autoencoder idea, in which input data is encoded into a low-dimensional feature space using a mechanism called an Encoder, and then the original data is reconstructed using a Decoder, to quantum computing. Each process of encoding and decoding data is realized on quantum bits, allowing for feature extraction and compression of data with quantum properties.

[0024] Next, we will explain the quantum circuit of the QAE. As shown in Figure 3(B), the QAE is constructed by a dissipative quantum neural network. Each neuron corresponds to a quantum bit, and a unitary circuit connects the neurons in the subsequent connection layer. Since the quantum bits in each layer dissipate after the forward process of the next layer, it is possible to construct the minimum space for the QAE.

[0025] For example, (m1, ,m M )(M≧2) structure (usually m M =m1). The unitary function acting on the jth neuron in the (i+1)th layer and the neuron in the layer before it is U j i Then, the unitary relationship between the i-th layer and the (i+1)-th layer is given by equation (1).

[0026]

number

[0027] U j i When the execution of m i Reset and reuse the qubit. m in the ith layer i Quantum state β with neurons i Then, β i and β i+1 The quantum channel between is given by equation (2). Q i is m i The quantum bits are (m i +m i+1 ) qubit state, and then trace out the qubit in the i-th layer to obtain m i+1 Reduce to the qubit state. Output state β of the QAE out is (Q=Q M-1 ...Q1) is applied, so "β out =Q(β1)=Q M-1 ···Q1(β1).

[0028]

number

[0029] (Noise Reduction QAE) Next, we will explain the QAE that performs noise removal. The noise removal QAE is a quantum circuit that separates noise from the compression by the Encoder to generate noise-free compressed information, and then converts it into the target state by the Decoder. The unitary that acts on the jth neuron in the (i+1)th layer and the neuron in the layer before that neuron is "U j i " is constructed as follows. For example, the circuit block "rotation gate for each qubit and two-qubit gate that generates entanglement" is applied L times, and finally the rotation gate for each qubit is applied. The rotation gate is R x , R Y , R Z Selected from the gate, the two-qubit gate V ij (acting on the i and j qubits) is chosen from the CX, CY, CZ, CRX, CRY, CRZ, RXX, RYY, and RZZ gates, and the configuration of the two-qubit gate is determined by choosing the pair (i,j).

[0030] The machine learning of such a denoising QAE is basically trained using the same process as an autoencoder for classical computers. Figure 4 is a diagram explaining the machine learning of a quantum autoencoder that performs denoising. The purpose of the machine learning of the denoising QAE shown in Figure 4 is to derive the true state "|ψ>" from the noisy quantum state "|ψ1>,|ψ2>".

[0031] To calculate the learning cost function, the following learning circuit is constructed: (I) a circuit that prepares input data and reference data for the QAE circuit, (II) a QAE circuit Q with parameter θ, θ (III) A circuit that calculates the fidelity (closeness) between the output of the QAE and the reference state. If the probability that the measurement quantum bit will obtain a measurement result of 0 is p0, then fidelity = 2p0-1.

[0032] In other words, the quantum circuit for machine learning of the noise removal QAE (hereinafter, sometimes referred to as the "quantum circuit for machine learning") is a quantum circuit that operates on qubits q0 to q 10 The quantum bit q0 is configured with a first circuit configuration having a gate (Amadal gate) that outputs a superposition state, and the quantum bits q1 to q4 are configured with a circuit that does not perform a gate operation on the input data. The quantum bits q5 to q 10 A second circuit configuration (QAE circuit) is set to perform a gate operation on the input data.

[0033] In such a circuit, a QAE circuit Q with parameter θ for N pairs (i1, i2) is θ When noisy data "|ψ1>" is input to θLearning is performed so that the fidelity between "|ψ1>" and the noisy data "|ψ2>" is high. In other words, learning is performed so as to maximize the learning cost shown in equation (3).

[0034]

number

[0035] (Noise Reduction QAE for VQE) The aforementioned denoising QAE is trained specifically for the VQE and is used to denoise the data generated by the VQE. In the VQE algorithm, the noise on the quantum device and the stochastic nature of the optimization method significantly affect the trainability of the VQE and the accuracy of the final result. As a result, the VQE generates a noisy quantum state as its output. Therefore, denoising using the denoising QAE is performed on the data output by the VQE.

[0036] Figure 5 illustrates machine learning of a quantum autoencoder that performs noise reduction for VQE. The difference from Figure 4 is that the input is data generated by a noisy VQE circuit. The noise-removing QAE for VQE shown in Figure 5 compresses the output state (data) from the noisy VQE circuit, maps it to a low-dimensional space, and restores the reduced state to the original data space. By maximizing the fidelity between the output of this QAE circuit and other outputs (reference data) generated by the noisy VQE circuit, the system can learn to distinguish between noise patterns and essential information of the target basis state, enabling more accurate basis state estimation.

[0037] For example, the machine learning of noise removal QAE for VQE aims to derive the true state "|ψ>" from the noisy quantum state "|ψ1>,|ψ2>". Specifically, N pairs of data "(|ψ 11 >,|ψ 12 >),···,(|ψ N1 >,|ψ N2 >)" is input to the QAE, and learning is performed to maximize the learning cost shown in equation (4).

[0038]

number

[0039] (Improvement points) The training of the noise-removing QAE for the VQE described above involves optimizing a cost function using a large amount of training data and a large number of variational parameters. This process requires multiple parameter updates, and the cost function must be calculated multiple times to calculate the update amounts, which takes a very long time. Furthermore, designing the quantum circuit structure and initializing the parameters are costly, making it difficult to achieve high accuracy. Furthermore, because the input and reference data are noisy, it is difficult to appropriately set the target value for maximizing the cost function.

[0040] For example, to explain the execution cost of machine learning for the noise removal QAE for VQE shown in Figure 5, it is necessary to try P initial values ​​for the parameters of the QAE circuit. For each value, the number of circuit evaluations (execution cost) required for learning is O(P×N×T), since the execution cost for determining the initial values ​​is incurred due to the scale = O(N×T) in addition to the "number of data (N) × number of iterations until convergence (T)".

[0041] Furthermore, there are S ways to design a QAE circuit, and the execution cost for determining the initial parameter values ​​for each way is O(P×N×T), so the execution cost required for designing the circuit is O(S×P×N×T). In learning such a QAE, N is very large (e.g., N=200), so the execution cost for designing the QAE circuit and determining the initial values ​​is large.

[0042] (Method proposed in Example 1) Therefore, in the information processing device 10 according to the first embodiment, since the learning of the noise reduction QAE tends to fall into a region where it is difficult to find a local solution or a solution as the problem size increases, in order to overcome this problem, the information processing device 10 starts learning by avoiding this region. In other words, the information processing device 10 designs subtasks for the main task that the noise reduction QAE wants to solve, and after solving the subtasks in advance (curriculum learning), determines the circuit design and parameter initialization.

[0043] 6 is a diagram illustrating machine learning of a quantum autoencoder by an information processing device 10 according to a first embodiment. As illustrated in FIG. 6, the information processing device 10 according to the first embodiment performs first machine learning on a denoising QAE using first input data and second input data in which the states of the quantum bits are the same. Then, the information processing device 10 performs second machine learning on the denoising QAE trained by the first machine learning using third input data and fourth input data in which the states of the quantum bits are different from each other.

[0044] For example, the information processing device 10 generates first input data and second input data from data A generated by a VQE or the like, and inputs the data to a quantum circuit for machine learning of a noise reduction QAE. Then, the information processing device 10 executes first machine learning (subtask learning) that reduces the error between first output data, which is the output result for the first input data, and second output data output by the noise reduction QAE in response to the input of the second input data.

[0045] When the first machine learning is completed, the information processing device 10 generates third input data from data B generated by the VQE or the like, generates fourth input data from data C, and inputs them to the quantum circuit for machine learning of the noise reduction QAE. Then, the information processing device 10 executes second machine learning (main task) that reduces the error between third output data, which is the output result for the third input data, and fourth output data output by the noise reduction QAE in response to the input of the fourth input data.

[0046] In this way, the information processing device 10 can avoid areas where it is difficult to find local solutions or solutions in machine learning for noise removal using a variational quantum algorithm, and can reduce the quantum resources required for machine learning, making it possible to generate a highly accurate quantum autoencoder through short machine learning times.

[0047] (Functional configuration) 7 is a functional block diagram illustrating a functional configuration of the information processing device 10 according to the first embodiment. As illustrated in FIG.

[0048] The communication unit 11 is a processing unit that controls communication with other devices, and is, for example, a communication interface, etc. For example, the communication unit 11 receives various information and instructions from an administrator terminal used by an administrator or the like, and transmits learning results and the like to the administrator terminal.

[0049] The storage unit 12 is a processing unit that stores various data and programs executed by the control unit 20, and is realized by, for example, a memory, a hard disk, etc. The storage unit 12 stores QAE information 13.

[0050] The QAE information 13 is circuit information for constructing a noise-reducing QAE, and the noise-reducing QAE that is the subject of machine learning is constructed using the information stored here. Note that the QAE information may also include training data.

[0051] The control unit 20 is a processing unit that controls the entire information processing device 10, and is realized by, for example, a processor. The control unit 20 has a first machine learning unit 30 and a second machine learning unit 40. Here, the first machine learning unit 30 is a processing unit that executes subtasks, and the second machine learning unit 40 is a processing unit that executes a main task.

[0052] The first machine learning unit 30 has a design unit 31, a learning data generation unit 32, a learning unit 33, and a selection unit 34, and is a processing unit that executes subtasks for the QAE using first input data and second input data in which the states of each quantum bit are the same.

[0053] The design unit 31 is a processing unit that designs and generates multiple QAEs with different configurations and initial parameters to be learned, according to the information stored in the QAE information 13. Specifically, the design unit 31 generates multiple QAEs (QAE circuit candidates) with different combinations of gates such as CZ and RY and different initial parameters as QAEs for subtasks.

[0054] Then, the design unit 31 uses each of the multiple QAE circuit candidates for the subtask to generate a quantum circuit for machine learning that has a first circuit configuration having a gate that outputs a superposition state and a circuit that does not perform a gate operation on input data, and a second circuit configuration (QAE circuit portion) that performs a gate operation on input data. Note that here, S QAE circuit candidates are used, where QAE={Q1, ,Q S} is generated, and each QAE has a first circuit configuration and a second circuit configuration.

[0055] The training data generation unit 32 is a processing unit that generates training data to be used for the subtask (machine learning of QAE circuit candidates). Specifically, the training data generation unit 32 generates training data using each of a plurality of quantum circuits that generate data to be subjected to noise removal, and that use the variational quantum fixed value method. For example, when there are N quantum circuits (quantum circuit 1 to quantum circuit N) as the VQE, the training data generation unit 32 uses the noisy generated data generated from quantum circuit 1 as input data to be input to the first quantum circuit configuration and the second quantum circuit configuration (the QAR circuit portion to be trained) of the quantum circuit for machine learning.

[0056] That is, the learning data generation unit 32 generates S QAEs={Q1, . . . ,Q S For each of these, we generate training data for the subtask using data in which the states of each quantum bit are the same as the two input data to be input to the quantum circuit for machine learning. For example, m Let,be M datasets {V1, ,V M} is generated.

[0057] FIG. 8 is a diagram illustrating the generation of training data for subtask training. As shown in FIG. 8, the training data generation unit 32 generates subtask training data "|ψ>" from a VQE circuit (V(β)), which is an example of a parameterized quantum circuit that generates data for a main task. For example, the training data generation unit 32 generates K parameter sets "β1,...,β k " is randomly selected, and the initial state "|Φ>" (usually |0>) is set to "V(β1)···V(β k As a result, the training data generation unit 32 applies K pieces of training data "|ψ1>, ,|ψ" as training data for the subtask. K >" generates "|ψ i >」=V(β i )|ψ>".

[0058] The learning unit 33 is a processing unit that performs machine learning of multiple QAE circuit candidates using the learning data generated by the learning data generation unit 32. Specifically, the learning unit 33 executes subtasks for multiple QAE circuit candidates.

[0059] For example, the learning unit 33 inputs input data A to a first circuit configuration of Q1, which is a QAE circuit candidate, to obtain output data A1, and inputs the same input data A to a second circuit configuration (QAE circuit portion) of Q1, which is also a QAE circuit candidate, to obtain output data A2 reconstructed by the QAE. The learning unit 33 then performs machine learning of the QAE by updating parameters of the second circuit configuration (QAE circuit portion) or the like so as to reduce the error between the output data A1 and the output data A2.

[0060] 9 is a diagram illustrating the subtask learning of the QAE. As shown in FIG. 9, the learning unit 33 sets {|ψ1>, . . . , |ψ as K pieces of data (quantum states). K >} and prepare the state |ψ i > to the same state |ψ iFor example, the learning unit 33 performs machine learning to restore the QAE (Q θ ) parameter θ and find the maximum value of the cost function and the corresponding parameter θ out get.

[0061] In the above example, the learning unit 33 generates a set of P initial values ​​of parameters (θ1 (Qs) ,θ2 (Qs) , θ p (Qs) Then, the learning unit 33 selects the known set θ p (Qs) From Q s and initialize each training dataset V m Here, the output Q of the QAE in the training dataset is θ The average fidelity between (|ψ>) and the input data (|ψ>) is maximized to a clear target value of 1.

[0062] The selection unit 34 is a processing unit that selects one quantum circuit for training based on the results of each of the first machine learning (subtasks) for the multiple quantum circuits for training. Specifically, the selection unit 34 selects one QAE circuit that has the best prediction accuracy (best performance) during training and the best prediction accuracy using verification data after training from among the multiple QAE circuit candidates designed by the design unit 31 and trained by the training unit 33.

[0063] In the above example, the selection unit 34 selects Q s , θ p (Qs) , V m The trained cost function value f spm Record the average f sp The selector 34 calculates and records Q s The average cost function f for a set of initial parameter values s is calculated using equation (6) and recorded.

[0064]

number

number

[0065] Then, the selector 34 selects the highest f s and the corresponding QAE(Q s* ) and the selection unit 34 selects QAE(Q s* ) as the initial value of the highest f s*p and the corresponding set of initial values ​​θ p* (Qs*) Determine.

[0066] Returning to Figure 7, the second machine learning unit 40 has a learning data generation unit 41 and a learning unit 42, and is a processing unit that executes the main task for the QAE using third input data and fourth input data in which the states of each quantum bit are different.

[0067] The training data generation unit 41 is a processing unit that generates training data to be used for the main task (machine learning of the QAE circuit). Specifically, the training data generation unit 41 generates training data using each of multiple quantum circuits using the variational quantum fixed value method. For example, when there are N quantum circuits (quantum circuit 1 to quantum circuit N) as the VQE, the training data generation unit 32 generates training data (data in which the states of each quantum bit are different) by combining noisy generated data generated from each quantum circuit.

[0068] 10 is a diagram illustrating the generation of learning data for main task learning. As shown in FIG. 10, the learning data generator 41 provides a VQE circuit (V(β)) with K randomly selected parameter sets “β1, . . . , β k " to obtain VQE(V(β1) V(β k Next, the learning data generating unit 41 generates each VQE(V(β1) V(β k )) and input the data of the initial state "|Φ>" to the output data {|ψ1>,···,|ψ K >}.

[0069] Then, the learning data generation unit 41 generates the output data {|ψ1>, . . . , |ψ K >}, two pairs are randomly selected from them to form pairs, and the pairs are used as training data for the main task. In the example of Figure 10, the training data generator 41 generates training data A{|ψ1>, |ψ2>}, training data B{|ψ2>, |ψ3>}, etc. Note that, for example, 200 pairs of noisy data may be generated using VQEs optimized with different random seeds.

[0070] The learning unit 42 is a processing unit that executes the second machine learning (main task) on one of the multiple learning quantum circuits selected by the selection unit 34. In other words, the learning unit 42 executes the main task on only one QAE circuit candidate with the best performance, which has achieved the best results in the subtasks, from among the multiple QAE circuit candidates designed by the design unit 31.

[0071] 11 is a diagram illustrating main task learning of QAE. As shown in FIG. 11, the learning unit 42 performs machine learning on “QAE(2),” which has the best subtask performance, among S QAE circuit candidates “QAE(1), QAE(2), . . . , QAE(S),” using the learning data A{|ψ1>, |ψ2>} and learning data B{|ψ2>, |ψ3>} generated by the learning data generation unit 41.

[0072] For example, the learning unit 42 inputs "|ψ1>" of the learning data A to the first circuit configuration of the QAE(2) to obtain output data A3, and inputs "|ψ2>" of the learning data A to the second circuit configuration (QAE circuit portion) of the QAE(2) to obtain output data A4 reconstructed by the QAE. The learning unit 42 then performs machine learning of the QAE by updating parameters of the second circuit configuration (QAE circuit portion) or the like so as to reduce the error between the output data A3 and the output data A4.

[0073] That is, the learning unit 42 processes the learning data including noise (learning data A{|ψ1>, |ψ2>}, learning data B{|ψ2>, |ψ3>}, etc.) into the QAE (Q θ ) and learns to maximize the cost function shown in equation (4). Then, in order to maximize the cost function, the learning unit 42 learns to maximize the cost function QAE(Q θ ) parameter θ and find the maximum value of the cost function and the corresponding parameter θ out get.

[0074] A QAE that performs noise removal is generated by the above-described two-stage machine learning. Such a QAE is used, for example, to remove noise from output data of a VQE. FIG. 12 is a diagram illustrating noise removal using a trained QAE. As shown in FIG. 12, when noisy data generated by a VQE is input to the trained QAE, the encoder separates the noise through compression to generate noise-free compressed information, which is then converted into a target state (noise-free data) by a decoder and output. Such noise removal can be performed by the information processing device that performed the machine learning (e.g., the control unit 20), or by another device.

[0075] (Processing flow) Fig. 13 is a flowchart showing the flow of the QAE learning process. As shown in Fig. 13, when the information processing device 10 is set not to use curriculum learning (S101: No), it executes QAE learning using a conventional method.

[0076] Specifically, the information processing device 10 assigns a QAE circuit and initial values ​​(S102) and executes learning of the main task using the assigned QAE (S103). The information processing device 10 then repeats S103 and subsequent steps until the number of QAE circuit and initial value assignments reaches a certain number (S104: No). On the other hand, if the number of QAE circuit and initial value assignments reaches a certain number (S104: Yes), the information processing device 10 determines the best-performing QAE circuit and learned parameters (S105). After learning is complete, the information processing device 10 executes noise removal on unknown data (S106).

[0077] On the other hand, when the information processing device 10 is set to use curriculum learning (S101: Yes), it executes two-stage QAE learning.

[0078] Specifically, the information processing device 10 assigns a QAE circuit and an initial value (S108), generates learning data for the subtask (S109), and executes learning of the subtask using the assigned QAE (S110).

[0079] Then, the information processing device 10 repeats S109 and subsequent steps until the number of times to generate learning data for the subtask is reached (S111: No), and when the number of times to generate learning data for the subtask is reached (S111: Yes), it determines whether the number of times to assign the QAE circuit and initial value is reached (S112).

[0080] If the number of times that the QAE circuit and initial value assignments have not been achieved (S112: No), the information processing device 10 repeats S108 and subsequent steps. On the other hand, if the number of times that the QAE circuit and initial value assignments have been achieved (S112: Yes), the information processing device 10 determines the QAE circuit and initial parameter values ​​with the best performance (S113), and performs learning of the main task using the determined QAE (S114). After learning is complete, the information processing device 10 performs noise removal on unknown data (S115).

[0081] (effect) As described above, the information processing device 10 designs subtasks from a main task aimed at noise removal in a variational quantum algorithm, and determines the structure of an Ansatu quantum circuit for a quantum autoencoder and the initial values ​​of the circuit parameters from the learning results of the subtasks. The information processing device 10 then uses the small learning data set of the subtasks as the output of a variational circuit (such as a VQE circuit) that generates data for the main task. As a result, the information processing device 10 can avoid areas where local solutions or solution search are difficult in learning noise removal in a variational quantum algorithm, thereby reducing the quantum resources required for learning.

[0082] Furthermore, the information processing device 10 can design subtasks for a main task to be solved by the noise QAE, and can solve the subtasks in advance before deciding on circuit design and parameter initialization. As a result, the information processing device 10 can reduce the execution costs for circuit design and parameter initialization, and can generate a highly accurate noise QAE in a short time.

[0083] For example, the information processing device 10 may use K pieces of training data {|ψ1>, . . . , |ψ K To explain the execution cost of a subtask using >}, it is necessary to try P initial values ​​for the parameters of the QAE circuit. For each value, the number of circuit evaluations (execution cost) required for learning is O(P × K × T), since it is the number of iterations (T) until the number of data (K) converges plus the execution cost for determining the initial values ​​due to the scale = O(K × T).

[0084] Furthermore, there are S ways to design a QAE circuit, and the execution cost for determining the initial parameter values ​​for each way is O(K × T), so the execution cost required for designing the circuit is O(S × P × K × T). In the subtask, K is small (for example, K = 2), so the execution cost for designing the QAE circuit and setting the initial values ​​is much smaller than that of the main task.

[0085] In addition, since the circuit design and initial parameter values ​​of the QAE obtained by learning the subtask are determined, the execution cost for determining the circuit design and initial parameter values ​​of the QAE in the main task is the same as that of the subtask.

[0086] Fig. 14 is a diagram illustrating the learning effect of subtasks. In Fig. 14, for 10 QAE candidates, K (=2) pieces of learning data {|ψ1>, ,|ψ K >}, and state |ψ i > to the same state |ψ iThe figure shows the results of maximizing the cost function in equation (3) to a target value of 1, with the goal of restoring the original data. The horizontal axis of the graph in Figure 14 represents the number of epochs, and the vertical axis represents "1.0 - value of cost function." As shown in Figure 14, when training is performed using data generated from the VQE circuit of the main task, the value of the cost function increases as the number of epochs increases, and the value of "1.0 - value of cost function" decreases. In this way, the accuracy of QAE can be improved by training the subtasks.

[0087] FIG. 15 is a diagram illustrating gradual learning of effects. FIG. 15 compares a conventional method (without curriculum learning) that performs learning only on the main task with a method according to Example 1 (curriculum learning) that performs main task learning after subtask learning. The horizontal axis of FIG. 15 represents the number of iterations, and the vertical axis represents infidelity with the target value (target state). The graph shows the learning results for 10 QAEs for both the conventional method and the method according to Example 1. As shown in FIG. 15, Example 1, which performed curriculum learning using data generated from the VQE of the main task, converged faster than the conventional method. Therefore, the learning time was reduced compared to the conventional method.

[0088] Figure 16 is a diagram explaining the determination of a QAE circuit. It shows the learning cost of a subtask and the learning cost of the main task without curriculum learning. The higher the learning cost, the closer the vertical axis is to "1.0," which means higher accuracy. As shown in Figure 16, if the learning cost of a subtask is high, the learning cost of the main task also tends to be high. Therefore, it is preferable to determine the circuit that has achieved a high learning cost for the subtask as the circuit for the main task. In the example of Figure 16, the highest accuracy is achieved by using "RY_CZ," which was executed in subtask learning, as the target for main task learning. [Example]

[0089] Although the embodiments of the present invention have been described above, the present invention may be embodied in various different forms other than the above-described embodiments.

[0090] (Numbers, etc.) The numerical values, learning data, graphs, etc. used in the above embodiments are merely examples and can be changed as desired. Furthermore, the process flow described in each flowchart can also be changed as appropriate within a consistent range.

[0091] (system) The information including the processing procedures, control procedures, specific names, various data and parameters shown in the above documents and drawings may be changed arbitrarily unless otherwise specified.

[0092] Furthermore, the specific form of distribution and integration of the components of each device is not limited to that shown in the figure. For example, the first machine learning unit 30 and the second machine learning unit 40 may be integrated. That is, all or some of the components may be functionally or physically distributed or integrated in any unit depending on various loads, usage conditions, etc. Furthermore, all or any part of the processing functions of each device may be realized by a CPU and a program analyzed and executed by the CPU, or may be realized as hardware using wired logic.

[0093] Furthermore, all or any part of the processing functions performed by each device may be realized by a CPU and a program analyzed and executed by the CPU, or may be realized as hardware using wired logic.

[0094] (Hardware) Fig. 17 is a diagram illustrating an example of a hardware configuration. Here, an information processing device 10 will be described as an example. As shown in Fig. 17, the information processing device 10 includes a communication device 10a, an HDD (Hard Disk Drive) 10b, a memory 10c, and a processor 10d. The components illustrated in Fig. 17 are connected to each other via a bus or the like.

[0095] The communication device 10a is a network interface card or the like, and communicates with other devices. The HDD 10b stores programs and DBs that operate the functions shown in FIG.

[0096] Processor 10d reads from HDD 10b or the like a program that executes the same processes as the processing units shown in FIG. 7 and loads it into memory 10c, thereby operating a process that executes the functions described in FIG. 7 or the like. For example, this process executes the same functions as the processing units of information processing device 10. Specifically, processor 10d reads from HDD 10b or the like a program that has the same functions as first machine learning unit 30, second machine learning unit 40, or the like. Processor 10d then executes a process that executes the same processes as first machine learning unit 30, second machine learning unit 40, or the like.

[0097] In this way, the information processing device 10 operates as an information processing device that executes a machine learning method by reading and executing a program. The information processing device 10 can also realize functions similar to those of the above-described embodiment by reading the program from a recording medium using a medium reading device and executing the read program. Note that the program in these other embodiments is not limited to being executed by the information processing device 10. For example, the above-described embodiment may also be applied in the same way to cases where another computer or server executes the program, or where these execute the program in cooperation with each other.

[0098] This program may be distributed via a network such as the Internet. Alternatively, this program may be recorded on a computer-readable recording medium such as a hard disk, a flexible disk (FD), a CD-ROM, a magneto-optical disk (MO), or a digital versatile disk (DVD), and may be read out from the recording medium and executed by a computer.

[0099] The following additional notes are provided regarding the embodiments including the above examples.

[0100] (Appendix 1) To the computer, performing first machine learning on the quantum autoencoder using first input data and second input data in which the states of the quantum bits are the same; performing second machine learning on the quantum autoencoder trained by the first machine learning using third input data and fourth input data in which the states of the quantum bits are different from each other; A machine learning program characterized by executing processing.

[0101] (Supplementary Note 2) The process of executing the first machine learning includes: In a quantum circuit for training, the quantum circuit has a quantum circuit that does not perform a gate operation on input quantum bits, and the quantum autoencoder that performs encoding and decoding on the input quantum bits, the first input data is input to the quantum circuit to obtain first output data, and the second input data is input to the quantum autoencoder to obtain reconstructed second output data; performing the first machine learning to reduce an error between the first output data and the second output data; 2. The machine learning program according to claim 1,

[0102] (Appendix 3) The process of executing the second machine learning includes: inputting the third input data into the quantum circuit to obtain third output data, and inputting the fourth input data into the quantum autoencoder trained by the first machine learning to obtain reconstructed fourth output data; performing the second machine learning to reduce an error between the third output data and the fourth output data; 3. The machine learning program according to claim 1 or 2,

[0103] (Supplementary Note 4) The quantum autoencoder is a quantum circuit used to remove noise from generated data generated by a quantum circuit using a variational quantum fixed value method after the second machine learning, The process of performing the first machine learning includes: performing the first machine learning on each of the pieces of generated data generated by each of the plurality of quantum circuits using the variational quantum fixed value method, using the first input data and the second input data; The process of performing the second machine learning includes: generating a set of the third input data and the fourth input data by combining each of the generated data generated by each of the plurality of quantum circuits using the variational quantum fixed value method; performing the second machine learning using the generated set of input data; 4. The machine learning program according to any one of claims 1 to 3.

[0104] (Supplementary Note 5) The quantum circuit for training has a plurality of quantum circuits for training, each including the quantum circuit and a quantum autoencoder having different gate operations or initial parameters; The process of performing the first machine learning includes: performing the first machine learning on each of the plurality of learning quantum circuits; selecting one training quantum circuit based on the results of each of the first machine learning for the plurality of training quantum circuits; The process of performing the second machine learning includes: performing the second machine learning on the selected one quantum circuit for learning; 5. The machine learning program according to claim 1,

[0105] (Appendix 6) The computer, performing first machine learning on the quantum autoencoder using first input data and second input data in which the states of the quantum bits are the same; performing second machine learning on the quantum autoencoder trained by the first machine learning using third input data and fourth input data in which the states of the quantum bits are different from each other; A machine learning method characterized by performing processing.

[0106] (Supplementary Note 7) Performing first machine learning on a quantum autoencoder using first input data and second input data in which the states of each quantum bit are the same; performing second machine learning on the quantum autoencoder trained by the first machine learning using third input data and fourth input data in which the states of the quantum bits are different from each other; An information processing device comprising a control unit. [Explanation of symbols]

[0107] 10. Information processing equipment 11 Communications Department 12 Storage section 13 QAE Information 20 Control Unit 30 Machine Learning Department 1 31 Design Department 32 Learning data generation unit 33 Learning Department 34 Selection section 40 Second Machine Learning Department 41 Learning data generation unit 42 Learning Department

Claims

1. On the computer, performing first machine learning on the quantum autoencoder using first input data and second input data in which the states of the quantum bits are the same; performing second machine learning on the quantum autoencoder trained by the first machine learning using third input data and fourth input data in which the states of the quantum bits are different from each other; A machine learning program characterized by executing processing.

2. The process of performing the first machine learning includes: In a quantum circuit for training, the quantum circuit has a quantum circuit that does not perform a gate operation on input quantum bits, and the quantum autoencoder that performs encoding and decoding on the input quantum bits, the first input data is input to the quantum circuit to obtain first output data, and the second input data is input to the quantum autoencoder to obtain reconstructed second output data; executing the first machine learning to reduce an error between the first output data and the second output data; The machine learning program according to claim 1 .

3. The process of performing the second machine learning includes: inputting the third input data into the quantum circuit to obtain third output data, and inputting the fourth input data into the quantum autoencoder trained by the first machine learning to obtain reconstructed fourth output data; performing the second machine learning to reduce an error between the third output data and the fourth output data; The machine learning program according to claim 2 .

4. the quantum autoencoder is a quantum circuit used to remove noise from generated data generated by a quantum circuit using a variational quantum fixed value method after the second machine learning; The process of performing the first machine learning includes: performing the first machine learning on each of the pieces of generated data generated by each of the plurality of quantum circuits using the variational quantum fixed value method, using the first input data and the second input data; The process of performing the second machine learning includes: generating a set of the third input data and the fourth input data by combining each of the generated data generated by each of the plurality of quantum circuits using the variational quantum fixed value method; performing the second machine learning using the generated set of input data; The machine learning program according to claim 1 .

5. The quantum circuit for training has a plurality of quantum circuits for training, each including the quantum circuit and a quantum autoencoder having different gate operations or initial parameters; The process of performing the first machine learning includes: performing the first machine learning on each of the plurality of learning quantum circuits; selecting one training quantum circuit based on the results of each of the first machine learning for the plurality of training quantum circuits; The process of performing the second machine learning includes: performing the second machine learning on the selected one quantum circuit for learning; 4. The machine learning program according to claim 3.

6. The computer performing first machine learning on the quantum autoencoder using first input data and second input data in which the states of the quantum bits are the same; performing second machine learning on the quantum autoencoder trained by the first machine learning using third input data and fourth input data in which the states of the quantum bits are different from each other; A machine learning method characterized by performing processing.

7. performing first machine learning on the quantum autoencoder using first input data and second input data in which the states of the quantum bits are the same; performing second machine learning on the quantum autoencoder trained by the first machine learning using third input data and fourth input data in which the states of the quantum bits are different from each other; An information processing device comprising a control unit.

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