Quantum computer, computer system and control method thereof, and control program

Abstract

According to the present invention, the estimation accuracy of machine learning by a quantum kernel method is improved. A quantum computer (3) estimates a kernel function k(xk,xl) of two feature vectors xk, xl (xk, xl have n elements in total, and n is an integer of 2 or more) using the two feature vectors xk, xl and phase parameters φp ,q(x) (xp and xq are the p-th and q-th elements, respectively, in one of the two feature vectors xk, xl). The phase parameters φp, q(x) are calculated by φp, q(x)=(π-αpxp)×(π-αqxq) using adjustment parameters αp and αq.

Description

Quantum computer, computer system, control method thereof, and control program

[0001] The present invention relates to a quantum computer, a computer system, a control method thereof, and a control program.

[0002] The quantum kernel method is one of the leading algorithms for machine learning using quantum computers, and is described in, for example, Patent Document 1 and Non-Patent Document 1. The encoding of classical data into a quantum state can be regarded as a feature mapping into a high-dimensional Hilbert space. Therefore, compared to classical kernel methods that perform machine learning using classical computers, quantum kernel methods can express a variety of feature mappings, and are therefore thought to have advantages in terms of the efficiency of machine learning.

[0003] Japan Special Publication No. 2023-546590

[0004] V. Havlicek et al., “Supervised learning with quantum-enhanced feature spaces”, Nature, 2019, Vol. 567, No. 7747, p. 209-212

[0005] However, conventional quantum kernel methods still have lower machine learning estimation accuracy than classical kernel methods.

[0006] One aspect of the present invention aims to improve the estimation accuracy of machine learning using quantum kernel methods.

[0007] In order to solve the above problem, a quantum computer according to aspect 1 of the present invention is provided that: ｋ , x ｌ (x ｋ , x ｌ and an acquisition unit for acquiring the two feature vectors x ｋ , x ｌ The kernel function k(x ｋ, x ｌ ) and an output unit that outputs the calculation result of the quantum circuit, and in the quantum circuit, the kernel function k(x ｋ, xｌ ) is expressed by the following formula (1): Here, the x ｐ and x ｑ are the two feature vectors x ｋ , x ｌ are the pth and qth elements in any of the above, and ｐ and α ｑ is a parameter for adjustment.

[0008] A quantum computer according to a second aspect of the present invention may be configured in the first aspect such that the adjustment parameters αp and αq have the same value.

[0009] A computer system according to a third aspect of the present invention includes the quantum computer of the first or second aspect and a classical computer, wherein the classical computer may include a first acquisition unit that acquires a set of teacher data, a setting unit that sets adjustment parameters, a selection unit that selects two feature vectors from a plurality of feature vectors that are a plurality of explanatory variables included in the set of teacher data, a calculation unit that calculates a phase parameter for each of the two feature vectors using the two feature vectors and the adjustment parameters, an output unit that outputs the two feature vectors and the phase parameter to the quantum computer, a second acquisition unit that acquires Kernel functions of the two feature vectors estimated by the quantum computer, and a learning unit that creates a learning model by performing machine learning using a plurality of Kernel functions acquired from the second acquisition unit for the plurality of feature vectors included in the set of teacher data and a plurality of objective variables included in the set of teacher data.

[0010] A computer system according to a fourth aspect of the present invention is the same as that of the third aspect, wherein the objective variable in the set of training data indicates to which class the feature vector, which is the explanatory variable, belongs, and the first acquisition unit may further include an estimation unit that acquires input data and estimates the class to which the input data belongs using a learning model created by the learning unit.

[0011] A computer system according to aspect 5 of the present invention may be the same as that according to aspect 3, wherein the setting unit sets the number of dimensions, and further includes a dimension reduction unit that reduces the data acquired by the first acquisition unit to the number of dimensions.

[0012] A control method for a computer system according to a sixth aspect of the present invention is a control method for a computer system including the quantum computer of the first or second aspect and a classical computer, and may include the following steps: a first acquisition step in which the classical computer acquires a set of teacher data; a setting step in which adjustment parameters are set; a selection step in which two feature vectors are selected from a plurality of feature vectors that are a plurality of explanatory variables included in the set of teacher data; a calculation step in which phase parameters are calculated for each of the two feature vectors using the two feature vectors and the adjustment parameters; an output step in which the two feature vectors and the phase parameters are output to the quantum computer; a second acquisition step in which Kernel functions of the two feature vectors estimated by the quantum computer are acquired; and a learning step in which a learning model is created by performing machine learning using the plurality of Kernel functions acquired in the second acquisition step for the plurality of feature vectors included in the set of teacher data and a plurality of objective variables included in the set of teacher data.

[0013] A control program according to aspect 7 of the present invention may be a control program for causing a classical computer in the computer system of aspect 3 to function, and may be a control program for causing a computer to function as the setting unit, the selection unit, the calculation unit, and the learning unit.

[0014] According to one aspect of the present invention, it is possible to improve the estimation accuracy of machine learning using the quantum kernel method.

[0015] 1 is a block diagram showing an overview of a quantum SVM according to an embodiment of the present invention. FIG. 2 is a circuit diagram showing an example of a quantum circuit portion in a quantum computer of the quantum SVM. FIG. 3 is a circuit diagram showing an example of the quantum circuit. FIG. 4 is a flowchart showing the flow of a learning process in the quantum SVM. FIG. 5 is a flowchart showing the flow of an evaluation process in the quantum SVM. FIG. 6 is a graph showing a set of training data used in an example of the embodiment. FIG. 7 is a diagram showing, in table form, calculation results of estimation accuracy in the example and comparative example. FIG. 8 is a graph showing examples of training kernel matrices and evaluation kernel matrices in the example and comparative example.

[0016] First Embodiment An embodiment of the present invention will be described with reference to FIGS.

[0017] (Quantum SVM) FIG. 1 is a block diagram showing an overview of a quantum SVM (support-vector machine) according to this embodiment.

[0018] SVM is a pattern recognition model that uses supervised learning and is applied to classification, regression, etc. The SVM optimizes a decision function (learning model) using a set of training data that is part of a set of teacher data. The SVM then uses the optimized decision function to estimate the class of input data. The SVM also evaluates the accuracy of the class estimation using a set of test data that is part or all of the remaining set of teacher data.

[0019] In order to cope with cases where linear separation is not possible, the SVM uses the feature vector x, which is an explanatory variable of the training data. ｋ , x ｌ (x ｋ , x ｌ Each of the vectors (x, y, z, z) has n elements, where n is an integer equal to or greater than 2) is mapped to a finite-dimensional or infinite-dimensional feature space, and linear separation is performed on the feature space. ｋ ) and φ(x ｌ ) does not need to be calculable individually, and the inner product φ(x ｌ ) Ｔ φ(x ｋ) can be calculated. This inner product is the kernel function k(x ｋ ,x ｌ ) is called k(x ｋ ,x ｌ ) = φ(x ｌ ) Ｔ φ(x ｋ ) The quantum SVM performs the mapping to the feature space and the calculation of the kernel function on a quantum computer.

[0020] As shown in FIG. 1, the quantum SVM 1 is a computer system including a classical computer 2 and a quantum computer 3. The quantum computer 3 is a computer that applies the principles of quantum mechanics to calculations. The quantum computer 3 performs calculation processing using quantum bits having values ​​between 0 and 1. As described above, the quantum computer 3 maps the training data to the feature space and calculates the kernel function. On the other hand, the classical computer 2 is a conventional computer that performs calculations using logic circuits based on classical physics. The classical computer 2 performs calculation processing using bits having values ​​of 0 or 1. Details of the classical computer 2 will be described later.

[0021] (Quantum Computer) As shown in FIG. 1 , the quantum computer 3 includes an acquisition unit 10 , a quantum circuit 11 , and an output unit 12 .

[0022] The acquisition unit 10 acquires two different feature vectors x ｋ , x ｌ from the classical computer 2. Furthermore, the acquisition unit 10 acquires a phase parameter φ ｐ，ｑ (x), where p and q are integers between 0 and (n-1). ｋ , x ｌ and the phase parameter φ ｐ，ｑ (x) is sent to the quantum circuit 11.

[0023] The quantum circuit 11 receives the feature vector x ｋ , x ｌ and the phase parameter φ ｐ，ｑ (x), the kernel function k(x ｋ, xｌ The quantum circuit 11 is calculated in detail later. The output unit 12 outputs the kernel function k(x ｋ, x ｌ ) is output to classical computer 2.

[0024] (Quantum Circuit) In the quantum circuit 11, the kernel function k(x ｋ, x ｌ ) is expressed by the following equation (1). Here, x ｐ and x ｑ are the two feature vectors x ｋ , x ｌ are the pth and qth elements in either of the above. ｐ and α ｑ are the pth and qth tuning parameters, respectively. ｐ and α ｑ Therefore, the element x ｐ and x ｑ The strength of quantum entanglement can be adjusted by adjusting the parameter α ｐ and α ｑ When the phase parameter φ is not used, that is, when the phase parameter φ is used, ｐ，ｑ (x)=(π-x ｐ )×(π-x ｑ ) is disclosed in Non-Patent Document 1.

[0025] FIG. 2 is a circuit diagram showing a part of the quantum circuit 11, which is a parameterized quantum circuit U corresponding to the above formula (3). φ（ｘ） 2 shows a circuit diagram of an example of the quantum circuit shown in FIG. 2. The example in FIG. 2 shows the case where p=0 and q=1. It should be noted that each element of the feature vector x input to the quantum circuit is assumed to be normalized in advance within the range of 0 to 2π.

[0026] The quantum circuit U shown in FIG. φ（ｘ） In the initial state |0>, the 0th qubit q ０ is superposed by the H (Hadamard) gate, and R ｚ (Z-axis rotation) The gate rotates the 0th element x of the feature vector x around the z-axis. ０This rotates the feature vector x by an angle corresponding to the 0th element x ０ The value of the 0th quantum bit q ０ is input (parametrized) to

[0027] Similarly, the first qubit q in the initial state |0> １ is superposed by the H gate, and R ｚ The gate calculates the first element x of the feature vector x around the z-axis. １ This rotates the feature vector x by an angle corresponding to the first element x １ The value of the first quantum bit q １ is parameterized to

[0028] Next, the parametrized first qubit q １ is the parameterized 0th qubit q by a CNOT gate. ０ The first qubit q １ is R ｚ The gate determines the phase parameter φ ｐ，ｑ The value of (x) is parameterized, and the parameterized 0th quantum bit q ０ The quantum circuit U shown in Figure 2 is in a quantum entangled state. φ（ｘ） Thus, the 0th element x of the feature vector x ０ and the first element x １ is mapped to the feature space.

[0029] 3 is a circuit diagram showing an example of the quantum circuit 11 corresponding to the above formula (1), that is, the quantum circuit 11 for calculating the kernel function k. In the example of FIG. 3, ｋ , x ｌ The number of elements of is 6. Therefore, the six quantum bits q ０ ~q ５ In the example of Fig. 3, in order to simplify the quantum circuit 11, q = p + 1, and quantum entanglement is generated only between adjacent quantum bits.

[0030] The quantum circuit 11 shown in FIG. 3 satisfies the following equation (1): |0> ６ On the other hand, the parameterized quantum circuit Uφ（ｘｋ） and U φ（ｘｌ） † are applied in order, and by measurement, |0> ６ The number of times that the state |0> is obtained can be measured. ６ The probability of obtaining the state of ｋ, x ｌ ), the quantum circuit 11 can calculate the kernel function k(x ｋ, x ｌ ) can be estimated (calculated).

[0031] (Classical Computer) As shown in FIG. 1 , the classical computer 2 includes an acquisition unit 20, a setting unit 21, a dimension reduction unit 22, a normalization unit 23, a data division unit 24, a phase parameter calculation unit 25, a matrix creation unit 26, a learning unit 27, a class estimation unit 28, and an evaluation unit 29.

[0032] The acquisition unit 20 (first acquisition unit) acquires the set of teacher data. The teacher data includes input data as explanatory variables and classes as objective variables. The acquisition unit 20 sends the input data included in the acquired set of teacher data to the dimension reduction unit 22. The acquisition unit 20 also sends the classes included in the acquired set of teacher data to the learning unit 27 and the evaluation unit 29.

[0033] The setting unit 21 sets the number of dimensions Dn after reduction by the dimension reduction unit 22 and the above-mentioned adjustment parameter α ０ ~α ｎ－１ The setting unit 21 sends the number of dimensions Dn to the dimension reduction unit 22 and also sets the adjustment parameter α ０ ~α ｎ－１ is sent to the phase parameter calculation unit 25.

[0034] The dimension reduction unit 22 performs dimension reduction on the input data from the acquisition unit 20 so that the number of elements included in the data input to the quantum circuit 11 matches the number of quantum bits used in the quantum circuit 11. Specifically, the dimension reduction unit 22 reduces the number of dimensions of the input data to the number of dimensions Dn from the setting unit 21. Examples of the dimension reduction method include principal component analysis (PCA), non-negative matrix factorization, and autoencoder. The dimension reduction unit 22 sends the dimension-reduced data (hereinafter referred to as "dimensionally reduced data") to the normalization unit 23.

[0035] The normalization unit 23 normalizes the dimension-reduced data from the dimension reduction unit 22 to a range usable by the quantum circuit 11. In the quantum circuit 11 of this embodiment, data is input as a rotation angle around the Z axis of the quantum bit, as shown in FIGS. 2 and 3 . Therefore, the normalization unit 23 normalizes the dimension-reduced data to a range of 0 to 2π. Normalization achieves parameterization that takes into account the unitary nature of the quantum bit. The normalization unit 23 sends the normalized dimension-reduced data (hereinafter referred to as "normalized data") to the data division unit 24.

[0036] The data division unit 24 (selection unit, output unit) divides the set of normalized data from the normalization unit 23, which is derived from the above-mentioned set of teacher data, into a set of training data for learning and a set of test data for evaluation.

[0037] The data division unit 24 selects the pairs of training data from the set of training data and sends them to the phase parameter calculation unit 25 and the quantum computer 3, and continues this process until all pairs have been selected. The data division unit 24 also selects the pairs of training data and test data from the set of training data and the set of test data and sends them to the phase parameter calculation unit 25 and the quantum computer 3, and continues this process until all pairs have been selected.

[0038] The phase parameter calculation unit 25 (calculation unit, output unit) calculates the phase parameter φ of the training data or test data from the data division unit 24. ｐ，ｑ (x) based on the above equation (4). The phase parameter calculation unit 25 calculates the calculated phase parameter φ ｐ，ｑ (x) is sent to quantum computer 3.

[0039] The quantum computer 3 receives from the classical computer 2 the training data pairs and the respective phase parameters φ of the pairs. ｐ，ｑ (x), one of the pair of training data is converted into a feature vector x ｋ and the other is the feature vector x ｌ Next, the quantum computer 3 calculates a feature vector x ｋ and its phase parameter φ ｐ，ｑ (x ｋ ) and feature vector x ｌ and its phase parameter φ ｐ，ｑ (x ｌ ) and input the kernel function k(x ｋ, x ｌ ) is estimated. Then, the quantum computer 3 estimates the estimated kernel function k(x ｋ, x ｌ ) to classical computer 2.

[0040] Furthermore, the quantum computer 3 receives pairs of training data and test data and respective phase parameters φ of the pairs from the classical computer 2. ｐ，ｑ (x), the training data is converted into a feature vector x ｋ The test data is expressed as a feature vector x ｌ Next, the quantum computer 3 calculates a feature vector x ｋ and its phase parameter φ ｐ，ｑ (x ｋ ) and feature vector x ｌ and its phase parameter φ ｐ，ｑ (x ｌ ) and input the kernel function k(x ｋ, x ｌ) is estimated. Then, the quantum computer 3 estimates the estimated kernel function k(x ｋ, x ｌ ) to classical computer 2.

[0041] The matrix creation unit 26 (second acquisition unit) calculates a kernel function k (x ｋ, x ｌ ) is obtained from the quantum computer 3, and this is repeated for all pairs of the training data to obtain the kernel function k(x ｋ, x ｌ The matrix creating unit 26 creates a Gram matrix (hereinafter referred to as a “learning kernel matrix”) having elements of the matrix . The matrix creating unit 26 sends the created learning kernel matrix to the learning unit 27.

[0042] Furthermore, the matrix creation unit 26 calculates a kernel function k(x ｋ, x ｌ ) from the quantum computer 3, and repeats this for all pairs of the training data and the test data. As a result, the matrix creation unit 26 obtains the kernel function k(x ｋ, x ｌ ) as elements (hereinafter referred to as the “evaluation kernel matrix”). The matrix creation unit 26 sends the created evaluation kernel matrix to the evaluation unit 29.

[0043] The learning unit 27 performs machine learning to generate a decision function that determines the classification of classes, using the learning kernel matrix from the matrix creation unit 26 and a set of classes that are included in the teacher data and correspond to the training data. The learning unit 27 sends the machine-learned decision function to the class estimation unit 28 and the evaluation unit 29.

[0044] An example of machine learning in the learning unit 27 will now be described. The decision function f(x) is expressed by the following equation (5). The learning unit 27 uses the learning kernel matrix and the class y ｉ and the parameters b and α in the above equation (6) are calculated using the set ｊThe learning unit 27 also performs fitting of a kernel function k (hereinafter referred to as "classical kernel function k") used in an SVM (hereinafter referred to as "classical SVM") that is executed only by the classical computer 2 without using the quantum computer 3. Examples of the classical kernel function k include a Gaussian kernel, a sigmoid kernel, a polynomial kernel, and a radial basis function (RBF) kernel. By fitting these, the decision function f(x) of the above formula (5) can be obtained.

[0045] The class estimation unit 28 (estimation unit) acquires input data for which classes are to be estimated via the acquisition unit 20, the dimension reduction unit 22, and the normalization unit 23, and estimates the class into which the acquired input data is classified using the decision function from the learning unit 27. Therefore, when the class estimation unit 28 estimates the class of the input data, there is no need to use the quantum computer 3. The class estimation unit 28 may display the estimated class via a display device (not shown), or may transmit the estimated class to an external device via a communication device (not shown).

[0046] The evaluation unit 29 evaluates the decision function from the learning unit 27. Specifically, the evaluation unit 29 first estimates a set of classes into which each of the test data sets is classified, using the evaluation kernel matrix from the matrix creation unit 26 and the decision function. At this time, the evaluation unit 29 uses a kernel function that is an element of the evaluation kernel matrix in place of the classical kernel function in the decision function. Next, the evaluation unit 29 compares the estimated set of classes with a set of classes included in the set of teacher data and corresponding to each of the test data sets, to calculate an estimation accuracy. The evaluation unit 29 may display the calculated estimation accuracy via a display device (not shown) or may transmit it to an external device via a communication device (not shown).

[0047] 4 is a flowchart showing the flow of the learning process (control method) in the quantum SVM 1 configured as described above. As shown in FIG. 4, first, the acquisition unit 20 acquires a set of teacher data including input data and classes (S10, first acquisition step). Next, the setting unit 21 sets the number of dimensions Dn and the adjustment parameter α ０ ~α ｎ－１ are set (S11, setting step).

[0048] Next, the dimension reduction unit 22 reduces the dimensions of the input data to create dimension-reduced data with the number of dimensions Dn (S12). Next, the normalization unit 23 normalizes the dimension-reduced data to a range usable by the quantum circuit 11 to create normalized data (S13). Next, the data division unit 24 divides the normalized data set derived from the teacher data set into a training data set for learning and a test data set for evaluation (S14).

[0049] Next, the data division unit 24 selects the training data pair from the training data set (S15, selection step). The data division unit 24 also outputs the selected training data pair to the quantum computer 3 (output step). Next, the phase parameter calculation unit 25 calculates the phase parameters φ of each of the training data pairs. ｐ，ｑ (x) = (π-α ｐ x ｐ ) × (π-α ｑ x ｑ ) (S16, calculation step). The phase parameter calculation unit 25 calculates the calculated phase parameter φ ｐ，ｑ (x) is output to the quantum computer 3 (output step).

[0050] Next, the quantum computer 3 calculates the training data pairs and their respective phase parameters φ ｐ，ｑ (x) into the quantum circuit 11 and measure it, the inner product value of the pair (kernel function k(x) ｋ, x ｌ) is calculated (S17). The inner product values ​​of the pairs calculated by the quantum computer 3 are acquired by the matrix creation unit 26 (second acquisition step). Next, steps S15 to S17 are repeated until all of the pairs of training data are selected from the set of training data (S18). As a result, the matrix creation unit 26 creates a learning kernel matrix whose elements are the inner product values ​​calculated for all of the pairs of training data (S19).

[0051] Next, the learning unit 27 performs machine learning to generate a decision function that determines the classification of classes using the learning kernel matrix and a set of classes that are included in the teacher data and correspond to the training data (S20, learning step). Specifically, the learning unit 27 performs machine learning to generate a decision function that determines the classification of classes using the parameters (b, α ｊ ) and a classical kernel function are fitted. The class estimation unit 28 can estimate the class into which the input data is classified using the decision function. Then, the learning process is terminated.

[0052] (Evaluation Process) Fig. 5 is a flowchart showing the flow of the evaluation process in the quantum SVM 1 configured as described above. The evaluation process is performed after the learning process shown in Fig. 4.

[0053] 5, the data dividing unit 24 selects the pair of training data and test data from the set of training data and the set of test data divided in step S14 of FIG. 4 (S30). Next, the phase parameter calculation unit 25 calculates the phase parameters φ of each pair of the training data and the test data. ｐ，ｑ (x) = (π-α ｐ x ｐ ) × (π-α ｑ x ｑ ) is calculated (S31).

[0054] Next, the quantum computer 3 calculates the pair of the training data and the test data and the respective phase parameters φ of the pair. ｐ，ｑ (x) into the quantum circuit 11 and measure it, the inner product value of the pair (kernel function k(x) ｋ, x ｌ) is calculated (S32). Next, steps S30 to S32 are repeated until all pairs of training data and test data are selected from the training data set and the test data set (S33). As a result, the matrix creation unit 26 creates an evaluation kernel matrix whose elements are the inner product values ​​calculated for all pairs of training data and test data (S34).

[0055] Next, the evaluation unit 29 uses the evaluation kernel matrix and the decision function machine-learned in step S20 of FIG. 4 to estimate a set of classes into which each of the test data sets is classified (S35). At this time, the decision function uses inner product values ​​(kernel functions) that are elements of the evaluation kernel matrix instead of a classical kernel function. Next, the evaluation unit 29 compares the estimated set of classes with the set of classes included in the set of teacher data acquired in step S10 of FIG. 4 and that correspond to each of the test data sets, to calculate the estimation accuracy (S36). Then, the evaluation process ends.

[0056] The learning process shown in FIG. 4 and the evaluation process shown in FIG. 5 are performed with the number of dimensions Dn and the adjustment parameter α ０ ~α ｎ－１ By changing the number of dimensions Dn and the adjustment parameter α ０ ~α ｎ－１ can be found.

[0057] An embodiment of the present invention will be described with reference to FIGS.

[0058] 6 is a graph showing a set of training data used in this example. The training data set is a data set extracted from a system log for fault diagnosis in a network system operated by the applicant.

[0059] The vertical axis of Fig. 6 indicates the failure data number that identifies 56 pieces of failure data. The horizontal axis of Fig. 6 indicates the command number that identifies 120 types of commands. In Fig. 6, when a certain command is sent to the network system for certain failure data, an abnormal result is obtained and colored. The failures are classified into seven types, which correspond to different color intensities in Fig. 6. That is, in the teacher data shown in Fig. 6, the failure data is the explanatory variable (input data) of the teacher data, the presence or absence of an abnormality in the command is an element of the failure data, and the type of failure is the objective variable (class) of the teacher data.

[0060] Using the set of teacher data shown in Fig. 6, the learning process shown in Fig. 4 and the evaluation process shown in Fig. 5 were performed to calculate the estimation accuracy. In this example, in order to shorten the processing time, a tensor network simulator was used instead of the quantum computer 3, and the adjustment parameter α ０ ~α ｎ－１ was set to the same value α.

[0061] 7 is a diagram showing the calculation results of the estimation accuracy in a table format. As shown in FIG. 7, the estimation accuracy was calculated for the cases where the number of quantum bits used, i.e., the number of dimensions Dn, is 10, 20, 30, 40, and 50, and where the adjustment parameter α is 0.2, 0.4, 0.6, and 0.8.

[0062] Comparative Example 1 is a phase parameter φ ｐ，ｑ (x) is used, i.e., the estimation accuracy is obtained without using the adjustment parameter α. Comparative Example 2 is the estimation accuracy obtained using a conventional quantum SVM. Comparative Example 3 is the estimation accuracy obtained using a classical SVM using an RBF kernel. In the classical SVM, the number of quantum bits corresponds to the number of dimensions Dn.

[0063] The conventional quantum SVM differs from the quantum SVM of this embodiment in the configuration of the quantum circuit, but the other aspects are the same. The quantum circuit of the conventional quantum SVM is a quantum circuit 11 shown in FIG. 3, which is obtained by adding a CNOT gate and a phase parameter φ ｐ，ｑ R for (x) ｚIn other words, a conventional quantum SMV quantum circuit only parameterizes each element of a feature vector for each quantum bit, and does not generate an entangled state between quantum bits.

[0064] 7 and Comparative Example 1, it can be seen that by using an adjustment parameter α of less than 1, the Example can obtain estimation accuracy equivalent to or greater than that of Comparative Example 1. Furthermore, by comparing the Example and Comparative Example 2 of FIG. 7, it can be seen that when the number of quantum bits is 10, 20, or 50, or when the number of quantum bits is 30 or 40 and the adjustment parameter α is 0.2 or 0.4, the Example can obtain estimation accuracy equivalent to or greater than that of Comparative Example 2. Therefore, it can be seen that by adjusting (tuning) the adjustment parameter α, estimation accuracy equivalent to or greater than that of the prior art can be obtained.

[0065] 7 and Comparative Example 3, it can be seen that when the number of quantum bits is 10, when the number of quantum bits is 20 and α is any of 0.6 and 0.8, or when the number of quantum bits is 30 and α is any of 0.2, 0.4 and 0.6, the Example can achieve estimation accuracy equal to or higher than that of Comparative Example 3. Note that when the number of quantum bits is 40 and 50, the estimation accuracy is lower than when the number of quantum bits is 10, 20, and 30, and various factors such as the complexity of the data can be considered as the cause of this.

[0066] From the above, it can be seen that the adjustment (tuning) of the adjustment parameter α by the classical computer 2 improves the estimation accuracy of the machine learning using the kernel function estimated by the quantum computer 3. Furthermore, it can be seen that the estimation accuracy is further improved by adjusting (tuning) the number of dimensions Dn.

[0067] 8 is a graph showing examples of a training kernel matrix and an evaluation kernel matrix. In FIG. 8, the training kernel matrix is ​​shown on the left side, and the evaluation kernel matrix is ​​shown on the right side. The upper part of FIG. 8 shows the case in FIG. 7 where the estimation accuracy is highest, i.e., the case of this embodiment where the number of quantum bits is 20 and the adjustment parameter α is 0.6. The lower part of FIG. 8 shows the case in FIG. 7 where the estimation accuracy is lowest, i.e., the case of Comparative Example 1 where the number of quantum bits is 40 and the adjustment parameter α is 1.

[0068] The graph in Figure 8 is brighter as the kernel function becomes larger. Generally, the larger the kernel function, the higher the similarity in feature space between two pieces of paired data. Therefore, it is thought that the more kernel functions with large (bright) values ​​there are, the more data there are near the classification boundary that separates the classes, and therefore the higher the estimation accuracy. The graph in the upper part of Figure 8 is brighter than the graph in the lower part of Figure 8, and therefore the higher the estimation accuracy.

[0069] (Modification) The class estimation unit 28 may estimate the class of the input data using the quantum computer 3. In this case, the learning unit 27 uses the learning kernel matrix and the class y ｉ and the parameters b and α in the above equation (6) are calculated using the set ｊ By performing fitting of the above equation, the decision function f(x) of the above equation (5) is obtained.

[0070] Next, when the acquisition unit 20 acquires input data for which classes are to be estimated, the dimension reduction unit 22 reduces the dimensions of the input data, and the normalization unit 23 normalizes the input data. The data division unit 24 selects pairs of normalized input data (hereinafter referred to as "normalized input data") and the training data in the training data set, and sends them to the phase parameter calculation unit 25 and the quantum computer 3. This is continued until all of the training data included in the training data set has been selected. The phase parameter calculation unit 25 calculates the phase parameter φ between the training data and the normalized input data from the data division unit 24. ｐ，ｑ (x) is calculated based on the above formula (4) and sent to the quantum computer 3.

[0071] On the other hand, the quantum computer 3 receives from the classical computer 2 pairs of training data and normalized input data and the respective phase parameters φ of the pairs. ｐ，ｑ Next, the quantum computer 3 converts the training data included in the pair into the feature vector x ｋ The normalized input data included in the pair is expressed as a feature vector x ｌ Next, the quantum computer 3 calculates a feature vector x ｋ and its phase parameter φ ｐ，ｑ (x ｋ ) and feature vector x ｌ and its phase parameter φ ｐ，ｑ (x ｌ ) and input the kernel function k(x ｋ, x ｌ ) is estimated. Then, the quantum computer 3 estimates the estimated kernel function k(x ｋ, x ｌ ) to classical computer 2.

[0072] On the other hand, in the classical computer 2, the class estimation unit 28 estimates the training data x included in the training data set. ｉ For each training data x ｉ and the kernel function k(x ｉ Next, the class estimation unit 28 obtains the obtained kernel function k(x ｉ , x) and the above training data x ｉ The class y corresponding to ｉ and the decision function f(x) of the above equation (5) that has been machine-learned by the learning unit 27, the class into which the normalized input data is classified is estimated.

[0073] (Additional Notes) In the above embodiment and example, a quantum SVM 1 is described, but the present invention is not limited to this. For example, the present invention can also be applied to a device that executes any algorithm that uses a kernel function estimated by a quantum computer 3, such as a kernel perceptron, a Gaussian process, a principal component analysis, a canonical correlation analysis, a ridge regression, a spectral clustering, or a linear adaptive filter.

[0074] [Example of Implementation by Software] The functions of the classical computer 2 (hereinafter referred to as the "device") can be realized by a program that causes a computer to function as the device, and that causes a computer to function as each control block of the device (in particular, each unit included in the dimension reduction unit 22, the normalization unit 23, the phase parameter calculation unit 25, the learning unit 27, the class estimation unit 28, and the evaluation unit 29).

[0075] In this case, the device includes a computer having at least one control device (e.g., a processor) and at least one storage device (e.g., a memory) as hardware for executing the program. The functions described in each of the above embodiments are realized by executing the program using the control device and storage device.

[0076] The program may be non-transitory and may be recorded on one or more computer-readable recording media. The recording media may or may not be included in the device. In the latter case, the program may be supplied to the device via any wired or wireless transmission medium.

[0077] Furthermore, some or all of the functions of the control blocks can be realized by logic circuits. For example, an integrated circuit in which a logic circuit that functions as each of the control blocks is formed is also included in the scope of the present invention. In addition, the functions of the control blocks can also be realized by, for example, a quantum computer.

[0078] The present invention is not limited to the above-described embodiments, and various modifications are possible within the scope of the claims. Embodiments obtained by appropriately combining the technical means disclosed in different embodiments are also included in the technical scope of the present invention.

[0079] 2 Classical computer 3 Quantum computer 10 Acquisition unit 11 Quantum circuit 12 Output unit 20 Acquisition unit (first acquisition unit) 21 Setting unit 22 Dimension reduction unit 23 Normalization unit 24 Data division unit (selection unit, output unit) 25 Phase parameter calculation unit (calculation unit, output unit) 26 Matrix creation unit (second acquisition unit) 27 Learning unit 28 Class estimation unit (estimation unit) 29 Evaluation unit

Claims

1. Two feature vectors x ｋ , x ｌ (x ｋ , x ｌ each having n elements, n being an integer equal to or greater than 2; ｋ , x ｌ The kernel function k(x ｋ, x ｌ ) and an output unit that outputs a calculation result of the quantum circuit, ｋ, x ｌ ) is expressed by the following formula (1): Here, the x ｐ and x ｑ are the two feature vectors x ｋ , x ｌ are the pth and qth elements in any of the above, and ｐ and α ｑ is a tuning parameter,quantum computer.

2. The adjustment parameter α ｐ and α ｑ The quantum computer of claim 1 , wherein 3. A computer system comprising: a quantum computer according to claim 1 or 2; and a classical computer, wherein the classical computer comprises: a first acquisition unit that acquires a set of teacher data; a setting unit that sets adjustment parameters; a selection unit that selects two feature vectors from a plurality of feature vectors that are a plurality of explanatory variables included in the set of teacher data; a calculation unit that calculates a phase parameter for each of the two feature vectors using the two feature vectors and the adjustment parameters; an output unit that outputs the two feature vectors and the phase parameter to the quantum computer; a second acquisition unit that acquires kernel functions of the two feature vectors estimated by the quantum computer; and a learning unit that creates a learning model by performing machine learning using a plurality of kernel functions acquired from the second acquisition unit for the plurality of feature vectors included in the set of teacher data and a plurality of objective variables included in the set of teacher data.

4. The computer system described in claim 3, wherein the objective variable in the set of training data indicates to which class the feature vector, which is the explanatory variable, belongs, and the first acquisition unit further acquires input data and further includes an estimation unit that estimates the class to which the input data belongs using a learning model created by the learning unit.

5. The computer system according to claim 3, wherein the setting unit sets the number of dimensions, and further comprising a dimension reduction unit that reduces the data acquired by the first acquisition unit to the number of dimensions.

6. A control method for a computer system comprising the quantum computer of claim 1 or 2 and a classical computer, comprising: a first acquisition step in which the classical computer acquires a set of teacher data; a setting step in which adjustment parameters are set; a selection step in which two feature vectors are selected from a plurality of feature vectors that are a plurality of explanatory variables included in the set of teacher data; a calculation step in which a phase parameter for each of the two feature vectors is calculated using the two feature vectors and the adjustment parameters; an output step in which the two feature vectors and the phase parameter are output to the quantum computer; a second acquisition step in which Kernel functions of the two feature vectors estimated by the quantum computer are acquired; and a learning step in which a learning model is created by performing machine learning using the plurality of Kernel functions acquired in the second acquisition step for the plurality of feature vectors included in the set of teacher data and a plurality of objective variables included in the set of teacher data.

7. A control program for causing a classical computer in the computer system of claim 3 to function, the control program causing the computer to function as the setting unit, the selection unit, the calculation unit, and the learning unit.

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