Information processing device, method, and program

Abstract

To provide an information processing device, a method and a program, which can simply determine quantum circuit performance.SOLUTION: An information processing device according to an embodiment includes an acquisition unit and a determination unit. The acquisition unit acquires an asymptotic density matrix representing a quantum state obtained by repeatedly executing an evaluation target quantum circuit a predetermined number of times. The determination unit determines performance of the quantum circuit based on similarity between the asymptotic density matrix and a maximal mixed state.SELECTED DRAWING: Figure 3

Description

[Technical Field]

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

[0002] Quantum computers, which utilize quantum mechanical behavior, are expected to be able to efficiently solve problems that are difficult for classical computers to handle. For example, Shor's algorithm can solve problems exponentially faster than algorithms designed to run on classical computers. However, currently available NISQ (Noisy Intermediate-Scale Quantum) devices are affected by noise generated during the calculation process, making it difficult to solve practical tasks with high accuracy. Therefore, development of practical algorithms for NISQ devices, such as quantum-classical hybrid algorithms, is underway. Quantum-classical hybrid algorithms organically combine a part that represents a high-dimensional space using the superposition of quantum states on a quantum computer with a part that can be efficiently calculated on a classical computer, and are expected to demonstrate high performance even for problems that are difficult for classical computers alone.

[0003] Quantum reservoirs are a type of quantum-classical hybrid algorithm. Quantum reservoirs use a quantum system, such as a parameterless quantum circuit, as a reservoir, and optimize a linear layer on a classical computer that converts the output of the quantum system, such as measurement probability, into a desired value. In this case, the only parameters to be trained are the classical linear layer, so the training method is less susceptible to noise from the actual machine than methods that train quantum circuits with parameters.

[0004] One challenge with quantum reservoirs is that it is not obvious which quantum circuits are suitable for them. The normalized root mean squared error (NRMSE) and memory capacity described in the following non-patent document are commonly used metrics for evaluating reservoirs, but their calculation requires explicitly specifying the time-series data, which is a training dataset, in addition to information about the quantum circuit, and also requires learning of a linear layer. Because the evaluation metrics depend on the time-series data and learning method used, they are influenced by aspects other than the quality of the quantum circuit itself. [Prior art documents] [Non-patent literature]

[0005] [Non-Patent Document 1] Kohei Tanaka, Ryomasa Nakane, Akira Hirose. "Reservoir Computing: Theory and Hardware of High-Speed ​​Machine Learning for Time Series Pattern Recognition." Morikita Publishing Co., Ltd. 2021. Summary of the Invention [Problem to be solved by the invention]

[0006] The problem to be solved by the present invention is to provide an information processing device, method, and program that can easily determine the performance of a quantum circuit. [Means for solving the problem]

[0007] An information processing device according to an embodiment includes an acquisition unit and a determination unit. The acquisition unit acquires an asymptotic density matrix representing a quantum state obtained by repeatedly executing a quantum circuit to be determined a predetermined number of times. The determination unit determines the performance of the quantum circuit based on the similarity between the asymptotic density matrix and a maximal mixed state. [Brief explanation of the drawings]

[0008] [Figure 1] FIG. 1 is a diagram showing an example of the hardware configuration of an information processing device according to an embodiment of the present invention; [Figure 2] Diagram showing an example of the quantum reservoir model configuration [Figure 3] FIG. 10 is a diagram showing an example of an operation flowchart of an information processing device in a performance determination process; [Figure 4] FIG. 10 is a diagram showing an example of a display screen for a determination result. [Figure 5] FIG. 1 is a diagram showing the circuit configuration of a quantum circuit according to a first specific example. [Figure 6] FIG. 10 is a diagram showing the circuit configuration of a quantum circuit according to specific example 2. [Figure 7] Distribution diagram of similarity according to specific example 1 [Figure 8] Distribution diagram of similarity according to specific example 2 DETAILED DESCRIPTION OF THE INVENTION

[0009] Hereinafter, an information processing device, method, and program according to the present embodiment will be described with reference to the drawings.

[0010] Fig. 1 is a diagram showing an example of the hardware configuration of an information processing device 100 according to this embodiment. As shown in Fig. 1, the information processing device 100 is a classical computer having a processor 1, a storage device 2, an input device 3, a display device 4, and a communication device 5. Transmission and reception of data and various signals between the processor 1, the storage device 2, the input device 3, the display device 4, and the communication device 5 is performed via a bus.

[0011] The processor 1 is an integrated circuit that controls the overall operation of the information processing device 100. For example, the processor 1 has a CPU (Central Processing Unit), a GPU (Graphics Processing Unit), a DSP (Digital Signal Processor), and / or an FPU (Floating-Point Unit). The processor 1 may also have an internal memory and an I / O interface. The processor 1 executes various processes by interpreting and calculating programs stored in advance in a storage device 2 or the like. The processor 1 may be partially or entirely realized by hardware such as an ASIC (Application Specific Integrated Circuit) or an FPGA (Field Programmable Gate Array).

[0012] The storage device 2 is a volatile memory and / or a non-volatile memory that stores various data. For example, the storage device 2 stores data and setting values ​​used when the processor 1 executes various processes, data generated by various processes in the processor 1, etc. The storage device 2 is configured with a ROM (Read Only Memory), a RAM (Random Access Memory), an HDD (Hard Disk Drive), an SSD (Solid State Drive), an integrated circuit storage device, etc. The storage device 2 may also include a non-transitory computer-readable storage medium that stores a program executed by the processor 1.

[0013] The input device 3 accepts various operation inputs from an operator. Examples of the input device 3 that can be used include a keyboard, a mouse, various switches, a touchpad, and a touch panel display. An electrical signal corresponding to the accepted operation input (hereinafter referred to as an operation signal) is supplied to the processor 1.

[0014] The display device 4 displays various data under the control of the processor 1. A CRT (Cathode-Ray Tube) display, a liquid crystal display, an organic EL (Electro Luminescence) display, an LED (Light-Emitting Diode) display, a plasma display, or any other display may be used as appropriate as the display device 4. The display device 4 may also be a projector.

[0015] The communication device 5 includes a communication interface such as a network interface card (NIC) for performing data communication with various devices connected to the information processing device 100 via a network. Note that an operation signal may be supplied from a computer connected via the communication device 5 or an input device included in the computer, and various data may be displayed on a display device or the like included in the computer connected via the communication device 5. However, for the sake of simplicity of the following description, unless otherwise specified, it is assumed that the source of the operation signal is the input device 3 and the display destination of the various data is the display device 4. The input device 3 can be replaced by a computer connected via the communication device 5 or an input device included in the computer, and the display device 4 can be replaced by a display device or the like included in the computer connected via the communication device 5.

[0016] The information processing device 100 does not need to include all of the processor 1, storage device 2, input device 3, display device 4, and communication device 5. If necessary, some of the storage device 2, input device 3, display device 4, and communication device 5 may not be provided. The information processing device 100 may also be provided with any additional hardware device useful for executing the processing according to this embodiment. The information processing device 100 does not need to be physically configured as a single computer, but may be configured as a computer system having multiple computers communicably connected via wires, a network, or the like. The allocation of the series of processing according to this embodiment to the multiple processors 1 implemented in each of the multiple computers can be arbitrarily set. All processors 1 may execute all processing in parallel, or specific processing may be assigned to one or some of the processors 1, and the series of processing according to this embodiment may be executed by the entire computer system.

[0017] The processor 1 simply determines the performance of a quantum circuit to be determined without performing machine learning. First, the quantum circuit to be determined will be described. The quantum circuit to be determined means a quantum circuit for which performance determination is performed. The network configuration of the quantum circuit to be determined is not particularly limited, but in the following embodiments, as an example, it is assumed to be a quantum circuit that is a reservoir part of a quantum reservoir model. Note that the quantum circuit to be determined is not limited to a quantum circuit included in a quantum reservoir model, and may be a quantum circuit to which trained parameters are assigned, or a quantum circuit to which parameters determined according to another algorithm are assigned.

[0018] FIG. 2 is a diagram showing an example configuration of a quantum reservoir model 20. As shown in FIG. 2, the quantum reservoir model 20 is a quantum-classical hybrid machine learning model including a quantum circuit 21 executed by a quantum computer and a linear layer 23 executed by a classical computer. The quantum circuit 21 is a quantum circuit assigned fixed parameters that are not the training target, and functions as a reservoir section. The linear layer 23 is an artificial neural network assigned network parameters that are the training target or have already been trained, and functions as a readout section.

[0019] In this way, the parameters to be trained for the quantum reservoir model 20 exist only in the linear layer 23, which is handled by a classical computer, and therefore have the characteristic of being less susceptible to noise during machine learning. By using the quantum circuit 21 as the reservoir, it is expected that high-dimensional space can be expressed by superposition of quantum states, and that performance that exceeds classical computation can be demonstrated for specific data such as quantum data.

[0020] As shown in FIG. 2, quantum circuit 21 has two series of quantum bits (qubits) and one or more cells 25 that act on the two series of quantum bits. Note that in FIG. 2, the circuit configuration of the first cell 25 is illustrated, while the circuit configurations of the other cells 25 are not illustrated. The quantum bit of the first series is the quantum bit ρ0 to be calculated. The quantum bit ρ0 is represented by a combination of H quantum bits (H=a natural number greater than or equal to 1). The quantum bit of the second series is an auxiliary quantum bit |0>. The quantum bit |0> is represented by a combination of I quantum bits (I=a natural number greater than or equal to 1). The quantum state is defined by the combination of quantum bits.

[0021] Each cell 25 performs quantum computation on input data 31 according to a predetermined task and outputs output data 33. Specifically, each cell 25 has an encoder block *, which is a combination of quantum gates that perform encoding, and a control block Uop, which is a combination of quantum gates that perform quantum operations controlled by fixed parameters. The encoder block * generates an encoded quantum state by encoding the input data 31, which is digital data processed by a classical computer, onto an auxiliary quantum bit |0>. The control block Uop performs a series of quantum operations on the quantum bit ρ0 to be computed and the encoded quantum state according to a combination of quantum gates assigned fixed parameters, thereby converting the quantum bit ρ0 to be computed into an output quantum state. The output quantum state is passed on to the subsequent cell 25. The encoded quantum state is initialized (reset) to the quantum bit |0> after the control block Uop. After the final cell 25, the output quantum state is measured by a measuring device 27. The measured output quantum state is converted into output data 33, which is digital data to be processed by a classical computer.

[0022] The classical computer receives output data 33 from the quantum computer. The classical computer inputs the received output data to the linear layer 23. Trained or to-be-trained network parameters are assigned to the linear layer 23. The network configuration of the linear layer 23 is not particularly limited, and may be a feedforward neural network, a recurrent neural network, or any other network configuration. The linear layer 23 performs a series of processes on the output data 33 according to the network configuration and network parameters, and outputs predicted data 35. The predicted data 35 is the final output of the quantum reservoir model 20 and can be used for various purposes.

[0023] As shown in FIG. 1 , the processor 1 functions as an acquisition unit 11, a determination unit 12, and a display control unit 13. The acquisition unit 11 acquires an asymptotic density matrix representing a quantum state obtained by repeatedly executing a quantum circuit to be evaluated a predetermined number of times. The term "density matrix" refers to a matrix representing a quantum state. The term "asymptotic density matrix" refers to a density matrix representing a quantum state obtained by repeatedly executing a quantum circuit a predetermined number of times. The "predetermined number of times" refers to the number of executions of the quantum circuit to be evaluated that is expected to result in the quantum state reaching the maximally mixed state, assuming that the quantum circuit to be evaluated converges the quantum state to the maximally mixed state. The predetermined number of times is set to an infinite number, for example, but may be set to any number, such as 1000, as long as it is sufficiently large. There are various methods for acquiring the asymptotic density matrix. For example, the acquisition unit 11 calculates the asymptotic density matrix based on a transition matrix representing the quantum circuit to be evaluated.

[0024] The determination unit 12 determines the performance of the quantum circuit to be determined based on the similarity between the asymptotic density matrix and the maximally mixed state acquired by the acquisition unit 11. When the similarity is greater than a threshold, the determination unit 12 determines that the quantum circuit to be determined does not function as a reservoir part in a quantum reservoir model because the asymptotic density matrix is ​​close to the maximally mixed state, and thus is a quantum circuit with poor performance. On the other hand, when the similarity is smaller than the threshold, the determination unit 12 determines that the quantum circuit to be determined may function as a reservoir part in a quantum reservoir model because the asymptotic density matrix is ​​far from the maximally mixed state, and thus is a quantum circuit with good performance.

[0025] The display control unit 13 displays on the display device 4 the judgment result of the performance of the quantum circuit to be judged, obtained by the judgment unit 12.

[0026] The performance determination process of a quantum circuit performed by the information processing device 100 will be described below.

[0027] 3 is a diagram showing an example of an operational flowchart of the information processing device 100 in the performance evaluation process. As shown in Fig. 3, first, the acquisition unit 11 acquires a transition matrix that represents the quantum circuit to be evaluated (step S1). The transition matrix is ​​acquired as digital data.

[0028] Generally, the transition ε(ρ) of the density matrix ρ due to the quantum circuit ε containing noise is transformed as shown in the following equation (1) by the operator sum representation of the quantum circuit. i is a matrix that represents the quantum circuit ε. E † denotes the Hermitian conjugate of E, which is a unitary matrix.

[0029]

number

[0030] In this case, the transition of vector x consisting of elements of density matrix ρ to vector x' is given in a linear form, and can be expressed by a transition matrix A as in the following equation (2).

[0031]

number

[0032] An example of the procedure for acquiring the transition matrix A will be described. First, the acquisition unit 11 expresses all quantum gates included in the quantum circuit to be determined by a matrix E, and expresses the quantum circuit in the form of equation (1). Next, the acquisition unit 11 calculates the right-hand side of equation (1) to find the coefficients of each element of the density matrix ρ. Finally, the acquisition unit 11 converts the density matrix ρ into a vector x, and calculates the transition matrix A by expressing each coefficient found to correspond to the elements of the vector x in matrix form.

[0033] After step S1 is performed, the acquisition unit 11 calculates an asymptotic density matrix based on the transition matrix acquired in step S1 (step S2). The asymptotic density matrix is ​​acquired as digital data. In step S2, the acquisition unit 11 calculates the asymptotic density matrix after repeatedly applying the transition matrix to the density matrix a predetermined number of times. Two methods for calculating the density matrix will be described below.

[0034] In the first calculation method, the acquisition unit 11 calculates an asymptotic density matrix based on an eigenvector corresponding to the largest eigenvalue of the transition matrix. More specifically, the acquisition unit 11 performs eigenvalue decomposition on the transition matrix to calculate an eigenvector corresponding to the eigenvalue with the largest absolute value among the multiple eigenvalues. The acquisition unit 11 then calculates the asymptotic density matrix by normalizing the calculated eigenvector so that the sum of the diagonal components of the corresponding density matrix becomes 1. This will be specifically described below.

[0035] Following equation (2), the density matrix vector x after applying the transition matrix A repeatedly n times is n can be expressed as the following equation (3) using the initial value x0 of the density matrix and the transition matrix A. Note that Λ is the eigenvalue of A, and P is the eigenvector of A. The number of executions n is the predetermined number of times, and is set to an infinite number of times, for example.

[0036]

number

[0037] Under the condition that the eigenvalue with the maximum absolute value of the transition matrix A is single, the maximum eigenvalue with the maximum absolute value is 1. If the corresponding eigenvector is p, when the number of executions n of the quantum circuit is sufficiently large, the vector x n can be expressed by the following equation (4): s=p † x0.

[0038]

number

[0039] Vector x n The density matrix ρ corresponding to n and the density matrix ρ corresponding to the vector sp sp And, Tr(ρ n )=Tr(ρ sp )=1 holds. s is a normalized value such that the trace of the eigenvector of the maximum eigenvalue is 1. When the number of executions n is sufficiently large, the acquisition unit 11 calculates an asymptotic density matrix by rearranging the elements of the vector sp into matrix elements. By calculating the density matrix including eigenvalues ​​whose absolute values ​​are not 1, it is also possible to obtain a density matrix for a finite number of iterations. When there are multiple eigenvalues ​​whose absolute values ​​of the transition matrix A are maximum, the asymptotic density matrix can be calculated in a similar manner by calculating the eigenvectors corresponding to all of the maximum eigenvalues.

[0040] The second calculation method will be described. In the second calculation method, the acquisition unit 11 utilizes the fact that the diagonal sum of a density matrix is ​​identically 1 to calculate a first vector corresponding to a density matrix in which the number of components is reduced by one compared to the density matrix representing the quantum state in the quantum circuit to be determined, calculates a matrix corresponding to the transition of the first vector and a second vector of translation, and calculates an asymptotic density matrix based on the eigenvector corresponding to the maximum eigenvalue of the matrix corresponding to the transition of the first vector and the second vector. The first calculation method and the second calculation method can be selected arbitrarily.

[0041] After step S2 is performed, the determination unit 12 calculates the similarity between the asymptotic density matrix calculated in step S2 and the maximal mixed state (step S3). The maximal mixed state is determined according to the number of qubits implemented in the quantum circuit to be determined. The maximal mixed state is a quantum state represented by a density matrix proportional to the identity matrix, and all quantum states are measured with equal probability regardless of the basis. If the asymptotic density matrix is ​​in the maximal mixed state, it means that the quantum circuit to be determined does not function as a reservoir part included in the quantum reservoir model. Therefore, if the asymptotic density matrix and the maximal mixed state are sufficiently close to each other, it can be determined that the quantum circuit to be determined has poor performance.

[0042] In step S3, the determination unit 12 first determines a matrix representing a maximum mixed state based on the number of quantum bits implemented in the quantum circuit to be determined. The maximum mixed state is represented by digital data. Next, the determination unit 12 calculates the similarity between the asymptotic density matrix and the maximum mixed state. Various indices can be used as the similarity. As one example, the determination unit 12 calculates the similarity using the difference between the area under the Lorenz curve drawn by the diagonal elements or eigenvalues ​​of the asymptotic density matrix and the area under the Lorenz curve corresponding to the maximum mixed state. As another example, the determination unit 12 may calculate the similarity using the difference between the von Neumann entropy of the asymptotic density matrix and the von Neumann entropy of the maximum mixed state. As another example, the determination unit 12 may calculate the similarity using the Frobenius norm of the difference matrix between the asymptotic density matrix and the maximum mixed state. As another example, the determination unit 12 may calculate the similarity using a Hilbert-Schmidt inner product based on the asymptotic density matrix and the maximum mixture state. As another example, the determination unit 12 may calculate the similarity using a weighted correlation coefficient that maximizes the correlation coefficient between the asymptotic density matrix and the maximum mixture state using canonical correlation analysis.

[0043] After step S3 is performed, the determination unit 12 determines whether the similarity calculated in step S3 is greater than a threshold (step S4). Below, a specific example of the determination process will be described in which the difference between the area under the Lorenz curve drawn by the diagonal components or eigenvalues ​​of the asymptotic density matrix and the area under the Lorenz curve corresponding to the maximal mixing state is used as the similarity.

[0044] First, the determination unit 12 uses the diagonal elements or eigenvalues ​​of the asymptotic density matrix to draw a Lorenz curve of the probability of obtaining each quantum state in the image space. Then, the determination unit 12 calculates the similarity using the difference between the area under the Lorenz curve and the area under the Lorenz curve in the maximally mixed state. The difference itself may be used as the similarity, or a value obtained by further performing an arbitrary operation on the difference may be used as the similarity.

[0045] In addition to using the area under the Lorenz curve, the similarity can be calculated using the above-mentioned methods such as the difference of von Neumann entropy, the Frobenius norm, the Hilbert-Schmidt inner product, canonical correlation analysis, etc. The determination unit 12 may determine whether the similarity calculated by these methods is an asymptotic density matrix close to the maximum mixture state by setting an appropriate threshold.

[0046] If it is determined in step S4 that the similarity is greater than the threshold (step S4: YES), the determination unit 12 determines that the quantum circuit to be determined does not function as a reservoir part in the quantum reservoir model and is a quantum circuit with poor performance because the asymptotic density matrix is ​​close to the maximally mixed state (step S5).If it is determined in step S4 that the similarity is not greater than the threshold (step S4: NO), the determination unit 12 determines that the quantum circuit to be determined has the potential to function as a reservoir part in the quantum reservoir model and is a quantum circuit with good performance because the asymptotic density matrix is ​​far from the maximally mixed state (step S6).

[0047] When step S5 or S6 is performed, the display control unit 13 displays the determination result of step S5 or S6 on the display device 4 (step S7).

[0048] FIG. 4 is a diagram showing an example of a display screen I1 of the judgment result. As an example, the judgment result in FIG. 4 is assumed to be the judgment result of step S5. As shown in FIG. 4, the display screen I1 displays a circuit diagram I11 of the quantum circuit to be judged and a message I12 of the judgment result. As the message I12, it is preferable to display a character string such as "Possibility of quantum circuit having poor performance." By displaying the circuit diagram I11 and the message I12, the user can know the judgment result of the quantum circuit corresponding to the circuit diagram I11. Note that if the display of the circuit diagram I11 is unnecessary, the display of the circuit diagram I11 can be omitted.

[0049] When step S7 is performed, the performance determination process shown in FIG. 3 ends.

[0050] As mentioned above, the indices used to evaluate the quantum reservoir model are the normalized mean square error (NRMSE) defined by the following formula and memory capacity C. As shown in the formula below, in order to calculate these indices, it is necessary to explicitly specify the training dataset and train the linear layer.

[0051]

number

[0052] According to this embodiment, once the asymptotic density matrix and the maximal mixing state are obtained, it becomes possible to determine the performance of the quantum circuit to be evaluated. As described above, the asymptotic density matrix can be calculated from the transition matrix, and the transition matrix can be calculated using a classical computer if the quantum gates included in the quantum circuit to be evaluated are known. In other words, since the asymptotic density matrix can be obtained without actually executing the quantum circuit, it is possible to complete the performance evaluation process using only a classical computer. This makes it possible to reduce various burdens associated with the use of a quantum computer. Accordingly, it becomes possible to widely utilize the performance evaluation process according to this embodiment as a basis for determining the selection and combination of quantum gates. Furthermore, according to the method according to this embodiment, since it is only necessary to use the asymptotic density matrix and the maximal mixing state, evaluation is possible without being limited by training data sets or learning methods.

[0053] Next, a specific example of this embodiment will be described. As a specific example, the performance of a two-qubit quantum circuit will be determined.

[0054] FIG. 5 is a diagram showing the circuit configuration of the quantum circuit according to Specific Example 1. As shown in FIG. 5, in the quantum circuit according to Specific Example 1, Ry encoding based on input data is applied to the first qubit, the parameterized quantum circuit U is applied, and a reset operation of the first qubit is performed. The rotation angles θ0 and θ1 of the Ry gates of the parameterized quantum circuit U are set randomly. The parameterized quantum circuit U applies a CNOT gate having the first qubit as a control qubit to the second qubit, applies Ry(θ0) to the first qubit, and applies an Ry(θ1) gate to the second qubit.

[0055] When the input data is u (−1 < u < 1), the Ry encoding is represented by the following equation (5).

[0056]

Equation

[0057] When the quantum circuit according to Specific Example 1 is represented as a matrix in the same manner as in equation (1), it can be represented as the following equation (6). Here, U is the matrix representation of the quantum gates excluding the reset operation in FIG. 5. P0, P1, and X are matrices related to the reset operation, P0 is the projection onto the state where qubit 0 becomes 0, P1 is the projection onto the state where qubit 0 becomes 1, and X is the X gate for qubit 0.

[0058]

Equation

[0059] Since U0 and U1 are matrices having values only in the first and third rows, the density matrix ρ before applying the quantum circuit and the density matrix ε(ρ) after applying it can be represented by the following equation (7). Each element x0, x1, and x2 of ε(ρ) can be represented by the following equations (8), (9), and (10), respectively.

[0060]

Equation

[0061] Here, let x=[x0,x1,x2] be the vector consisting of the components of ρ. T Then, the transition matrix A corresponding to the action of the quantum circuit can be expressed as follows (11).

[0062]

number

[0063] FIG. 6 is a diagram showing the circuit configuration of a quantum circuit according to specific example 2. As shown in FIG. 6, in the quantum circuit according to specific example 2, Ry encoding based on input data is applied to the first quantum bit, and a parameterized quantum circuit V is applied to perform a reset operation on the first quantum bit. The rotation angles θ0 and θ1 of the Ry gate of the parameterized quantum circuit V are set randomly. The parameterized quantum circuit V applies a CNOT gate with the first quantum bit as the control quantum bit to the second quantum bit, applies Ry(θ0) to the first quantum bit, applies an Ry(θ1) gate to the second quantum bit, and applies a CNOT gate with the first quantum bit as the control quantum bit to the second quantum bit. When the transition matrix A is calculated in the same way for the quantum circuit according to specific example 2 of FIG. 6, it can be expressed by the following equation (12).

[0064]

number

[0065] Next, the asymptotic density matrix after executing the quantum circuit a predetermined number of times is obtained using the transition matrices for the two-qubit quantum circuit in equations (11) and (12). Here, since analysis with a reduced matrix size is possible, the second density matrix calculation method is used to obtain the asymptotic density matrix. First, for the transition matrix in equation (11), by subtracting both sides of equation (8) by equation (10), the following equation (13) is obtained.

[0066]

number

[0067] Next, by using equations (2), (9), and (13), the following equation (14) is obtained: x ~ represents the first vector corresponding to the density matrix with one fewer component.

[0068]

number

[0069] By performing the same calculation on the transition matrix of equation (12), equation (15) can be obtained. ~ corresponds to the second vector of translation. In equation (14), the second vector of translation b ~ is zero.

[0070]

number

[0071] transition matrix A ~ Under the condition that the absolute value of the eigenvalue of is less than 1, after executing the quantum circuit enough times, ~ →(IA ~ ) -1 b ~ Therefore, (IA ~ ) -1 b ~ can be obtained as an asymptotic density matrix. b ~ = 0 corresponds to the maximally mixed state.

[0072] Finally, the asymptotic density matrices obtained from equations (14) and (15) are used to calculate the similarity with the maximum mixed state, and the performance of the quantum circuit is judged. In this specific example, the reciprocal of the Frobenius norm is used as the similarity between the asymptotic density matrix and the maximum mixed state.

[0073] FIG. 7 is a distribution diagram of similarities according to Specific Example 1. The left diagram of FIG. 7 is a distribution diagram of similarities before threshold processing, and the right diagram of FIG. 7 is a distribution diagram of similarities after threshold processing. FIG. 8 is a distribution diagram of similarities according to Specific Example 2. The left diagram of FIG. 8 is a distribution diagram of similarities before threshold processing, and the right diagram of FIG. 8 is a distribution diagram of similarities after threshold processing. The horizontal axis of each distribution diagram represents the serial number (seed value) of the combination of random values ​​set for the parameters θ0 and θ1 of the quantum circuit U or V, and there are 100 combinations. The vertical axis represents the input value θ to the quantum circuit shown in FIGS. 5 and 6, which is varied between -1 and +1 in increments of 0.02. The similarity was calculated for each combination of the seed value and input value θ. Each point on the distribution diagram is assigned a similarity or a gray value corresponding to the similarity. In this case, ±1 is removed because it is a singular point.

[0074] In the distribution diagrams after threshold processing in Figures 7 and 8, the threshold for similarity is 10 10 For each combination of the above seed value and input value θ, a value of 1 was assigned if the similarity was greater than the threshold, and a value of 0 if the similarity was less than the threshold. If the similarity was greater than the threshold, the quantum circuit being evaluated was close to the maximum mixed state, and therefore did not function as a reservoir part in the quantum reservoir model, and was determined to be a quantum circuit with poor performance. If the similarity was less than the threshold, the quantum circuit being evaluated was not close to the maximum mixed state, and therefore had the potential to function as a reservoir part in the quantum reservoir model, and was determined to be a quantum circuit with good performance.

[0075] From the right diagram of Figure 7, we can see that the similarity of quantum circuit U is greater than the threshold in all cases, and that quantum circuit U in Figure 5 does not function as a reservoir part in the quantum reservoir model, and can be determined to be a quantum circuit with poor performance. On the other hand, from the right diagram of Figure 8, we can see that the similarity of quantum circuit V is less than the threshold in all cases, and that quantum circuit V in Figure 6 has the potential to function as a reservoir part in the quantum reservoir model, and can be determined to be a quantum circuit with good performance.

[0076] Depending on the quantum circuit to be judged, the magnitude relationship of some seed values ​​with respect to the threshold value of similarity may differ from that of other seed values. In this case, for example, it means that the parameters θ0 and θ1 corresponding to the seed values ​​to which similarity smaller than the threshold is assigned are judged to be quantum circuits with good performance, and the parameters θ0 and θ1 corresponding to the seed values ​​to which similarity larger than the threshold is assigned are judged to be quantum circuits with poor performance.

[0077] The display control unit 13 may display the distribution diagrams shown in Figures 7 and 8 on the display device 4. This allows the display control unit 13 to provide the user with the basis for the determination result.

[0078] Although an example of processing by the information processing device 100 according to this embodiment has been described above, this embodiment is not limited to this, and various elements can be deleted, added, and / or changed.

[0079] (Variation 1) In the above embodiment, the acquisition unit 11 calculates the asymptotic density matrix based on the transition matrix (S2). The acquisition unit 11 according to the first modification may acquire a prepared asymptotic density matrix. It is assumed that the asymptotic density matrix is ​​determined empirically or arbitrarily. According to the first modification, it is possible to omit the step of calculating the asymptotic density matrix based on the transition matrix, thereby improving the processing speed of the performance evaluation process and reducing memory usage.

[0080] (Variation 2) In the above embodiment, the acquiring unit 11 calculates the asymptotic density matrix based on the transition matrix (S2). The acquiring unit 11 according to Modification 2 may directly execute the quantum circuit to be determined and acquire the asymptotic density matrix by quantum state tomography. In this case, the quantum circuit to be determined is implemented on a quantum computer. The acquiring unit 11 repeatedly executes the quantum circuit to be determined a predetermined number of times and acquires output data from the quantum circuit to be determined. The predetermined number of times according to Modification 2 is set to a sufficient number of times, such as 1000 or more times. The acquiring unit 11 can calculate the asymptotic density matrix by performing quantum state tomography on the output data.

[0081] According to the second modification, it is possible to omit the step of calculating the asymptotic density matrix based on the transition matrix, thereby improving the processing speed of the performance evaluation process and reducing memory usage. Furthermore, according to the second modification, the asymptotic density matrix can be obtained based on output data obtained by actually executing the quantum circuit to be evaluated, which is expected to enable performance evaluation of quantum circuits with a number of qubits that cannot be handled by classical computers. Note that, in the second modification, there is also no need to train the quantum circuit to be evaluated, so similar to the present embodiment, when constructing a quantum circuit to be used in a quantum reservoir model, evaluation is possible without being bound by training data sets or learning methods.

[0082] (Variation 3) In the above embodiment, the acquiring unit 11 acquires the transition matrix by expressing the quantum circuit to be judged as a matrix (S1). The acquiring unit 11 according to the third modification may acquire a transition matrix prepared in advance. It is assumed that the transition matrix is ​​determined empirically or arbitrarily. According to the third modification, it is possible to omit the step of expressing the quantum circuit to be judged as a matrix, thereby improving the processing speed of the transition matrix acquisition process and reducing memory usage.

[0083] (Variation 4) In the above-described embodiment, the acquiring unit 11 acquires the transition matrix by expressing the quantum circuit to be evaluated as a matrix (S1). The acquiring unit 11 according to the fourth modification may acquire the transition matrix of a black-box quantum process by quantum process tomography. According to the fourth modification, the transition matrix can be obtained based on output data obtained by actually executing the quantum circuit, which is expected to enable performance evaluation of a quantum circuit with a number of qubits that cannot be handled by a classical computer.

[0084] Although several embodiments of the present invention have been described, these embodiments are presented as examples and are not intended to limit the scope of the invention. These novel embodiments can be embodied in various other forms, and various omissions, substitutions, and modifications can be made without departing from the spirit of the invention. These embodiments and their modifications are included within the scope and spirit of the invention, and are also included in the scope of the invention and its equivalents as defined in the claims. [Explanation of symbols]

[0085] 1...processor, 2...storage device, 3...input device, 4...display device, 5...communication device, 11...acquisition unit, 12...determination unit, 13...display control unit, 100...information processing device.

Claims

1. an acquisition unit that acquires an asymptotic density matrix that represents a quantum state obtained by repeatedly executing the quantum circuit to be determined a predetermined number of times; a determination unit that determines the performance of the quantum circuit based on the similarity between the asymptotic density matrix and a maximal mixed state; An information processing device comprising:

2. The acquisition unit obtaining a transition matrix representing the quantum circuit; calculating the asymptotic density matrix representing the quantum state after iteratively applying the transition matrix the predetermined number of times; 2. The information processing device according to claim 1.

3. The information processing apparatus according to claim 2 , wherein the acquisition unit calculates the asymptotic density matrix based on an eigenvector corresponding to a maximum eigenvalue of the transition matrix.

4. The acquisition unit calculating a first vector corresponding to a density matrix in which the number of components is reduced by one compared to a density matrix representing a quantum state in the quantum circuit; calculating a matrix and a translation second vector corresponding to the shift of the first vector; calculating the asymptotic density matrix based on the second vector and an eigenvector corresponding to a maximum eigenvalue of a matrix corresponding to a transition of the first vector; 3. The information processing device according to claim 2.

5. The information processing device according to claim 1 , wherein the acquisition unit acquires the asymptotic density matrix representing the quantum state output from the quantum circuit by actually executing the quantum circuit the predetermined number of times.

6. 2. The information processing device according to claim 1, wherein the determination unit calculates the similarity using a difference between an area under a Lorenz curve drawn by diagonal components or eigenvalues ​​of the asymptotic density matrix and an area under a Lorenz curve corresponding to the maximum mixing state.

7. The information processing apparatus according to claim 1 , wherein the determination unit calculates the similarity using a difference between the von Neumann entropy of the asymptotic density matrix and the von Neumann entropy of the maximally mixed state.

8. The information processing apparatus according to claim 1 , wherein the determining unit calculates the similarity using a Frobenius norm of a difference matrix between the asymptotic density matrix and the maximum mixture state.

9. The information processing apparatus according to claim 1 , wherein the determining unit calculates the similarity using a Hilbert-Schmidt inner product based on the asymptotic density matrix and the maximal mixture state.

10. The information processing apparatus according to claim 1 , wherein the determining unit calculates the similarity using a weighted correlation coefficient that maximizes a correlation coefficient between the asymptotic density matrix and the maximum mixture state by using canonical correlation analysis.

11. 2. The information processing device according to claim 1, wherein the determination unit determines that the performance of the quantum circuit is poor when the similarity is greater than a threshold value because the asymptotic density matrix is ​​close to the maximum mixed state, and determines that the performance of the quantum circuit is good when the similarity is smaller than the threshold value because the asymptotic density matrix is ​​far from the maximum mixed state.

12. The information processing apparatus according to claim 1 , further comprising a display control unit that displays the performance determination result on a display device.

13. The processor: obtaining an asymptotic density matrix representing a quantum state obtained by repeatedly executing the quantum circuit to be determined a predetermined number of times; determining the performance of the quantum circuit based on the similarity between the asymptotic density matrix and a maximal mixed state; An information processing method comprising:

14. The processor a function of acquiring an asymptotic density matrix representing a quantum state obtained by repeatedly executing the quantum circuit to be judged a predetermined number of times; a function of determining the performance of the quantum circuit based on the similarity between the asymptotic density matrix and a maximal mixed state; An information processing program that makes this possible.

Images