Control device, control method, and program

Abstract

A control device comprising: a coefficient calculation unit which calculates a coefficient on the basis of information relating to the calculation of the gradient of an objective function; a measurement planning unit which generates, on the basis of the calculated coefficient, a sequence illustrating quantum operations at given points in time for certain qubits of a quantum circuit provided in a quantum computer, and which transmits information indicating the generated sequence to the quantum computer; and a measurement aggregation unit which receives, from the quantum computer, information indicating expected values that represent an assessment result, and which calculates the gradient by means of an aggregation based on the expected values.

Description

[Technical Field]

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

[0002] Quantum computers are a technology that performs calculations by utilizing the principle of superposition in quantum mechanics, and are expected to be able to quickly solve problems such as prime factorization and quantum chemistry calculations, so their development is being actively pursued around the world. The qubits used by quantum computers not only suffer from errors in which 0 and 1 are swapped, as occurs in classical computers, but also from unique errors in which the ratio of the "superposition" of 0 and 1 is shifted. Therefore, methods are being researched to suppress the errors (quantum errors) that occur in quantum computers.

[0003] There is a trade-off between the ease of control and the magnitude of errors in quantum bits. This is because, while a strong interaction with the outside world is necessary to enable high-speed control, a strong interaction with the outside world can also cause large errors through that interaction. Variational quantum computation is one of the quantum algorithms that has been proposed to perform practical calculations using quantum bits with large errors (e.g., Non-Patent Document 1, Non-Patent Document 2).

[0004] One of the operations known to be physically easy to construct on a quantum computer is the Pauli rotation gate, and conventional gradient calculation methods assume that the operation typically performed is the Pauli rotation gate.

[0005] Independently of the context of typical variational quantum computation using Pauli rotation gates, research has been conducted into how arbitrary unitary operations can be approximated using only operations that are physically easy to implement. The operation that is considered to be the easiest to physically realize is the operation in which a physical system evolves in free time without any control. For example, Non-Patent Documents 3 and 4 disclose variational methods that are physically easy to implement. Parameterized circuits constructed using this method are called variational circuits with free time evolution, and are distinguished from the variational circuits using Pauli rotation gates mentioned above. [Prior art documents] [Non-patent literature]

[0006] [Non-Patent Document 1] Peruzzo, A., McClean, J., Shadbolt, P., Yung, MH, Zhou, XQ, Love, PJ, ... & O'brien, JL (2014). A variational eigenvalue solver on a photonic quantum processor. Nature communications, 5(1), 1-7. [Non-patent document 2] Mitarai, K., Negoro, M., Kitagawa, M., & Fujii, K. (2018). Quantum circuit learning. Physical Review A, 98(3), 032309. [Non-patent document 3] Lloyd, S., Landahl, AJ, & Slotine, JJE (2004). Universal quantum interfaces. Physical Review A, 69(1), 012305. [Non-patent document 4] Burgarth, D., Maruyama, K., Murphy, M., Montangero, S., Calarco, T., Nori, F., & Plenio, MB (2010). Scalable quantum computation via local control of only two qubits. Physical Review A, 81(4), 040303. Summary of the Invention [Problem to be solved by the invention]

[0007] Although free-time variational circuits have the advantage of being easy to implement, they have the problem that parameter optimization cannot be performed efficiently. For example, mainstream parameter optimization methods, such as parameter gradient methods, assume that the parameters are used as Pauli rotation gates in the circuit, and therefore cannot be applied to free-time variational circuits.

[0008] The disclosed technology aims to efficiently perform variational quantum computation using a variational circuit with free time evolution. [Means for solving the problem]

[0009] The disclosed technology is a control device that includes a coefficient calculation unit that calculates coefficients based on information related to the calculation of the gradient of an objective function, a measurement design unit that generates a sequence indicating quantum operations at each time for some quantum bits of a quantum circuit provided in a quantum computer based on the calculated coefficients and transmits information indicating the generated sequence to the quantum computer, and a measurement aggregation unit that receives information indicating an expected value indicating an evaluation result from the quantum computer and calculates the gradient by aggregation based on the expected value. [Effects of the Invention]

[0010] According to the disclosed technology, variational quantum computation can be efficiently performed using a variational circuit with free time evolution. [Brief explanation of the drawings]

[0011] [Figure 1] FIG. 1 is a diagram illustrating an example of a system configuration of a quantum measurement system. [Figure 2] FIG. 2 is a diagram illustrating an example of the functional configuration of each device included in the quantum measurement system. [Figure 3] 10 is a flowchart illustrating an example of the flow of a gradient calculation process. [Figure 4] FIG. 1 is a first diagram for explaining the operation of a quantum bit. [Figure 5] FIG. 10 is a second diagram for explaining the operation of quantum bits. [Figure 6] FIG. 10 is a third diagram for explaining the operation of quantum bits. [Figure 7] FIG. 2 illustrates an example of a hardware configuration of a computer. DETAILED DESCRIPTION OF THE INVENTION

[0012] Hereinafter, an embodiment of the present invention (the present embodiment) will be described with reference to the drawings. The embodiment described below is merely an example, and the embodiment to which the present invention is applied is not limited to the following embodiment.

[0013] (Previous problems) First, let's explain the problems with conventional technology. Quantum computers are a technology that performs calculations by utilizing the principle of superposition in quantum mechanics. They are expected to be able to quickly solve problems such as prime factorization and quantum chemistry calculations, and their development is being actively pursued around the world. A (classical) bit, which is an element that makes up a classical computer, takes on a value of 0 or 1. On the other hand, a qubit, which is an element that makes up a quantum computer, can take on a continuous superposition state of 0 and 1 in addition to 0 and 1. Using this superposition state, it is possible to simultaneously perform calculations where the bit value is 0 and 1, but when the qubit is observed, its value is fixed at 0 or 1, and the superposition state is destroyed.

[0014] There is a trade-off between the ease of control and the magnitude of errors in quantum bits, because while a strong interaction with the outside world is necessary to enable high-speed control, a strong interaction with the outside world can also be a factor in generating large errors through that interaction. Variational quantum computation is one of the quantum algorithms that have been proposed to perform practical calculations using quantum bits with large errors (for example, Non-Patent Document 1, Non-Patent Document 2). A typical variational quantum computation is performed as follows.

[0015] It is defined as a 2x2 complex matrix as follows:

[0016]

number

[0017] The Pauli matrix is ​​made up of four matrices, each of which is a tensor product of the identity matrix I. n 4 of a Kind n ×4 n A set of complex matrices

[0018]

number

[0019] The state of a quantum computer consisting of n noiseless qubits is called a state vector. n It is defined as a complex vector whose L2 norm of the dimension is 1. In the process of quantum computing, operations and measurements can be performed that change a state vector into another state vector within the physically permitted range.

[0020] The operation to the noiseless quantum state in a quantum computer is the state vector

[0021]

number

[0022]

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[0023] On the other hand, the number of operations that are technically possible in a short time on a quantum computer is limited. Therefore, to realize a desired unitary matrix operation U, U must be constructed from a combination of given technically possible operations.

[0024] One of the operations known to be physically easy to construct on a quantum computer is the Pauli rotation gate. This gate is characterized by an element P of the Pauli matrix of n qubits and a real number θ between 0 and 2π, called the rotation angle. The Pauli rotation gate is n This is an operation that changes the state vector shown in equation (1) of dimension into the form shown in equation (2). Here, U is a unitary matrix defined as U=exp(-iθP / 2), which is a matrix that preserves the norm of the vector.

[0025] In variational quantum circuits, a quantum circuit called a trial function is specified by a sequence of Pauli rotation gates. For example, if m is a positive integer, then ((P1,θ1),(P2,θ2),...(P m ,θ m )) is a circuit characterized by converting the quantum state shown in equation (1) into

[0026]

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[0027] By choosing a sufficiently large m and a variety of Pauli matrices, we can obtain a series of suitable rotation angles (θ1 θ m ) can be chosen to approximate any U.

[0028] Another operation that can be performed on a quantum computer is the evaluation of observables. n ×2 n The Hermitian complex matrix O of the quantum state shown in equation (1) is called the expectation value of the observable by sampling.

[0029]

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[0033] The typical objective of variational quantum computation can be formulated as follows: Given the initial quantum state shown in equation (1), a list of Pauli matrices (P1 P m ) and an observable O. In this case, the goal of variational quantum computation is to obtain the quantum state after applying all the Pauli rotation matrices

[0034]

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[0035]

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[0037] The function that represents this evaluation value is called the objective function. j =exp(-iθ j P j / 2). In many applications, by appropriately setting the observable O, it is possible to obtain the energy of the lowest energy state of a molecule as a result of optimization, or to minimize the error rate of classification in machine learning.

[0038] A typical way to perform optimization in variational quantum circuits is to evaluate the observable

[0039]

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[0040]

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[0042] Here, λ is a positive real number called the learning rate, and the evaluation value is

[0043]

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[0044] Therefore, to perform optimization, we use the following formula for an integer k between 1 and m:

[0045]

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[0046] A typical method for obtaining the gradient is the parameter shift method described in Non-Patent Document 2. In this method, the value of the gradient is

[0047]

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[0048]

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[0050] There are various other methods for calculating the gradient, but conventional gradient calculation methods assume that the operation typically performed is a Pauli rotation gate.

[0051] Independently of the context of typical variational quantum computation using Pauli rotation gates, research has been conducted into how arbitrary unitary operations can be approximated using only operations that are physically easy to implement. For example, to realize a Pauli rotation gate with arbitrary Pauli matrices and rotation angles, it is necessary to calibrate and irradiate the quantum bits with complex light or electromagnetic pulses in advance, but this is an expensive experimental technique. In addition, installing numerous control systems introduces noise, which degrades the accuracy of quantum computation. Therefore, if arbitrary unitary operations can be approximated using only operations that are easier to implement, the potential for quantum computing would be enhanced.

[0052] The operation that is thought to be the easiest to physically realize is the operation of "allowing a physical system to evolve in free time without any control." This operation is easy to implement because it is literally a dynamics that occurs without any control. The operation of waiting t seconds without any control on the physical system that comprises quantum bits can be written as follows. Note that a physical system consisting of n quantum bits has a corresponding Hamiltonian called 2 n ×2 n The Hermitian matrix H is defined as follows:

[0053] When a quantum system in the state shown in equation (1) is not controlled for t seconds, its quantum state changes from the state shown in equation (1) to

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[0055]

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[0057] When a fixed H is given, it is generally not possible to create an arbitrary unitary matrix simply by changing the waiting time t without control. On the other hand, when the Hamiltonian H satisfies certain conditions, it is possible to create an arbitrary Hamiltonian simply by periodically controlling the unitary operation V on only a portion of the n quantum bits. The following are known to be necessary and sufficient conditions for this.

[0058] When physical qubits are arranged in space, typical qubit interactions can be considered to occur only with those that are spatially close. The graph obtained by connecting qubits as vertices and connecting edges between interacting qubits is called the qubit coupling graph. For example, when qubits are arranged horizontally in one dimension, the coupling graph becomes a unidimensional chain, and when they are arranged in a two-dimensional plane, it becomes a graph that can be embedded in a two-dimensional plane. A similar definition is also used for higher-dimensional arrangements. When the coupling graph is connected, it is known that, except for corner cases where the interaction or operation V is special, a partial operation V can be performed on one vertex or two adjacent vertices in the graph (e.g., Non-Patent Document 3 and Non-Patent Document 4).

[0059] Using a Hamiltonian that satisfies the above conditions, the calculation starts from the reference time of 0 seconds and finishes in T seconds. In this case, the time when the control operation V for a part is performed is

[0060]

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[0061]

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[0062] However, by definition, each interval is t1 t m ≥ 0. Except for the different ranges of the parameters defined, such periodic control operations can be thought of as a kind of easily controlled parameterized circuit.

[0063] Therefore, for a sufficiently large positive integer m and appropriate H, V, and O,

[0064]

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[0065] If the optimal parameters (Equation (3)) can be found in a variational circuit with free time evolution, it is possible to perform variational quantum computation, which is easy to implement on a real machine. However, it is difficult to perform this calculation in the same way as a variational circuit with Pauli rotation gates. This is because, in order to efficiently optimize the parameters, it is necessary to calculate the gradient with respect to the objective function using a quantum computer. However, mainstream methods such as parameter gradient methods assume that the parameters are used as Pauli rotation gates in the circuit, and therefore it is difficult to perform a variational circuit with free time evolution, i.e., the exponential form of the Hamiltonian matrix.

[0066]

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[0067] In fact, when trying to apply the theory, it becomes clear that it is necessary to individually control all qubits at each timing of t. To achieve this, all qubits must be controllable, but this would defeat the purpose of using a variational circuit with free time evolution, which is easy to implement. For this reason, although optimization using a variational circuit with free time evolution has the advantage of being easy to implement, it has not been implemented in the past because optimization cannot be performed efficiently.

[0068] (Outline of this embodiment) In this embodiment, in order to address the above-mentioned conventional problems, the gradient value can be calculated by simply controlling some of the quantum bits that were originally controlled in the gradient calculation and the quantum bits around them.

[0069]

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[0070] This enables variational quantum computation of variational circuits with free time evolution to be performed efficiently, making variational quantum computation easy to implement.

[0071] 1 is a diagram showing an example of the system configuration of a quantum measurement system 1. The quantum measurement system 1 includes a control device 10 and a quantum computer 20. The control device 10 and the quantum computer 20 are connected so as to be able to communicate with each other.

[0072] The control device 10 is an example of the classical computer described above, and measures the quantum state of the quantum computer 20 and learns the quantum state by performing calculations based on the measurement results.

[0073] The quantum computer 20 is an example of the quantum computer described above, and is a device that includes quantum bits that are controlled or measured by the control device 10.

[0074] 2 is a diagram showing an example of the functional configuration of each device included in the quantum measurement system. The control device 10 includes a coefficient calculation unit 11, a measurement design unit 12, and a measurement aggregation unit 13. The quantum computer 20 includes an expected value evaluation unit 21.

[0075] The coefficient calculation unit 11 calculates a list of coefficients and Pauli matrices {α P ,P} P∈Pc Here, the information for the gradient calculation is the differential index k, the Hamiltonian H, the observable O, the initial state (Equation (1)), and the parameters at the input time (Equation (3)).

[0076] The measurement design unit 12 generates a list of coefficients and Pauli matrices {α P ,P} P∈Pc The measurement design unit 12 generates a sequence of quantum operations for each P∈Pc based on the above. The measurement design unit 12 transmits information indicating the generated sequence to the quantum computer 20.

[0077] The expected value evaluation unit 21 evaluates the expected value for each PεPc based on the information indicating the transmitted sequence, and transmits information indicating the evaluation result to the quantum computer 20.

[0078] The measurement and aggregation unit 13 aggregates the expected values ​​indicating the evaluation results and calculates the expected value (equation (5)) of the derivative of the k-th time parameter of the objective function.

[0079] Next, a description will be given of the operation of the control device 10. Fig. 3 is a flowchart showing an example of the flow of gradient calculation processing. When information related to gradient calculation is input, the control device 10 starts the gradient calculation processing.

[0080] The coefficient calculation unit 11 calculates the coefficients based on information related to the gradient calculation (step S101). Next, the expected value evaluation unit 21 transmits a sequence of the quantum circuit for calculating the expected value to the quantum computer (step S102). Subsequently, the measurement and compilation unit 13 receives the measurement result of the expected value from the quantum computer (step S103). Then, the measurement and compilation unit 13 calculates the gradient of the objective function based on the measurement result (step S104).

[0081] Here, the operation of a quantum bit will be explained. FIG. 4 is the first diagram for explaining the operation of a quantum bit. As an example of a quantum system, the example in FIG. 4 shows a state in which n quantum bits 901 are arranged in a two-dimensional grid and interact with the nearest quantum bits. Note that FIG. 4 is just one example, and any other variational circuit with free time evolution may be used.

[0082] 5 is a second diagram for explaining the operation of quantum bits. As shown in FIG. 5, an operation V for controlling a part acts on the quantum bits surrounded by a dotted line 902. At times t1, t2, t m If you want to operate only on a part of the area, you can use (t1, t2, t m ) is selected, a desired state can be realized at time T.

[0083] To evaluate equation (4) for the parameters (equation (3)) at a given input time, all that is needed is to irradiate the range indicated by dotted line 902 with electromagnetic waves for each time included in equation (3), perform a predetermined operation V, and evaluate the expected value of the resulting quantum state. Therefore, in this embodiment, a method for finding equation (5) for an integer k between 1 and m is shown.

[0084] Analytical calculations show that the value of equation (5) is equal to:

[0085]

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[0086] Here, the definition of the above formula is as follows: State

[0087]

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[0088]

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[0089]

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[0090]

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[0091] where:

[0092]

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[0093] Va , V b , U P is defined as follows:

[0094] V a =U(TT m )V···VU(t k+1 -t k )

[0095] V b =U(t k -t k-1 )V···VU(t1)

[0096]

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[0097]

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[0098] Here, the range for taking the sum is

[0099]

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[0100] Let C be the set of vertices in the connected graph that the local operation V acts on. V Also, C V and C V Let C be the set of vertices adjacent to the vertex of . Equation (8) is a set of Pauli matrices that act only on the indices of the vertices included in C with {X, Y, Z}, and assign I to the remaining vertices. Therefore, if the vertices included in C are |C|, then the types of the Pauli matrices are at most 4. |C| is.

[0101] 6 is a third diagram for explaining the operation of a quantum bit. The set of vertices surrounded by the dotted line 903 shown in FIG. 6 corresponds to C. The parameter t j If you want to know the derivative of time t j Then, we perform an operation that spans the periphery C of the region.

[0102] The differential equation above is

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[0106] Therefore, it can be said that it can be implemented using quantum computing.

[0107] Based on the above-described operation of quantum bits, the gradient calculation process performed by each functional unit will now be described in detail.

[0108] In step S101 of the gradient calculation process, the coefficient calculation unit 11 performs the above-mentioned A C Decompose the matrix into the form of a sum of Pauli matrices, and α PIn practical situations, the value of |C| is small, so this calculation can be done trivially using properties such as matrix multiplication and the orthogonality of the Pauli matrices.

[0109] In step S102 of the gradient calculation process, the measurement design unit 12 calculates the gradient {α P , P}, the sequence of quantum circuits for calculating the respective expectation values ​​shown in equations (9) and (10), i.e., (V a ,U P ,V b ) and (V a ,U P † ,V b ), and transmits information indicating the constructed sequence to the quantum computer 20.

[0110] Furthermore, following step S102 of the gradient calculation process, the expected value evaluation unit 21 calculates (V a ,U P ,V b ) and (V a ,U P † ,V b ) for each P, and evaluates the expected value. The expected value evaluation unit 21 transmits the expected values ​​shown in equations (9) and (10) to the control device 10.

[0111] In step S104 of the gradient calculation process, the measurement and aggregation unit 13 calculates a weight α corresponding to the obtained expected value. P The value of equation (5) is calculated by summing using

[0112] The control device 10 is realized, for example, by the hardware configuration of a computer 500 shown in Fig. 7. The computer 500 shown in Fig. 7 has an input device 501, a display device 502, an external I / F 503, a communication I / F 504, a processor 505, and a memory device 506. Each of these pieces of hardware is connected to each other via a bus 507 so as to be able to communicate with each other.

[0113] The input device 501 is, for example, a keyboard, a mouse, a touch panel, etc. The display device 502 is, for example, a display, etc. Note that the computer 500 does not necessarily have to have at least one of the input device 501 and the display device 502.

[0114] The external I / F 503 is an interface with an external device such as a recording medium 503a. Examples of the recording medium 503a include a CD (Compact Disc), a DVD (Digital Versatile Disk), an SD memory card (Secure Digital memory card), and a USB (Universal Serial Bus) memory card.

[0115] The communication I / F 504 is an interface for performing data communication with other devices, equipment, systems, etc. The processor 505 is, for example, various types of arithmetic devices such as a CPU, etc. The memory device 506 is, for example, various types of storage devices such as an HDD, SSD, RAM (Random Access Memory), ROM (Read Only Memory), flash memory, etc.

[0116] The control device 10 can realize various processes described below by having the hardware configuration of the computer 500 shown in Fig. 7. Note that the hardware configuration of the computer 500 shown in Fig. 7 is an example, and the computer 500 may have other hardware configurations. For example, the computer 500 may have multiple processors 505 or multiple memory devices 506.

[0117] According to this embodiment, in variational quantum computation using a variational circuit based on free time evolution, the gradient of the objective function can be calculated by quantum computation, which makes it possible to perform variational quantum computation on a quantum computer in which only some of the quantum bits can be controlled.

[0118] Two specific application scenarios are conceivable. The first scenario involves quantum bits formed by trapped atoms or some integrated materials (e.g., nitrogen defects). These quantum bits can switch between a state that is easy to control and a state that has a long lifetime and is easy to evolve in free time but is difficult to control, making this embodiment a natural application. The second scenario involves systems that perform partial error correction. While quantum error correction can reduce the error rate for quantum bits with large errors, quantum error correction requires a large overhead, making it difficult to scale up to large scale in early quantum computing. In this case, too, this embodiment can be applied by not correcting errors in the majority of the computer, i.e., by treating the majority of the computer as a code with a code distance of 1 and allowing it to evolve in free time, and controlling only a portion in an error-tolerant manner. In this way, variational quantum computation with small errors can be performed by controlling some of the quantum bits and allowing the remaining majority to evolve in free time.

[0119] The fact that arbitrary operations on the whole quantum system can be realized by manipulating only a part of the quantum system is described in Non-Patent Documents 3 and 4.

[0120] (Addendum) The following additional clauses are disclosed in relation to the above-described embodiment. (Additional note 1) Memory and at least one processor coupled to the memory, The processor: Calculating coefficients based on information about the calculation of the gradient of the objective function; generating a sequence indicating quantum operations for each time on some quantum bits of a quantum circuit included in the quantum computer based on the calculated coefficients, and transmitting information indicating the generated sequence to the quantum computer; receiving information indicating an expected value indicating an evaluation result from the quantum computer, and calculating the gradient by aggregation based on the expected value; Control device. (Additional note 2) The quantum circuit is a free-time evolution variational circuit. Item 1. The control device according to item 1. (Additional note 3) The information regarding the calculation of the gradient of the objective function is a differential index, a Hamiltonian, an observable, an initial state, and parameters at an input time point; the processor calculates a list of coefficients and Pauli matrices based on information regarding the calculation of the gradient of the objective function; generating a sequence of quantum operations for each element included in the list of Pauli matrices based on the coefficients and the list of Pauli matrices, and transmitting information indicating the generated sequence to the quantum computer; receiving information indicating an expectation value for each element included in the list of Pauli matrices from the quantum computer, and calculating the gradient by aggregating the expectation values ​​for each element included in the list of Pauli matrices; 3. The control device according to claim 1 or 2. (Additional note 4) A computer-implemented control method comprising: Calculating coefficients based on information about the calculation of the gradient of the objective function; generating a sequence indicating quantum operations for each time on some quantum bits of a quantum circuit included in the quantum computer based on the calculated coefficients, and transmitting information indicating the generated sequence to the quantum computer; receiving information indicating an expected value indicating an evaluation result from the quantum computer, and calculating the gradient by aggregation based on the expected value; Control method. (Additional note 5) A non-transitory storage medium storing a program for causing a computer to function as each unit in the control device described in any one of appendixes 1 to 3.

[0121] Although the present embodiment has been described above, the present invention is not limited to such a specific embodiment, and various modifications and changes are possible within the scope of the gist of the present invention described in the claims. [Explanation of symbols]

[0122] 1. Quantum Measurement System 10 Control device 11 Coefficient calculation section 12 Measurement Design Department 13 Measurement and Counting Department 20 Quantum computer 21 Expected Value Evaluation Section 500 computers 501 Input Device 502 Display device 503 External I / F 503a Recording media 504 Communication I / F 505 processor 506 Memory Device 507 Bus

Claims

1. a coefficient calculation unit that calculates coefficients based on information regarding the calculation of the gradient of the objective function; a measurement design unit that generates a sequence indicating quantum operations for each time on some quantum bits of a quantum circuit included in a quantum computer based on the calculated coefficients, and transmits information indicating the generated sequence to the quantum computer; a measurement and aggregation unit that receives information indicating an expected value indicating an evaluation result from the quantum computer and calculates the gradient by aggregation based on the expected value, Control device.

2. The quantum circuit is a free-time evolution variational circuit. The control device according to claim 1 .

3. The information regarding the calculation of the gradient of the objective function is a differential index, a Hamiltonian, an observable, an initial state, and parameters at an input time point; the coefficient calculation unit calculates a list of coefficients and Pauli matrices based on information regarding the calculation of the gradient of the objective function; the measurement design unit generates a sequence of quantum operations for each element included in the list of Pauli matrices based on the coefficients and the list of Pauli matrices, and transmits information indicating the generated sequence to the quantum computer; the measurement and aggregation unit receives information indicating an expected value for each element included in the list of Pauli matrices from the quantum computer, and calculates the gradient by aggregating the expected value for each element included in the list of Pauli matrices. The control device according to claim 1 .

4. A computer-implemented control method comprising: calculating coefficients based on information about the calculation of the gradient of the objective function; generating a sequence indicating quantum operations for each time on some quantum bits of a quantum circuit included in the quantum computer based on the calculated coefficients, and transmitting information indicating the generated sequence to the quantum computer; receiving information indicating an expected value indicating an evaluation result from the quantum computer, and calculating the gradient by aggregation based on the expected value; Control method.

5. A program for causing a computer to function as each unit in the control device according to any one of claims 1 to 3.

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