Quantum information processing method, quantum information processing program, classical computer, and hybrid system

Abstract

To enable calculation of an eigenfrequency of a target system using a quantum phase estimation algorithm.SOLUTION: A classical computer 110 transmits, to a quantum computer 120, a quantum circuit that is for performing quantum phase estimation, and that is generated on the basis of a quantum state |ψ>corresponding to an eigenstate of a target system, and information on a coefficient matrix when an equation of motion of the target system is expressed by a matrix format. The quantum computer 120 acquires a measurement result of an eigenvalue of the coefficient matrix by executing the quantum circuit, and transmits the measurement result of the eigenvalue to the classical computer 110. The classical computer 110 calculates an eigenfrequency of the target system on the basis of the measurement result of the eigenvalue.SELECTED DRAWING: Figure 1

Description

[Technical field]

[0001] The disclosed technology relates to a quantum information processing method, a quantum information processing program, a classical computer, and a hybrid system. [Background technology]

[0002] Conventionally, a quantum phase estimation algorithm is known, which is an algorithm capable of solving a so-called eigenvalue problem. [Prior art documents] [Non-patent literature]

[0003] [Non-Patent Document 1] A.Yu.Kitaev, "Quantum measurements and the Abelian Stabilizer Problem", https: / / arxiv.org / abs / quant-ph / 9511026 Summary of the Invention [Problem to be solved by the invention]

[0004] However, the above-mentioned Non-Patent Document 1 does not disclose the use of a quantum phase estimation algorithm to calculate the natural frequency.

[0005] The disclosed technology has been made in consideration of the above-mentioned circumstances, and aims to provide a quantum information processing method, a quantum information processing program, a classical computer, and a hybrid system that can calculate the natural frequency of a target system using a quantum phase estimation algorithm. [Means for solving the problem]

[0006] A quantum information processing method of a first aspect of the present disclosure is a quantum information processing method executed by a classical computer of a hybrid system including a classical computer and a quantum computer, in which the classical computer transmits to the quantum computer information related to a coefficient matrix when an equation of motion of a target system is expressed in matrix form and a quantum circuit generated based on a quantum state |ψ> corresponding to an eigenstate of the target system, and a quantum circuit for performing quantum phase estimation, the quantum computer obtains measurement results of eigenvalues ​​of the coefficient matrix by executing the quantum circuit, transmits the measurement results of the eigenvalues ​​to the classical computer, and the classical computer calculates the eigenfrequency of the target system based on the measurement results of the eigenvalues.

[0007] A quantum information processing program of a second aspect of the present disclosure is a quantum information processing program executed by a classical computer of a hybrid system including a classical computer and a quantum computer, in which the classical computer transmits to the quantum computer information about a coefficient matrix when an equation of motion of a target system is expressed in matrix form and a quantum circuit generated based on a quantum state |ψ> corresponding to an eigenstate of the target system, and the quantum circuit is for performing quantum phase estimation, and the quantum computer acquires measurement results of eigenvalues ​​of the coefficient matrix by executing the quantum circuit, transmits the measurement results of the eigenvalues ​​to the classical computer, and the classical computer calculates the eigenfrequency of the target system based on the measurement results of the eigenvalues. This quantum information processing program causes the classical computer to execute a process.

[0008] A hybrid system of a third aspect of the present disclosure is a hybrid system including a classical computer and a quantum computer, in which the classical computer transmits to the quantum computer information regarding a coefficient matrix when an equation of motion of a target system is expressed in matrix form and a quantum circuit generated based on a quantum state |ψ> corresponding to an eigenstate of the target system, and a quantum circuit for performing quantum phase estimation, the quantum computer obtains measurement results of eigenvalues ​​of the coefficient matrix by executing the quantum circuit, transmits the measurement results of the eigenvalues ​​to the classical computer, and the classical computer calculates the eigenfrequency of the target system based on the measurement results of the eigenvalues. Effect of the Invention

[0009] The disclosed technique has the advantage that it is possible to calculate the natural frequency of a target system using a quantum phase estimation algorithm. [Brief description of the drawings]

[0010] [Figure 1] 1 is a diagram illustrating an example of a schematic configuration of a hybrid system 100 according to an embodiment of the present invention. [Diagram 2] FIG. 1 is a schematic block diagram of a classical computer 110, a control device 121, and a computer functioning as a user terminal 130. [Diagram 3] FIG. 2 illustrates an example of a quantum circuit for performing quantum phase estimation. [Figure 4] FIG. 2 illustrates an example of a quantum circuit for performing quantum phase estimation. [Diagram 5] FIG. 2 is a diagram for explaining an adder. [Figure 6] FIG. 1 is a diagram for explaining a first oracle quantum circuit OF. [Figure 7] FIG. 13 is a diagram for explaining a second oracle quantum circuit OH. [Figure 8] FIG. 13 is a diagram for explaining a modified second oracle quantum circuit OH. [Figure 9]FIG. 2 is a diagram showing an example of a sequence executed by the hybrid system 100 of the present embodiment. [Figure 10] FIG. 1 is a diagram for explaining an embodiment. [Figure 11] FIG. 1 is a diagram for explaining an embodiment. [Figure 12] FIG. 1 is a diagram for explaining an embodiment. [Figure 13] FIG. 1 is a diagram for explaining an embodiment. [Figure 14] FIG. 1 is a diagram for explaining an embodiment. [Figure 15] FIG. 1 is a diagram for explaining an embodiment. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0011] Hereinafter, embodiments of the disclosed technology will be described in detail with reference to the drawings.

[0012] <Hybrid system 100 according to the embodiment>

[0013] Fig. 1 shows a hybrid system 100 according to the first embodiment. The hybrid system 100 of the present embodiment includes a classical computer 110, which is an example of an information processing device, a quantum computer 120, and a user terminal 130. As shown in Fig. 1, the classical computer 110, the quantum computer 120, and the user terminal 130 are connected via a computer network, such as an IP network, for example.

[0014] In the hybrid system 100 of this embodiment, the quantum computer 120 performs a predetermined quantum computation in response to a request from the classical computer 110, and outputs the computation result of the quantum computation to the classical computer 110. The classical computer 110 outputs the computation result according to the quantum computation to the user terminal 130. In this way, the hybrid system 100 as a whole executes a predetermined computation process.

[0015] The classical computer 110 is configured by having a communication unit 111 such as a communication interface, a processing unit 112 such as a processor or a CPU (Central processing unit), and an information storage unit 113 including a storage device or storage medium such as a memory or a hard disk, and by executing a program for performing each process. The classical computer 110 may include one or more devices or servers. The program may include one or more programs, and may be recorded in a computer-readable storage medium to form a non-transient program product.

[0016] As an example, quantum computer 120 generates an electromagnetic wave to be irradiated to at least any one of quantum bits in quantum bit group 123 based on information transmitted from classical computer 110. Then, quantum computer 120 executes a quantum circuit by irradiating at least any one of quantum bits in quantum bit group 123 with the generated electromagnetic wave.

[0017] In the example of FIG. 1, the quantum computer 120 includes a control device 121 that communicates with the classical computer 110, an electromagnetic wave generating device 122 that generates electromagnetic waves in response to a request from the control device 121, and a group of quantum bits 123 that receives electromagnetic wave irradiation from the electromagnetic wave generating device 122. The electromagnetic wave generating device 122 and the group of quantum bits 123 in the quantum computer 120 are also QPUs (Quantum Processing Units). Note that in this embodiment, the term "quantum computer" does not mean that no operations are performed using classical bits, but refers to a computer that includes operations using quantum bits or a computer that simulates the behavior of a quantum computer. A computer that simulates the behavior of a quantum computer is, for example, a classical computer that executes quantum simulation.

[0018] The control device 121 is a classical computer that performs operations using classical bits, and alternatively performs some or all of the processing described in this specification as being performed by the classical computer 110.

[0019] The user terminal 130 is a classical computer that performs operations using classical bits. The user terminal 130 accepts information input by a user and executes processing according to the information.

[0020] The classical computer 110, the control device 121, and the user terminal 130 can be realized, for example, by a computer 50 shown in Fig. 2. The computer 50 includes a central processing unit (CPU) 51, a memory 52 as a temporary storage area, and a non-volatile storage unit 53. The computer 50 also includes an input / output interface (I / F) 54 to which an external device, an output device, etc. are connected, and a read / write (R / W) unit 55 that controls reading and writing of data from and to a recording medium. The computer 50 also includes a network I / F 56 that is connected to a network such as the Internet. The CPU 51, the memory 52, the storage unit 53, the input / output I / F 54, the R / W unit 55, and the network I / F 56 are connected to one another via a bus 57.

[0021] [Outline of this embodiment] The hybrid system 100 of the present embodiment calculates the natural frequency of the target system using a quantum phase estimation algorithm. Specifically, the hybrid system 100 of the present embodiment calculates the natural frequency of the target system using a quantum phase estimation algorithm by taking into account the following four points.

[0022] (1) How to prepare the initial state of the natural frequency. (2) First Oracle Quantum Circuit O F and the second oracle quantum circuit O H Implementation of. (3) First Oracle Quantum Circuit O F and the modified second oracle quantum circuit O H mod Implementation of. (4) Implementation of quantum circuits that take into account the repetitive structure of the target system.

[0023] The specific details will be explained below.

[0024] [Quantum phase estimation] Fig. 3 shows an example of a quantum circuit for performing quantum phase estimation. As shown in Fig. 3, when a quantum state |ψ> is input to the quantum circuit for performing quantum phase estimation, one of the eigenvalues ​​is output as a measurement result. The quantum state |ψ> represents an eigenvector close to the eigenvector (eigenstate) of the target system.

[0025] In addition, if the size of the matrix for which the eigenvalue problem is to be solved is N × N, the relationship between the number of quantum bits n of the quantum state |ψ> and the size of the matrix is ​​N = 2 n It becomes.

[0026] For example, the eigenvectors of the target system (c 0 ,c 1 ,···,c N-1 ) and the corresponding quantum state |ψ> are in one-to-one correspondence as follows:

[0027]

number

[0028] In Fig. 3, |0> represents an ancillary quantum bit, and |0> represents that the ancillary quantum bit is in the 0 state. When the quantum circuit is executed, these quantum bits output eigenvalues ​​from the quantum circuit. When the quantum circuit is executed, each quantum bit shown in Fig. 3 holds the value of each digit when the eigenvalue, which is the output result, is expressed in binary.

[0029] Moreover, H in the quantum circuit shown in Figure 3 represents a Hadamard gate. The Hadamard gate is one of the basic gates used in many quantum computers and can be easily implemented.

[0030] In the quantum circuit shown in Figure 3, U is a quantum circuit equivalent to the unitary matrix for which eigenvalues ​​are to be found. The black circles and vertical lines in Figure 3 are symbols that control each U. For example, in the quantum circuit shown in Figure 3, if the second quantum bit from the top connected to the quantum circuit expressed by the following formula is |1>, it indicates that the quantum circuit expressed by the following formula is applied to the superposition component.

[0031]

number

[0032] Furthermore, since the following equation (A) holds, the following equation (B) is equivalent to multiplying U twice.

[0033]

number

[0034] Also, the QFT shown in Figure 3 † represents the quantum inverse Fourier transform, which can be realized by known quantum circuits. The rightmost detector shown in Fig. 3 measures whether each quantum bit is 0 or 1. The result of this measurement is the binary representation of the eigenvalue obtained as the calculation result.

[0035] [1. How to prepare the initial state of the natural frequency] When using a quantum phase estimation algorithm, it is necessary to prepare a state that approximates the eigenstate as an input. However, until now, no method has been known for preparing an appropriate initial state when calculating the eigenfrequency.

[0036] Therefore, the classical computer 110 of the hybrid system 100 of the present embodiment coarsens a model representing the target system, and sets, as the initial state |ψ>, the solution obtained by calculating the coarsened model. Then, the quantum computer 120 of the hybrid system 100 of the present embodiment calculates the natural frequency of the target system using the initial state |ψ> obtained by the coarsened model. As a result, it becomes possible to accurately calculate the natural frequency of the target system. Hereinafter, a specific explanation will be given while setting up the problem.

[0037] Assume that the model representing the target system has N = 2 n particles. In this case, the classical computer 110 coarsens the model representing the target system into a system having M = 2 m particles (where M < N), and classically calculates the initial state |ψ m > of the quantum state |ψ>. For example, the classical computer 110 coarsens the model representing the target system by, for example, combining a plurality of particles existing in the model representing the target system into one. Assume that the coarsened model having these M particles is a model that can be exactly solved by the classical computer 110. Therefore, for example, M is appropriately set by the user. In a system having N particles, each of the N particles has a position coordinate, and each of the position coordinates is set as a variable.

[0038] The initial state |ψ m > is a quantum state corresponding to the exact eigenstate and can be represented by m quantum bits.

[0039] Next, the initial state |ψ m > represented by m quantum bits is prepared on the quantum computer 120. For example, by a known QROM method (see, for example, the reference (https: / / journals.aps.org / prx / abstract / 10.1103 / PhysRevX.8.041015)), the initial state |ψ m> can be prepared.

[0040] Next, the quantum computer 120 calculates the initial state |ψ as shown in the following equation: m >, a quantum state of nm quantum bits is added to the quantum state |ψ n (m) > to generate a new

[0041]

number

[0042] Specifically, a |0> state is prepared for all of the nm quantum bits, and the initial state |ψ is generated by applying a Hadamard gate to each of the nm quantum bits. m > is added a state in which nm quantum bit strings are equally superposed. This generates a state in which the solution of the coarse-grained model is embedded into the target system.

[0043] For example, if m = 2 and n = 4, the new state |ψ n (m) > is expressed by the following formula.

[0044]

number

[0045] The initial state |ψ m > is a state where the solution of a coarse-grained model is embedded in a more detailed model, and is useful as an initial state. Therefore, the initial state |ψ mBy using the above, it becomes possible to calculate the natural frequency of a target system with high accuracy using a quantum computer. As will be described later, the above-mentioned method for preparing an initial state is not limited to calculation of natural frequency, but can also be used for other methods. For example, the above-mentioned method for preparing an initial state can be applied to quantum calculations using the finite element method, such as fluid calculations and electromagnetic field calculations. Details will be described later.

[0046] 2. First Oracle Quantum Circuit O F and the second oracle quantum circuit O H Implementation of The implementation of the quantum circuit U shown in FIG. 3 is very complicated. Therefore, the hybrid system 100 of the present embodiment includes a first oracle quantum circuit O F and the second oracle quantum circuit O H We use this to implement the quantum circuit U in Figure 3.

[0047] In addition, the first oracle quantum circuit O F and the second oracle quantum circuit O H Implementations of the above are disclosed, for example, in the following references:

[0048] Dominic W. Berry, Andrew M. Childs, "Black-box Hamiltonian simulation and unitary implementation", https: / / arxiv.org / abs / 0910.4157

[0049] Here, we consider the case where the coefficient matrix H to be diagonalized is embedded (block encoding) into the quantum circuit U. In this case, the first oracle quantum circuit O F is configured to satisfy the following formula (1) for row number x=1, , N of the coefficient matrix H and number of non-zero components i=1, , d. For this reason, the first oracle quantum circuit O F is the position x,y of a non-zero element in the coefficient matrix H i This is a quantum circuit for outputting

[0050]

number

[0051] In equation (1), y i represents the column index of the i-th nonzero element in the x-th row of the coefficient matrix H, and |x,i> represents the state of the quantum bit. |x,i> holds the binary representation of x and i. For example, if x=2 and i=1, then |x,i>=|1001>. In this case, the first two digits represent x, and the next two digits represent i.

[0052] Second Oracle Quantum Circuit O H is configured to satisfy the following formula (2). In the following formula (2), |x,y>|z> represents a composite system of quantum bits representing x and y and quantum bits representing z. Furthermore, the row number x of the coefficient matrix H and the column number y of the coefficient matrix H are x,y=1,...,N, z is a binary number, and H xy is the binary representation of the x-row, y-column element of the coefficient matrix H. Therefore, the second oracle quantum circuit O H is the component value H at the specified position x, y in the coefficient matrix H. xy This is a quantum circuit for outputting

[0053]

number

[0054] JPEG2025013037000010.jpg1010

[0055] Figure 4 shows the quantum circuit U that is incorporated into U in the quantum circuit of Figure 3. H * Specifically, the quantum circuit U shown in Fig. 4 H * corresponds to U in the quantum circuit in Fig. 3. In the following, we use the quantum circuit U H* When performing quantum phase estimation using the first oracle quantum circuit O F and the second oracle quantum circuit O H The implementation of |1> shown in Figure 4 is explained below. sgn ,a 1 ,a 2 represents a single ancillary qubit, and a s , s represent the quantum bit groups that hold the inputs and outputs, respectively, and the quantum circuit U H ,U H † is the first oracle quantum circuit O F and the second oracle quantum circuit O H The present invention is configured to include the following.

[0056] The quantum circuit U shown in Figure 4 H * The quantum circuit U shown in Figure 4 can be implemented by using a technique called qubitization. For example, see the following references. H * It is known that quantum circuits can be simplified by performing quantum phase estimation using

[0057] DW Berry and AM Childs, "Black-box hamiltonian simulation and unitary implementation", Quantum Info. Comput. 12 (2012) 29-62, arXiv:0910.4157 [quant-ph].

[0058] Here, we consider the case where the coefficient matrix H is a 2-sparse matrix. A 2-sparse matrix is ​​a matrix in which there are two nonzero elements in each row and the remaining elements are zero. Furthermore, each element H xy is expressed by the following formula:

[0059]

number

[0060] In this case, the coefficient matrix H is a matrix as shown below.

[0061]

number

[0062] In addition, the first oracle quantum circuit O F and the second oracle quantum circuit O H The basic element in implementing and is the adder. For example, by referring to the following references, it is possible to construct the adder shown in Figure 5:

[0063] SA Cuccaro, TG Draper, SA Kutin, and DP Moulton, "A new quantum ripple-carry addition circuit", arXiv:quant-ph / 0410184.

[0064] In this embodiment, the first oracle quantum circuit O F and the second oracle quantum circuit O H Implement and.

[0065] In this case, the first oracle quantum circuit O F is a quantum circuit as shown in Figure 6. H x(x+1) is the binary representation of the element in row x, column x+1 of the coefficient matrix H. On the other hand, the second oracle quantum circuit O H is a quantum circuit as shown in Fig. 7. † represents an adder and its inverse operation († represents an inverse operation).

[0066] In this way, the first oracle quantum circuit O F and the second oracle quantum circuit O HBy incorporating the above, it becomes possible to calculate the natural frequency of the target system using a quantum computer. Specifically, a first oracle quantum circuit O F and the second oracle quantum circuit O H By incorporating the first oracle quantum circuit O, it is possible to simplify the quantum circuit for performing quantum phase estimation, and therefore it is possible to perform quantum phase estimation efficiently. This makes it possible to calculate the eigenfrequency using quantum phase estimation without implementing a complex quantum circuit. More specifically, F and the second oracle quantum circuit O H By using the above, it becomes possible to easily embed the coefficient matrix H to be diagonalized into the quantum circuit U, and it becomes possible to simplify the quantum circuit for performing quantum phase estimation.

[0067] 3. First Oracle Quantum Circuit O F and the modified second oracle quantum circuit O H mod Implementation of To actually perform quantum phase estimation, a second oracle quantum circuit O H Not all of the functions of the second oracle quantum circuit O are required. H is each element H of the coefficient matrix H xy It is used only to perform a gate operation called Controlled-Ry rotation using an angle calculated based on the value of

[0068] Therefore, in this embodiment, the second oracle quantum circuit O H Figure 8 shows the modified second oracle quantum circuit O H As shown in FIG. 8, a modified second oracle quantum circuit O H contains rotation gates corresponding to each element of the coefficient matrix H. Specifically, the modified second oracle quantum circuit O H contains the following two gates: y represents a rotating gate.

[0069]

number

[0070] These gates differ from the following gates in Figure 6 in that they xy Since it is not necessary to perform various calculations on the value of , it is possible to efficiently perform quantum phase estimation.

[0071]

number

[0072] Modified second oracle quantum circuit O H includes the above-mentioned gate operation. This allows for the case where there are few types of values, for example when all non-zero elements of the coefficient matrix H are 1, to xy By calculating the angle based on the value of in advance, the calculation of the angle becomes unnecessary on the quantum computer. Since there is no need to execute unnecessary processing, it becomes possible to efficiently execute quantum phase estimation.

[0073] In the above embodiment, a 2-sparse matrix has been described, but the present invention is not limited to this. For example, even if a d-sparse matrix in which d non-zero elements exist in each row is used, the same processing as above can be performed.

[0074] Also, the modified second oracle quantum circuit O H contains rotation gates corresponding to each component of the coefficient matrix H as elements. In this way, the angles are calculated in advance according to each component of the coefficient matrix H. This method can be applied to a variety of algorithms.

[0075] [4. Implementation of quantum circuits taking into account repetitive structures in the target system] It is also assumed that the target system may have a repetitive structure. Therefore, in this embodiment, the first oracle quantum circuit O F and the second oracle quantum circuit O H Implement.

[0076] Here, consider a case where there are L unit structures constituting the repeating structure, each unit structure has K mass points, and the target system has K×L=N mass points.

[0077] In this case, the first oracle quantum circuit O F is the first oracle quantum circuit O for the entire system of interest. F full and is expressed by the following formula (1A). In the following formula (1A), i is an identification number for identifying the spring in the l-th unit structure, and the relationship between the x-th mass point in the l-th unit structure and l+Δl i y in the th unit structure i is the identification number of the spring that connects the th mass point. i takes on values ​​of -1, 0, and +1. In addition, when the unit structures constituting the repeating structure are repeated on a two-dimensional plane, Δl i can take on a wider variety of values.

[0078]

number

[0079] In addition, the second oracle quantum circuit O H is the second oracle quantum circuit O for the entire system of interest. H full and is represented by the following formula (2A). Δl≠0,xy represents the elements of the coefficient matrix H at the connection points between different unit structures, and H -1,xy =-H +1,yx It is.

[0080]

number

[0081] In this case, the first oracle quantum circuit O F sub is expressed by the following formula (3A). Also, the second oracle quantum circuit O H sub is expressed by the following equation (4A).

[0082]

number

[0083] In addition, the first oracle quantum circuit for the entire system O F full is the first oracle quantum circuit of the unit structure O F sub This can be realized by combining the following addition operation. In addition, the second oracle quantum circuit O H full is the second oracle quantum circuit of the unit structure O H sub That is it.

[0084] In addition, by combining an identification number l for identifying a unit structure and an identification number x for identifying a mass point within one unit structure, it is possible to express the number X of a mass point of interest within the entire structure as follows:

[0085]

number

[0086] By using the above formula, it becomes possible to consider l and x separately as follows:

[0087]

number

[0088] Taking the above into consideration, the following equation holds:

[0089]

number

[0090] As can be seen from the above equation, the first oracle quantum circuit O F full is a normal first oracle quantum circuit O F This also works as a second oracle quantum circuit for the entire system, O H full and the usual second oracle quantum circuit O H The same applies to.

[0091] As described above, the first oracle quantum circuit O F sub and the second oracle quantum circuit of unit structure O H sub If it is possible to construct the first oracle quantum circuit O for the entire system based on them, F full and the second oracle quantum circuit for the whole system O H full It is possible to construct the following:

[0092] In this embodiment, the size of the matrix is ​​N×N for N mass points, but if the mass points can move in three directions, x, y, and z, the size of the matrix will be 3N×3N. In such a case, the above items can be applied by regarding the mass point label x as the coordinate label (x=1, , 3N).

[0093] [Operation of the Hybrid System 100 of the Embodiment]

[0094] Next, a specific operation of the hybrid system 100 according to the embodiment will be described. Each device of the hybrid system 100 executes each process shown in FIG.

[0095] First, in step S100, the user terminal 130 transmits to the classical computer 110 computation target information, which is information on a computation target, and computation method information, which is information on a computation method, both input by the user.

[0096] The calculation target information includes, for example, information about the target system (e.g., information about the coefficient matrix H when the equation of motion of the target system is expressed in matrix form) and quantum computer information (e.g., the type of quantum computer or type of pseudo-quantum computer used by the user).

[0097] The calculation method information includes, for example, information about the quantum phase estimation algorithm. The information about the quantum phase estimation algorithm includes, for example, a state preparation quantum circuit, which is a quantum circuit for executing the quantum phase estimation algorithm, an initial state, various oracle quantum circuits (e.g., O F ,O H ,O H mod ,O F sub ,O F full ,O H sub , and O H full) include the number of executions and various other parameters (e.g., the number of digits of the eigenvalue to be obtained, etc.).

[0098] Next, in step S102, the classical computer 110 receives the calculation target information and the calculation method information transmitted from the user terminal 130.

[0099] In step S104, the classical computer 110 generates a quantum circuit for performing quantum phase estimation based on the information about the coefficient matrix H when expressing the equation of motion of the target system in matrix form using the method as described above, and the quantum state |ψ> corresponding to the eigenstate of the target system.

[0100] For example, the classical computer 110 coarsens the system with M = 2 m (where M < N) particles to classically calculate the initial state |ψ m > of the quantum state |ψ>. Then, the classical computer 110 sets this initial state |ψ m > of the quantum state |ψ> to the quantum state |ψ> of the quantum circuit for performing quantum phase estimation.

[0101] Also, for example, the classical computer 110 incorporates the first oracle quantum circuit O shown in FIG. 6 F and the second oracle quantum circuit O shown in FIG. 7 H into the state preparation quantum circuit to generate a quantum circuit for performing quantum phase estimation.

[0102] Also, for example, the classical computer 110 incorporates the first oracle quantum circuit O shown in FIG. 6 F and the second oracle quantum circuit O shown in FIG. 8 H mod into the state preparation quantum circuit to generate a quantum circuit for performing quantum phase estimation.

[0103] Also, for example, the classical computer 110 is the first oracle quantum circuit O for the entire target systemF full , the second oracle quantum circuit O for the entire system of interest H full , the first oracle quantum circuit of unit structure O F sub , and the second oracle quantum circuit of the unit structure O H sub By incorporating the above into the state preparation quantum circuit, a quantum circuit for performing quantum phase estimation is generated.

[0104] It should be noted that the generation of a quantum circuit for performing quantum phase estimation may employ any one of the above methods, or a combination of the above methods.

[0105] In step S106, the classical computer 110 transmits various information necessary for quantum computation to the quantum computer 120. Specifically, the classical computer 110 transmits to the quantum computer 120 the quantum circuit for estimating the quantum phase estimation generated in step S104.

[0106] In step S108, the control device 121 of the quantum computer 120 receives the various information transmitted from the classical computer 110 in step S104.

[0107] In step S110, the control device 121 of the quantum computer 120 causes the quantum computer 120 to execute quantum calculations according to the various information received in step S108. Specifically, the quantum computer 120 acquires measurement results of eigenvalues ​​of the coefficient matrix H by executing a quantum circuit for estimating the quantum phase estimate generated in step S104.

[0108] Specifically, quantum computer 120 generates electromagnetic waves to be irradiated to at least any one of quantum bits in quantum bit group 123 in response to the control of control device 121. Then, quantum computer 120 irradiates at least any one of quantum bits in quantum bit group 123 with the generated electromagnetic waves to execute a quantum circuit. The gate operation of each quantum gate included in the quantum circuit is converted into a corresponding electromagnetic wave waveform, and the generated electromagnetic waves are irradiated to quantum bit group 123 by electromagnetic wave generating device 122. Then, quantum computer 120 outputs the result of the quantum calculation.

[0109] In step S112, the control device 121 transmits the measurement result obtained in step S110 to the classical computer 110.

[0110] In step S114, the classical computer 110 receives the measurement result transmitted from the control device 121 in step S112.

[0111] In step S116, the classical computer 110 calculates the eigenfrequency of the target system by, for example, appropriately processing the measurement result obtained in step S114. Specifically, since the eigenvalues ​​output from the quantum circuit are binary numbers, the classical computer 110 obtains the decimal eigenvalues ​​by, for example, converting the binary numbers to decimal numbers. This eigenvalue corresponds to the eigenfrequency. In addition, for example, when multiple measurement results are obtained by executing the quantum circuit multiple times, the classical computer 110 calculates the eigenfrequency of the target system by, for example, taking a majority vote of the multiple measurement results.

[0112] In step S118, the classical computer 110 transmits the calculation result obtained in step S116 to the user terminal 130.

[0113] In step S120, the user terminal 130 receives the result transmitted from the classical computer 110.

[0114] The user checks the results displayed on a display unit (not shown) of the user terminal 130.

[0115] As described above, the classical computer of the hybrid system of the embodiment transmits to the quantum computer information on the coefficient matrix when the equation of motion of the target system is expressed in matrix form, and a quantum circuit that receives as input a quantum state |ψ> corresponding to the eigenstate of the target system and is for performing quantum phase estimation. The quantum computer executes the quantum circuit to obtain measurement results of eigenvalues ​​of the coefficient matrix, and transmits the measurement results of the eigenvalues ​​to the classical computer. The classical computer calculates the eigenfrequency of the target system based on the measurement results of the eigenvalues. This makes it possible to calculate the eigenfrequency of the target system using a quantum phase estimation algorithm.

[0116] Conventionally, a technique for calculating an eigenfrequency using a quantum phase estimation algorithm has not been known. In contrast, in this embodiment, the classical computer 110 calculates the eigenfrequency of the first oracle quantum circuit O F and the second oracle quantum circuit O H By incorporating these into a quantum circuit for performing quantum phase estimation, it is possible to calculate the natural frequency of a target system using a quantum phase estimation algorithm.

[0117] More specifically, the classical computer 110 transmits a first oracle quantum circuit O to a quantum circuit for performing quantum phase estimation. F and the second oracle quantum circuit O H By incorporating the first oracle quantum circuit O, it is possible to simplify the quantum circuit for performing quantum phase estimation. Therefore, it is possible to perform quantum phase estimation efficiently. This allows the quantum computer 120 to calculate the eigenfrequency using quantum phase estimation without executing a complex quantum circuit. More specifically, the first oracle quantum circuit O F and the second oracle quantum circuit O HBy using the above, it becomes possible to easily embed the coefficient matrix H to be diagonalized into the quantum circuit U, and it becomes possible to simplify the quantum circuit for performing quantum phase estimation.

[0118] In this embodiment, the classical computer 110 also generates a second oracle quantum circuit O H The second oracle quantum circuit O H mod By incorporating the second oracle quantum circuit O into the quantum circuit for performing quantum phase estimation, it is possible to reduce the gate operations and to execute the quantum phase estimation algorithm more efficiently. H By removing functions that are not essentially necessary for quantum phase estimation from among the functions of the conventional method, it is possible to reduce gate operations and execute the quantum phase estimation algorithm more efficiently.

[0119] In this embodiment, the model representing the target system is coarse-grained to obtain the initial state |ψ of the quantum state |ψ m > classically, generate a state in which the solution of the coarse-grained model is embedded in the target system, and then execute the quantum circuit, making it possible to calculate the eigenfrequency with high accuracy. For example, by setting the result obtained by coarse-graining as the initial state, it becomes possible to obtain calculation results with high accuracy compared to when the initial state is random. Note that by coarse-graining the model representing the target system, the initial state |ψ of the quantum state |ψ> can be calculated with high accuracy. m Classical methods for computing > are also available in other quantum algorithms, such as the Harrow-Hassidim-Lloyd (HHL) algorithm.

[0120] For example, the classical computer 110 may obtain the initial state |ψ of the quantum state |ψ by coarse-graining a model representing the target system. m > is classically calculated. Then, the classical computer 110 calculates the initial state |ψ m>, a quantum circuit for executing the target calculation is generated. The quantum computer 120 generates a state in which the solution of the coarse-grained model is embedded in the target system, and executes the quantum circuit based on that state. This allows an appropriate initial state |ψ to be generated for quantum algorithms other than the eigenfrequency calculation by quantum phase estimation. m > It becomes possible to prepare and obtain highly accurate calculation results.

[0121] In addition, in this embodiment, when the target system has a repetitive structure, the first oracle quantum circuit O F full and the second oracle quantum circuit O for the whole system of interest. H full and the first oracle quantum circuit O F sub and the second oracle quantum circuit O H sub By incorporating these into a quantum circuit for performing quantum phase estimation, it is possible to calculate the natural frequency of a system having a repetitive structure. For example, it is now possible to calculate the natural frequency of an object having a repetitive structure, such as a building, a bridge, or a polymer, using a quantum computer. Note that the proposal in this embodiment in which the target system is a system having a repetitive structure is not limited to calculation of the natural frequency, but can also be applied to other calculations. For example, it can also be applied to fluid calculations. Furthermore, the proposal in this embodiment in which the target system is a system having a repetitive structure is not limited to quantum phase estimation, but can also be applied to calculation of the oracle quantum circuit O F ,O H Any algorithm that utilizes the above can be applied.

[0122] For example, when the target system has a repetitive structure, the classical computer 110 generates a first oracle quantum circuit O for the entire target system. F full and the second oracle quantum circuit O for the whole system of interest. H fulland the first oracle quantum circuit O F sub and the second oracle quantum circuit O H sub By incorporating these into a quantum circuit, various calculations of a system having a repeating structure can be performed. For example, when a polymer is the target, the unit structure and mass points are determined based on the molecular structure of the polymer, and the coefficient matrix H is obtained from the absorption spectrum of the polymer, and then the natural frequency of the polymer can be calculated by the above-mentioned method.

[0123] In the above embodiment, the system has N mass points, and each of the N mass points has a variable called a position coordinate. However, when performing other calculations such as fluid calculations, the variable is set to a value corresponding to the fluid calculation. EXAMPLES

[0124] Next, examples corresponding to the above embodiment will be described. In Example 1, the natural frequency of the following equation of motion is calculated. Note that k represents the spring constant and m represents the mass. Note that the following H xy is obtained by dividing each element of the coefficient matrix by k.

[0125]

number

[0126] The first oracle quantum circuit O that is set when calculating the eigenfrequency of the above system F corresponds to the quantum circuit in FIG. 7. FIG. 10 shows the first oracle quantum circuit O F FIG. 1 is a diagram showing an example of a quantum circuit incorporating the above. EXAMPLES

[0127] In the second embodiment, the natural frequency of the following equation of motion is calculated. 1 ,k 2represents the spring constant and m represents the mass. k 1 <k 2 It is.

[0128]

number

[0129] FIG. 11 shows the modified second oracle quantum circuit O that is set up when calculating the eigenfrequency of the above system. H mod FIG. 12 is a diagram showing an example of a first oracle quantum circuit O F and the modified second oracle quantum circuit O H mod FIG. 1 is a diagram showing an example of a quantum circuit incorporating the above. EXAMPLES

[0130] In Example 3, a simulation experiment is performed to calculate the natural frequency of the equation of motion used in Example 2. Specifically, in Example 3, the accuracy of a method for setting an initial state by coarse-graining a target system is verified.

[0131] By classically calculating the values ​​of the following equations, the initial state |ψ m If this calculation is implemented using a quantum circuit, it will be the quantum circuit shown in Figure 13. JPEG2025013037000030.jpg2167 JPEG2025013037000031.jpg49120

[0132] Figures 14 and 15 show the simulation results. Figure 14 shows the state that can be prepared when m is changed for n=10, and it can be seen that the accuracy improves by increasing m. Figure 15 examines the accuracy (infidelity, i.e. the magnitude of error) of the prepared state for various combinations of m and n, and it can be seen that even with a small m=4, the error is sufficiently small at 0.1 or less.

[0133] The technology of the present disclosure is not limited to the above-described embodiment and examples, and various modifications and applications are possible without departing from the spirit and scope of the present invention.

[0134] For example, in the above embodiment, information may be transmitted and received in any manner between the classical computer 110 and the quantum computer 120. For example, transmission and reception of parameters of a quantum circuit and transmission and reception of measurement results between the classical computer 110 and the quantum computer 120 may be performed sequentially each time a predetermined calculation is completed, or may be performed after all calculations are completed.

[0135] In the above embodiment, the calculation target information is transmitted from the user terminal 130 to the classical computer 110, and the classical computer 110 executes a calculation according to the calculation target information. However, the present invention is not limited to this. The user terminal 130 may transmit the calculation target information to the classical computer 110 or a storage medium or storage device accessible to the classical computer 110 via a computer network such as an IP network, or may store the calculation target information in a storage medium or storage device and hand it over to the operator of the classical computer 110, who may input the calculation target information to the classical computer 110 using the storage medium or storage device.

[0136] In addition, in the above embodiment, the quantum circuit is executed by irradiating electromagnetic waves. However, the present invention is not limited to this, and the quantum circuit may be executed by a different method.

[0137] In the above embodiment, the quantum computer 120 executes the calculations, but the present invention is not limited to this. For example, the calculations may be executed by a classical computer that mimics the behavior of a quantum computer.

[0138] Furthermore, in the above embodiment, it is assumed that the classical computer 110 and the quantum computer 120 are managed by different organizations, but the classical computer 110 and the quantum computer 120 may be managed as a single entity by the same organization. In this case, it is not necessary to transmit quantum chemical calculation information from the classical computer 110 to the quantum computer 120 and to transmit measurement results from the quantum computer 120 to the classical computer 110. In this case, it is considered that the control device 121 of the quantum computer 120 plays the role of the classical computer 110 in the above description.

[0139] In addition, if there is a quantum computer that can replace part or all of the processing of the classical computer described in this embodiment, the quantum computer may be configured to perform part or all of the processing.

[0140] It should be noted that in the above embodiment, unless there is a statement such as "based only on XX", "depending only on XX", or "only in the case of XX", it is assumed in this specification that additional information may be taken into consideration. As an example, the statement "do b if a" does not necessarily mean "always do b if a" unless expressly stated otherwise.

[0141] In addition, in the above embodiment, expressions such as "optimize" or "optimized parameters" are used, but it should be noted that these expressions of "optimization" mean approaching an optimal state. Therefore, when trying to obtain parameters that minimize a certain function, it should be noted that the parameters obtained by optimizing the function may be a local solution rather than a global solution that minimizes the function.

[0142] Furthermore, even if there is an aspect of a method, program, terminal, device, server or system (hereinafter referred to as a "method, etc.") that performs an operation different from that described in this specification, each aspect of the disclosed technology is directed to an operation that is identical to any of the operations described in this specification, and the existence of an operation different from that described in this specification does not make the method, etc. outside the scope of each aspect of the technology disclosed herein.

[0143] Furthermore, although the present specification has been described as an embodiment in which the program is pre-installed, the program may also be provided by being stored on a computer-readable recording medium.

[0144] Furthermore, each component of the hybrid system of this embodiment does not have to be realized by a single computer or server, but may be realized in a distributed manner across multiple computers connected by a network.

[0145] For example, the processing executed by the classical computer of each of the above embodiments may be distributed among multiple classical computers connected by a network. Or, for example, the processing executed by the quantum computer of each of the above embodiments may be distributed among multiple quantum computers connected by a network. In this case, a hybrid system is formed by at least one classical computer and at least one quantum computer.

[0146] All publications, patent applications, and standards mentioned in this specification are herein incorporated by reference to the same extent as if each individual publication, patent application, or standard was specifically and individually indicated to be incorporated by reference.

[0147] (Additional Note) The following additional notes are given regarding aspects of the present disclosure.

[0148] (Appendix 1) A quantum information processing method executed by a classical computer in a hybrid system including a classical computer and a quantum computer, The classical computer transmits to the quantum computer information on a coefficient matrix when an equation of motion of a target system is expressed in a matrix form and a quantum circuit generated based on a quantum state |ψ> corresponding to an eigenstate of the target system, the quantum circuit being for performing quantum phase estimation; The quantum computer executes the quantum circuit to obtain measurement results of eigenvalues ​​of the coefficient matrix and transmits the measurement results of the eigenvalues ​​to the classical computer; The classical computer calculates the natural frequency of the target system based on the measurement results of the eigenvalues. Quantum information processing methods.

[0149] (Appendix 2) The quantum circuit for performing the quantum phase estimation includes: a first oracle quantum circuit O for outputting the position within the coefficient matrix of a non-zero element of the coefficient matrix; F and, A second oracle quantum circuit O for outputting a component value at a specified position in the coefficient matrix. H and The quantum circuit for performing the quantum phase estimation includes the first oracle quantum circuit O F and the second oracle quantum circuit O H The quantum circuit is embedded with the coefficient matrix by incorporating the above. 2. A quantum information processing method according to claim 1.

[0150] (Appendix 3) The quantum circuit for performing the quantum phase estimation includes: a first oracle quantum circuit O for outputting the position within the coefficient matrix of a non-zero element of the coefficient matrix; F and, A modified second oracle quantum circuit O including rotation gates corresponding to the respective elements of the coefficient matrix. Hmod comprising; and The quantum circuit for performing the quantum phase estimation incorporates the first oracle quantum circuit O F and the modified second oracle quantum circuit O H mod such that the quantum circuit in which the coefficient matrix is embedded is formed by incorporating them, The quantum information processing method according to Appendix 1.

[0151] (Appendix 4) The model representing the target system has N = 2 n variables, The classical computer coarsens the model representing the target system into a system having M = 2 m variables (where M < N), and classically calculates the initial state |ψ m > of the quantum state |ψ, Based on the initial state |ψ m > of the quantum state |ψ, a quantum circuit for performing the quantum phase estimation is generated, The quantum computer For the initial state |ψ m > of the quantum state |ψ, a state in which the solution of the coarsened model is embedded in the target system is generated by adding a state that is the quantum state of n - m qubits and in which n - m qubit strings are superimposed, and the measurement result of the eigenvalue of the coefficient matrix is obtained by executing the quantum circuit, The quantum information processing method according to any one of Appendices 1 to 3.

[0152] (Appendix 5) The target system is a system having a repetitive structure, There are L unit structures constituting the repetitive structure, and one unit structure has K mass points, The target system is a system having K × L = N mass points, The first oracle quantum circuit O F is the first oracle quantum circuit O for the entire target system Ffull is expressed by the following formula (1A), where i is an identification number for identifying the spring in the l-th unit structure, and the x-th mass point in the l-th unit structure and l+Δl i y in the th unit structure i is an identification number representing the spring that connects the th mass point, The second oracle quantum circuit O H is a second oracle quantum circuit O for the entire target system H full and is represented by the following formula (2A): Δl≠0,xy represents the components of the coefficient matrix at the connection points between different unit structures, and H -1,xy =-H +1,yx and First Oracle Quantum Circuit of Unit Structure O F sub is represented by the following formula (3A): Second Oracle Quantum Circuit of Unit Structure O H sub is represented by the following formula (4A): 3. A quantum information processing method according to claim 2.

number

[0153] (Appendix 6) A quantum information processing program executed by a classical computer in a hybrid system including a classical computer and a quantum computer, The classical computer transmits to the quantum computer information on a coefficient matrix when an equation of motion of a target system is expressed in a matrix form and a quantum circuit generated based on a quantum state |ψ> corresponding to an eigenstate of the target system, the quantum circuit being for performing quantum phase estimation; The quantum computer executes the quantum circuit to obtain measurement results of eigenvalues ​​of the coefficient matrix and transmits the measurement results of the eigenvalues ​​to the classical computer; The classical computer calculates the natural frequency of the target system based on the measurement results of the eigenvalues. A quantum information processing program that allows processing to be performed by a classical computer.

[0154] (Appendix 7) A hybrid system including a classical computer and a quantum computer, The classical computer transmits to the quantum computer information on a coefficient matrix when an equation of motion of a target system is expressed in a matrix form and a quantum circuit generated based on a quantum state |ψ> corresponding to an eigenstate of the target system, the quantum circuit being for performing quantum phase estimation; The quantum computer executes the quantum circuit to obtain measurement results of eigenvalues ​​of the coefficient matrix and transmits the measurement results of the eigenvalues ​​to the classical computer; The classical computer calculates the natural frequency of the target system based on the measurement results of the eigenvalues. Hybrid system.

[0155] (Appendix 8) 1. A hybrid system including a plurality of classical computers and a plurality of quantum computers, One or more classical computers among the multiple classical computers transmit to the quantum computer information on a coefficient matrix when an equation of motion of a target system is expressed in a matrix form and a quantum circuit generated based on a quantum state |ψ> corresponding to an eigenstate of the target system, the quantum circuit being for performing quantum phase estimation; One or more quantum computers among the plurality of quantum computers execute the quantum circuit to obtain measurement results of eigenvalues ​​of the coefficient matrix, and transmit the measurement results of the eigenvalues ​​to the classical computer; one or more classical computers among the plurality of classical computers calculates the natural frequencies of the target system based on the measurements of the eigenvalues. Hybrid system. [Explanation of symbols]

[0156] 100 Hybrid System 110 Classical Computers 111 Communications Department 112 Processing section 113 Information storage section 120 Quantum Computer 121 Control device 122 Electromagnetic wave generation device 123 qubit group 130 User terminal

Claims

1. A quantum information processing method executed by a classical computer in a hybrid system including a classical computer and a quantum computer, The classical computer transmits to the quantum computer information on a coefficient matrix when an equation of motion of a target system is expressed in a matrix form and a quantum circuit generated based on a quantum state |ψ〉 corresponding to an eigenstate of the target system, the quantum circuit being for performing quantum phase estimation; The quantum computer executes the quantum circuit to obtain measurement results of eigenvalues ​​of the coefficient matrix and transmits the measurement results of the eigenvalues ​​to the classical computer; The classical computer calculates the natural frequency of the target system based on the measurement results of the eigenvalues. Quantum information processing methods.

2. The quantum circuit for performing the quantum phase estimation includes: a first oracle quantum circuit O for outputting the position within the coefficient matrix of a non-zero element of the coefficient matrix; Ｆ and, A second oracle quantum circuit O for outputting a component value at a specified position in the coefficient matrix. Ｈ and The quantum circuit for performing the quantum phase estimation is the first oracle quantum circuit O Ｆ and the second oracle quantum circuit O Ｈ The quantum circuit is embedded with the coefficient matrix by incorporating the above.

2. The quantum information processing method according to claim 1.

3. The quantum circuit for performing the quantum phase estimation includes: a first oracle quantum circuit O for outputting the position within the coefficient matrix of a non-zero element of the coefficient matrix; Ｆ and, A modified second oracle quantum circuit O including rotation gates corresponding to the respective components of the coefficient matrix as elements. Ｈ ｍｏｄ and The quantum circuit for performing the quantum phase estimation is the first oracle quantum circuit O Ｆ and the modified second oracle quantum circuit O Ｈ ｍｏｄ The quantum circuit is embedded with the coefficient matrix by incorporating the above.

2. The quantum information processing method according to claim 1.

4. The model representing the target system is N=2 ｎ variables, The classical computer is The model representing the target system is M=2 ｍ By coarse-graining the quantum state |ψ〉 into a system having M<N variables, the initial state |ψ ｍ > classically, The initial state |ψ of the quantum state |ψ ｍ Quantum circuits for performing the quantum phase estimation are generated based on the The quantum computer includes: The initial state |ψ of the quantum state |ψ ｍ >, a quantum state of nm quantum bits and a state in which nm quantum bit strings are superimposed are added to generate a state in which the solution of the coarse-grained model is embedded in the target system, and the quantum circuit is executed to obtain a measurement result of the eigenvalues ​​of the coefficient matrix.

2. The quantum information processing method according to claim 1.

5. The target system is a system having a repeating structure, the repeating structure includes L unit structures, each unit structure has K mass points, The target system is a system having K×L=N mass points, The first oracle quantum circuit O Ｆ is a first oracle quantum circuit O for the entire target system Ｆ ｆｕｌｌ is expressed by the following formula (1A), where i is an identification number for identifying a spring in the l-th unit structure, and the x-th mass point in the l-th unit structure and l+Δl ｉ y in the th unit structure ｉ is an identification number representing the spring that connects the th mass point, The second oracle quantum circuit O Ｈ is a second oracle quantum circuit O for the entire target system Ｈ ｆｕｌｌ and is represented by the following formula (2A): Δｌ≠０，ｘｙ represents the components of the coefficient matrix at the connection points between different unit structures, and H －１，ｘｙ = -H ＋１，ｙｘ and First oracle quantum circuit of unit structure O Ｆ ｓｕｂ is represented by the following formula (3A): Second Oracle Quantum Circuit of Unit Structure O Ｈ ｓｕｂ is represented by the following formula (4A): The quantum information processing method according to claim 2 . [0010] (1A) 【number】 (2A) 【number】 (3A) 【number】 (4A)

6. A quantum information processing program executed by a classical computer in a hybrid system including a classical computer and a quantum computer, The classical computer transmits to the quantum computer information on a coefficient matrix when an equation of motion of a target system is expressed in a matrix form and a quantum circuit generated based on a quantum state |ψ〉 corresponding to an eigenstate of the target system, the quantum circuit being for performing quantum phase estimation; The quantum computer executes the quantum circuit to obtain measurement results of eigenvalues ​​of the coefficient matrix and transmits the measurement results of the eigenvalues ​​to the classical computer; The classical computer calculates the natural frequency of the target system based on the measurement results of the eigenvalues. A quantum information processing program that allows processing to be performed by a classical computer.

7. A hybrid system including a classical computer and a quantum computer, The classical computer transmits to the quantum computer information on a coefficient matrix when an equation of motion of a target system is expressed in a matrix form and a quantum circuit generated based on a quantum state |ψ〉 corresponding to an eigenstate of the target system, the quantum circuit being for performing quantum phase estimation; The quantum computer executes the quantum circuit to obtain measurement results of eigenvalues ​​of the coefficient matrix and transmits the measurement results of the eigenvalues ​​to the classical computer; The classical computer calculates the natural frequency of the target system based on the measurement results of the eigenvalues. Hybrid system.

8. 1. A hybrid system including a plurality of classical computers and a plurality of quantum computers, One or more classical computers among the multiple classical computers transmit to the quantum computer information on a coefficient matrix when an equation of motion of a target system is expressed in a matrix form and a quantum circuit generated based on a quantum state |ψ〉 corresponding to an eigenstate of the target system, the quantum circuit being for performing quantum phase estimation; One or more quantum computers among the plurality of quantum computers execute the quantum circuit to obtain measurement results of eigenvalues ​​of the coefficient matrix, and transmit the measurement results of the eigenvalues ​​to the classical computer; one or more classical computers among the plurality of classical computers calculates the natural frequencies of the system of interest based on the measurements of the eigenvalues; Hybrid system.

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