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

Abstract

This classical computer transmits, to a quantum computer, a quantum circuit that is for performing quantum phase estimation, and that is generated on the basis of a quantum state |ψ> corresponding to the eigenstate of a target system, and information on a coefficient matrix when the equation of motion of the target system is expressed by a matrix format. The quantum computer acquires a measurement result of the eigenvalue of the coefficient matrix by executing the quantum circuit, and transmits the measurement result of the eigenvalue to the classical computer. The classical computer calculates the eigenfrequency of the target system on the basis of the measurement result of the eigenvalue.

Description

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

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

[0002] Conventionally, a quantum phase estimation algorithm is known, which is an algorithm capable of solving a so-called eigenvalue problem.

[0003] However, Reference 1 (A. Yu. Kitaev, "Quantum measurements and the Abelian Stabilizer Problem", https: / / arxiv.org / abs / quant-ph / 9511026) does not disclose the use of a quantum phase estimation algorithm to calculate the natural frequency.

[0004] The disclosed technology has been developed in consideration of the above 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.

[0005] A quantum information processing method according to a first aspect of the present disclosure is a quantum information processing method executed by a classical computer in a hybrid system including a classical computer and a quantum computer, in which the classical computer transmits to the quantum computer information relating 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 the quantum circuit is for performing quantum phase estimation, the quantum computer executes the quantum circuit to obtain measurement results of the eigenvalues ​​of the coefficient matrix, 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.

[0006] A quantum information processing program of a second aspect of the present disclosure is a quantum information processing program executed by a classical computer in a hybrid system including a classical computer and a quantum computer, in which the classical computer transmits to the quantum computer information relating 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 the quantum circuit is for performing quantum phase estimation, the quantum computer executes the quantum circuit to obtain measurement results of the eigenvalues ​​of the coefficient matrix, 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.

[0007] A hybrid system according to a third aspect of the present disclosure is a hybrid system including a classical computer and a quantum computer, wherein the classical computer transmits to the quantum computer information relating 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, the quantum circuit being for performing quantum phase estimation; the quantum computer executes the quantum circuit to obtain measurement results of the eigenvalues ​​of the coefficient matrix, 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.

[0008] The disclosed technique has the advantage that the natural frequency of a target system can be calculated using a quantum phase estimation algorithm.

[0009] FIG. 1 is a diagram showing an example of a schematic configuration of a hybrid system 100 of this embodiment. FIG. 2 is a schematic block diagram of computers functioning as a classical computer 110, a control device 121, and a user terminal 130. FIG. 3 is a diagram showing an example of a quantum circuit for performing quantum phase estimation. FIG. 4 is a diagram for explaining an adder. Ｆ 1 is a diagram for explaining a second oracle quantum circuit O Ｈ 1 is a diagram for explaining the modified second oracle quantum circuit O Ｈ FIG. 1 is a diagram for explaining an example of a sequence executed by the hybrid system 100 of the present embodiment. FIG. 2 is a diagram for explaining an example of an embodiment. FIG. 3 is a diagram for explaining an example of an embodiment. FIG. 4 is a diagram for explaining an example of an embodiment. FIG. 5 is a diagram for explaining an example of an embodiment. FIG. 6 is a diagram for explaining an example of an embodiment.

[0010] Hereinafter, embodiments of the disclosed technology will be described in detail with reference to the drawings.

[0011] <Hybrid system 100 according to the embodiment>

[0012] Fig. 1 shows a hybrid system 100 according to the first embodiment. The hybrid system 100 of this 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.

[0013] 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 of the quantum computation to the user terminal 130. In this way, the predetermined computation process is executed by the hybrid system 100 as a whole.

[0014] The classical computer 110 includes a communication unit 111 such as a communication interface, a processing unit 112 such as a processor or a central processing unit (CPU), and an information storage unit 113 including a storage device or storage medium such as a memory or a hard disk, and is configured to execute programs 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 on a computer-readable storage medium to form a non-transitory program product.

[0015] As an example, quantum computer 120 generates an electromagnetic wave to be irradiated onto at least 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 one of quantum bits in quantum bit group 123 with the generated electromagnetic wave.

[0016] 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 requests 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 of the quantum computer 120 are also QPUs (Quantum Processing Units). Note that in this embodiment, the term "quantum computer" does not mean a computer that does not perform any operations 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 performs quantum simulations.

[0017] 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.

[0018] The user terminal 130 is a classical computer that performs calculations using classical bits. The user terminal 130 receives information input by a user and executes processing according to the information.

[0019] 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 serving 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 external devices and output devices 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, memory 52, storage unit 53, input / output I / F 54, R / W unit 55, and network I / F 56 are connected to one another via a bus 57.

[0020] [Outline of the Present Embodiment] The hybrid system 100 of the present embodiment calculates the natural frequency of a target system using a quantum phase estimation algorithm. Specifically, the hybrid system 100 of the present embodiment calculates the natural frequency of a target system using the quantum phase estimation algorithm by taking the following four points into consideration:

[0021] (1) A method for preparing the initial state of the natural frequency. (2) A first oracle quantum circuit O Ｆ and the second oracle quantum circuit O Ｈ (3) First oracle quantum circuit O Ｆ and the modified second oracle quantum circuit O Ｈ ｍｏｄ (4) Implementation of quantum circuits that take into account the repetitive structure of the target system.

[0022] The specific details will be explained below.

[0023] [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.

[0024] When 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 This becomes:

[0025] For example, the eigenvectors (c ０ , c １ , ..., c Ｎ－１ ) and the corresponding quantum state |ψ〉 are in one-to-one correspondence as shown in the following equation:

[0026]

[0027] In Figure 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. Note that when the quantum circuit is executed, each quantum bit shown in Figure 3 holds the value of each digit when the eigenvalue, which is the output result, is expressed in binary.

[0028] Furthermore, H in the quantum circuit shown in Fig. 3 represents a Hadamard gate. The Hadamard gate is one of the basic gates used in many quantum computers and can be easily implemented.

[0029] U in the quantum circuit shown in Figure 3 is a quantum circuit equivalent to the unitary matrix for which eigenvalues ​​are to be found. The black circles and vertical lines shown in Figure 3 are symbols that control each U. For example, if the second quantum bit from the top of the quantum circuit shown in Figure 3 connected to the quantum circuit expressed by the following formula is |1>, this indicates that the quantum circuit expressed by the following formula is applied to the superposition component.

[0030]

[0031] Furthermore, since the following equation (A) holds, the following equation (B) corresponds to multiplying U twice.

[0032] (A) (B)

[0033] Also, the QFT shown in FIG. † represents the quantum inverse Fourier transform, which can be realized by known quantum circuits. The rightmost measuring device shown in Figure 3 measures whether each quantum bit is 0 or 1. The measurement result is the binary representation of the eigenvalue obtained as the calculation result.

[0034] [1. Method for preparing the initial state of the eigenfrequency] 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 appropriate method for preparing the initial state when calculating the eigenfrequency has been known.

[0035] Therefore, the classical computer 110 of the hybrid system 100 of this embodiment coarse-grains a model representing the target system, and sets the solution obtained by calculating this coarse-grained model as the initial state |ψ>. Then, the quantum computer 120 of the hybrid system 100 of this embodiment calculates the natural frequency of the target system using the initial state |ψ> obtained by the coarse-grained model. This makes it possible to calculate the natural frequency of the target system with high accuracy. Below, a specific explanation will be given while setting up the problem.

[0036] The model representing the target system is N=2 ｎ In this case, the classical computer 110 generates a model representing the target system with M=2 ｍ By coarse-graining the system into one with M<N particles, the initial state |ψ of the quantum state |ψ ｍ> is classically calculated. For example, the classical computer 110 coarse-grains the model representing the target system by, for example, combining multiple mass points present in the model representing the target system into one. This coarse-grained model having M mass points is assumed to be a model that can be exactly solved by the classical computer 110. For this reason, for example, M is set appropriately by the user. Note that in a system having N mass points, each of the N mass points has a position coordinate, and each of the position coordinates is set as a variable.

[0037] Initial state |ψ ｍ > is a quantum state corresponding to an exact eigenstate and can be represented by m qubits.

[0038] Next, the initial state |ψ represented by m qubits ｍ 〉 is prepared on the quantum computer 120. For example, an initial state |ψ is prepared on the quantum computer 120 by a known QROM method (see, for example, the reference (https: / / journals.aps.org / prx / abstract / 10.1103 / PhysRevX.8.041015)). ｍ > can be prepared.

[0039] Next, the quantum computer 120 calculates the initial state |ψ as shown in the following equation: ｍ >, a quantum state of nm quantum bits, in which nm quantum bit strings are equally superimposed, is added to ｎ （ｍ） >to generate.

[0040]

[0041] Specifically, a |0> state is prepared for all of the nm quantum bits, and a Hadamard gate is applied to each of the nm quantum bits to generate the initial state |ψ ｍ > is added a state in which nm quantum bit strings are equally superimposed. This generates a state in which the solution of the coarse-grained model is embedded in the target system.

[0042] For example, if m=2 and n=4, the new state |ψ ｎ （ｍ） > is expressed by the following formula:

[0043]

[0044] The initial state |ψ obtained in this way ｍ > is a state in which the solution of a coarse-grained model is embedded in a more detailed model, and is useful as an initial state. ｍ By using the above, it becomes possible to accurately calculate the natural frequency of a target system using a quantum computer. As will be described later, the above-described method for preparing an initial state is not limited to calculation of natural frequencies, but can also be used for other techniques. For example, the above-described 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.

[0045] [2. First Oracle Quantum Circuit O Ｆ and the second oracle quantum circuit O Ｈ 3 is very complicated. Therefore, the hybrid system 100 of this embodiment implements the first oracle quantum circuit O Ｆ and the second oracle quantum circuit O Ｈ We implement the quantum circuit U in FIG.

[0046] 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:

[0047] Dominic W. Berry, Andrew M. Childs, "Black-box Hamiltonian simulation and unitary implementation", https: / / arxiv.org / abs / 0910.4157

[0048] Here, consider the case where the coefficient matrix H to be diagonalized is embedded into the quantum circuit U (block encoding). In this case, the first oracle quantum circuit OＦ is configured to satisfy the following equation (1) for the row number x=1,...,N of the coefficient matrix H and the number i=1,...,d of the non-zero components. Ｆ is the position x, y of a non-zero element in the coefficient matrix H ｉ This is a quantum circuit for outputting

[0049] (1)

[0050] y in formula (1) ｉ represents the column number where the i-th non-zero element in the x-th row of the coefficient matrix H exists, 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.

[0051] 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 a quantum bit representing x and y and a quantum bit 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 a binary representation of the component of the xth row and yth column of the coefficient matrix H. Therefore, the second oracle quantum circuit O Ｈ When a position x, y in the coefficient matrix H is specified, the component value H ｘｙ This is a quantum circuit for outputting

[0052] (2) Furthermore, the following symbols in equation (2) represent XOR operations for each quantum bit:

[0053]

[0054] FIG. 4 shows the quantum circuit U embedded in the quantum circuit U of FIG. Ｈ ＊ Specifically, the quantum circuit U shown in FIG. Ｈ ＊corresponds to U in the quantum circuit of FIG. 3. In the following, the quantum circuit U shown in FIG. 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 will be described. ｓｇｎ , a １ , a ２ represents a single ancillary qubit, and a ｓ , s represent groups of quantum bits that hold 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.

[0055] The quantum circuit U shown in FIG. Ｈ ＊ The quantum circuit U shown in FIG. Ｈ ＊ It is known that quantum circuits can sometimes be simplified by performing quantum phase estimation using

[0056] DW Berry and AM Childs, "Black-box hamiltonian simulation and unitary implementation", Quantum Info. Comput. 12 (2012) 29-62, arXiv:0910.4157 [quant-ph].

[0057] Here, consider the case where the coefficient matrix H is a 2-sparse matrix. A 2-sparse matrix is ​​a matrix in which each row has two non-zero elements and the remaining elements are zero. Furthermore, each element H of the coefficient matrix H is ｘｙ is expressed by the following formula:

[0058]

[0059] In this case, the coefficient matrix H is a matrix as shown below.

[0060]

[0061] In addition, the first oracle quantum circuit O Ｆ and the second oracle quantum circuit O Ｈ The basic element in implementing (a) and (b) is the adder. For example, by referring to the following references, it is possible to construct the adder shown in FIG.

[0062] SA Cuccaro, TG Draper, SA Kutin, and DP Moulton, "A new quantum ripple-carry addition circuit", arXiv:quant-ph / 0410184.

[0063] In this embodiment, the first oracle quantum circuit O Ｆ and the second oracle quantum circuit O Ｈ Implement and.

[0064] In this case, the first oracle quantum circuit O Ｆ is a quantum circuit as shown in Figure 6. H shown in Figure 6 ｘ（ｘ＋１） is the binary representation of the element in row x and column x+1 of the coefficient matrix H. On the other hand, the second oracle quantum circuit O Ｈ becomes a quantum circuit as shown in Fig. 7. † represents an adder and its inverse operation († represents an inverse operation).

[0065] In this way, the first oracle quantum circuit O Ｆ and the second oracle quantum circuit O Ｈ By incorporating the above, it becomes possible to calculate the natural frequency of a target system using a quantum computer. Specifically, a first oracle quantum circuit O Ｆ and the second oracle quantum circuit O ＨBy incorporating the first oracle quantum circuit O, it is possible to simplify the quantum circuit for performing quantum phase estimation, and therefore quantum phase estimation can be performed 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.

[0066] [3. First Oracle Quantum Circuit O Ｆ and the modified second oracle quantum circuit O Ｈ ｍｏｄ 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 component H of the coefficient matrix H ｘｙ It is used only to perform gate operations called Controlled-Ry rotation using the angle calculated based on the value of

[0067] Therefore, in this embodiment, the second oracle quantum circuit O Ｈ FIG. 8 shows the modified second oracle quantum circuit O Ｈ As shown in FIG. 8, the modified second oracle quantum circuit O Ｈ contains rotation gates corresponding to the elements of the coefficient matrix H. Specifically, the modified second oracle quantum circuit O Ｈ contains the following two gates: ｙ represents a revolving gate.

[0068]

[0069] These gates differ from the following gates in FIG. 6 in that each element H ｘｙ Since it is not necessary to perform various calculations on the value of , it becomes possible to efficiently perform quantum phase estimation.

[0070]

[0071] Modified second oracle quantum circuit O Ｈ The above-mentioned gate operation is included in the case where there are few kinds of values, for example, when all non-zero elements of the coefficient matrix H are 1, each element H of the coefficient matrix H 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 perform unnecessary processing, quantum phase estimation can be performed efficiently.

[0072] In the above embodiment, a 2-sparse matrix has been described, but the present invention is not limited to this. For example, a d-sparse matrix in which each row has d non-zero elements can also be processed in the same manner as above.

[0073] Also, the modified second oracle quantum circuit O Ｈ contains, as elements, rotation gates corresponding to the respective components of the coefficient matrix H. In this way, the method of calculating angles in advance according to the respective components of the coefficient matrix H can be applied to various algorithms.

[0074] [4. Implementation of a quantum circuit taking into account a repetitive structure in a target system] It is also possible that a target system has a repetitive structure. Therefore, in this embodiment, the first oracle quantum circuit O is implemented taking into account the repetitive structure in the target system. Ｆ and the second oracle quantum circuit O Ｈ Implement.

[0075] Here, consider a case where there are L unit structures that make up the repeating structure, each unit structure has K mass points, and the target system has K×L=N mass points.

[0076] In this case, the first oracle quantum circuit O Ｆ is the first oracle quantum circuit O for the entire system of interest. Ｆ ｆｕｌｌand 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 x-th mass point in the l-th unit structure and l+Δl ｉ y in the th unit structure ｉ It is an identification number that represents the spring that connects the th mass point. ｉ takes on the 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.

[0077] (1A)

[0078] In addition, the above-mentioned 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): H in the following formula (2A) Δｌ≠０，ｘｙ represents the components of the coefficient matrix H at the connection points between different unit structures, and H －１，ｘｙ =-H ＋１，ｙｘ is.

[0079] (2A)

[0080] In this case, the first oracle quantum circuit O Ｆ ｓｕｂ is expressed by the following formula (3A). Ｈ ｓｕｂ is expressed by the following equation (4A).

[0081] (3A) (4A)

[0082] The first oracle quantum circuit O for the entire system Ｆ ｆｕｌｌ is the first oracle quantum circuit O Ｆ ｓｕｂThis can be realized by combining the following addition operation. Also, the second oracle quantum circuit O H ｆｕｌｌ is the second oracle quantum circuit O H ｓｕｂ That is it.

[0083] Furthermore, by combining an identification number l for identifying a unit structure with an identification number x for identifying a mass point within one unit structure, the number X of the mass point of interest within the entire structure can be expressed as follows:

[0084]

[0085] By using the above formula, it becomes possible to consider l and x separately as follows:

[0086]

[0087] Taking the above into consideration, the following equation holds:

[0088]

[0089] 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 O Ｈ ｆｕｌｌ and the usual second oracle quantum circuit O Ｈ The same is true for .

[0090] As described above, the first oracle quantum circuit O Ｆ ｓｕｂ and the second oracle quantum circuit O of the unit structure 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 O for the whole system Ｈ ｆｕｌｌ It is possible to build a

[0091] In this embodiment, the matrix size is N×N where N is the number of mass points, but if the mass points can move in three directions, x, y, and z, the matrix size will be 3N×3N. In such a case, the above-mentioned items can be applied by regarding the mass point label x as the coordinate label (x=1, . . . , 3N).

[0092] [Operation of the Hybrid System 100 of the Embodiment]

[0093] Next, a specific operation of the hybrid system 100 according to the embodiment will be described. Each device in the hybrid system 100 executes the processes shown in FIG.

[0094] First, in step S100, the user terminal 130 transmits to the classical computer 110 computation target information, which is information about the computation target, and computation method information, which is information about the computation method, both input by the user.

[0095] 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 pseudo-quantum computer used by the user).

[0096] 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 ), the number of executions, and various other parameters (for example, the number of digits of the desired eigenvalues, etc.).

[0097] Next, in step S102, the classical computer 110 receives the computation target information and computation method information transmitted from the user terminal 130.

[0098] In step S104, the classical computer 110 uses the method described above to generate a quantum circuit for performing quantum phase estimation based on information about the coefficient matrix H when the equation of motion of the target system is expressed in matrix form and the quantum state |ψ> corresponding to the eigenstate of the target system.

[0099] For example, the classical computer 110 may generate a model representing the target system with M=2 ｍ By coarse-graining the system into one with M<N particles, the initial state |ψ of the quantum state |ψ ｍ Then, the classical computer 110 calculates the initial state |ψ of this quantum state |ψ ｍ 〉 to the quantum state |ψ〉 of the quantum circuit for performing quantum phase estimation.

[0100] Also, for example, the classical computer 110 may implement the first oracle quantum circuit O shown in FIG. Ｆ and the second oracle quantum circuit O shown in FIG. Ｈ into the quantum circuit for state preparation, a quantum circuit for performing quantum phase estimation is generated.

[0101] Also, for example, the classical computer 110 may implement the first oracle quantum circuit O shown in FIG. Ｆ and the second oracle quantum circuit O shown in FIG. Ｈ ｍｏｄ into the quantum circuit for state preparation, a quantum circuit for performing quantum phase estimation is generated.

[0102] Furthermore, for example, the classical computer 110 may generate a first oracle quantum circuit O for the entire target system. Ｆ ｆｕｌｌ , the second oracle quantum circuit O for the entire target system Ｈ ｆｕｌｌ , the first oracle quantum circuit O of the unit structure Ｆ ｓｕｂ, and the second oracle quantum circuit O of the unit structure Ｈ ｓｕｂ into the quantum circuit for state preparation, a quantum circuit for performing quantum phase estimation is generated.

[0103] It should be noted that the quantum circuit for performing quantum phase estimation may be generated by using any one of the above methods, or by combining the above methods.

[0104] In step S106, the classical computer 110 transmits various pieces of 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 estimate generated in step S104.

[0105] 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.

[0106] In step S110, the control device 121 of the quantum computer 120 causes the quantum computer 120 to perform quantum computations according to the various information received in step S108. Specifically, the quantum computer 120 executes the quantum circuit for estimating the quantum phase estimate generated in step S104, thereby acquiring measurement results of the eigenvalues ​​of the coefficient matrix H.

[0107] Specifically, quantum computer 120 generates an electromagnetic wave to be irradiated onto at least one of quantum bits in quantum bit group 123 in accordance with the control of control device 121. Then, quantum computer 120 irradiates the generated electromagnetic wave onto at least one of quantum bits in quantum bit group 123, and executes 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 wave is irradiated onto quantum bit group 123 by electromagnetic wave generating device 122. Then, quantum computer 120 outputs the result of the quantum computation.

[0108] In step S112, the control device 121 transmits the measurement results obtained in step S110 to the classical computer 110.

[0109] In step S114, the classical computer 110 receives the measurement results transmitted from the control device 121 in step S112.

[0110] In step S116, the classical computer 110 calculates the natural frequency of the target system by, for example, appropriately processing the measurement results obtained in step S114. Specifically, because 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 natural frequency. Furthermore, for example, if multiple measurement results are obtained by executing the quantum circuit multiple times, the classical computer 110 calculates the natural frequency of the target system by, for example, taking a majority vote of the multiple measurement results.

[0111] In step S118, the classical computer 110 transmits the calculation result obtained in step S116 to the user terminal 130.

[0112] In step S120, the user terminal 130 receives the results sent from the classical computer 110.

[0113] The user checks the results displayed on the display unit (not shown) of the user terminal 130 .

[0114] As described above, the classical computer of the hybrid system of the embodiment transmits to the quantum computer information regarding 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 that performs quantum phase estimation. The quantum computer executes the quantum circuit to obtain measurement results of the 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.

[0115] Conventionally, there has been no known technology for calculating the eigenfrequency using a quantum phase estimation algorithm. 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.

[0116] More specifically, the classical computer 110 provides 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, quantum phase estimation can be performed efficiently. This allows the quantum computer 120 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.

[0117] In this embodiment, the classical computer 110 also implements 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 gate operations and to more efficiently execute the quantum phase estimation algorithm. Ｈ By removing functions that are not essentially necessary for quantum phase estimation, it has become possible to reduce gate operations and execute the quantum phase estimation algorithm more efficiently.

[0118] In this embodiment, the model representing the target system is coarse-grained to obtain the initial state |ψ of the quantum state |ψ>.ｍ By classically calculating |ψ>, generating a state in which the solution of the coarse-grained model is embedded in the target system, and then executing the quantum circuit, it is possible to calculate the eigenfrequency with high accuracy. For example, compared to when the initial state is random, by setting the result obtained by coarse-graining as the initial state, it is possible to obtain calculation results with high accuracy. In addition, 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.

[0119] For example, the classical computer 110 coarse-grains a model representing a target system to obtain the initial state |ψ of the quantum state |ψ>. ｍ 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 for the generation of an appropriate initial state |ψ even for quantum algorithms other than the eigenfrequency calculation using quantum phase estimation. ｍ >, and it becomes possible to obtain highly accurate calculation results.

[0120] In addition, in this embodiment, when the target system is a system having a repetitive structure, the first oracle quantum circuit O Ｆ ｆｕｌｌ and the second oracle quantum circuit O for the entire system of interest. Ｈ ｆｕｌｌ and the first oracle quantum circuit O Ｆ ｓｕｂ and the second oracle quantum circuit O Ｈ ｓｕｂBy incorporating these into a quantum circuit for performing quantum phase estimation, it has become possible to calculate the natural frequency of a system having a repetitive structure. For example, it has become 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 when 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 when the target system is a system having a repetitive structure is not limited to quantum phase estimation, but can also be applied to other calculations. Ｆ , O Ｈ Any algorithm that utilizes the above can be applied.

[0121] 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 entire 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, various calculations can be performed on systems with repeating structures. For example, when targeting a polymer, the unit structure and mass points may be determined based on the molecular structure of the polymer, and the coefficient matrix H may be obtained from the absorption spectrum of the polymer, and then the natural frequency of the polymer may be calculated using the above-mentioned method.

[0122] 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 other calculations such as fluid calculations are performed, the variable is set to a value corresponding to the fluid calculation.

[0123] Next, examples corresponding to the above-described 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 Hｘｙ is obtained by dividing each element of the coefficient matrix by k.

[0124]

[0125] The first oracle quantum circuit O that is set when calculating the natural frequency of the above system Ｆ corresponds to the quantum circuit of FIG. 7. Also, FIG. 10 shows the first oracle quantum circuit O Ｆ FIG. 1 is a diagram illustrating an example of a quantum circuit incorporating

[0126] In Example 2, the natural frequency of the following equation of motion is calculated. １ , k ２ represents the spring constant and m represents the mass. １ <k ２ is.

[0127]

[0128] FIG. 11 shows the modified second oracle quantum circuit O that is set when calculating the natural frequency of the above system. Ｈ ｍｏｄ FIG. 12 is a diagram showing an example of the first oracle quantum circuit O Ｆ and the modified second oracle quantum circuit O Ｈ ｍｏｄ FIG. 1 is a diagram illustrating an example of a quantum circuit incorporating the above.

[0129] 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 the method of setting the initial state by coarse-graining the target system is verified.

[0130] By classically calculating the values ​​of the following equations, the initial state |ψ ｍ If this calculation is implemented by a quantum circuit, the quantum circuit will be as shown in FIG.

[0131] 14 and 15 show the simulation results. Fig. 14 shows the prepared state when m is changed for n = 10, and it can be seen that accuracy improves by increasing m. Fig. 15 examines the accuracy (infidelity, i.e., the magnitude of error) of the prepared state for various combinations of m and n, and shows that the error is sufficiently small, at 0.1 or less, even when m is as small as 4.

[0132] The technology of the present disclosure is not limited to the above-described embodiments and examples, and various modifications and applications are possible within the scope of the gist of this disclosure.

[0133] For example, in the above embodiment, any method may be used to transmit and receive information between the classical computer 110 and the quantum computer 120. For example, transmission and reception of quantum circuit parameters and 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.

[0134] Furthermore, in the above embodiment, an example has been described in which calculation target information is transmitted from the user terminal 130 to the classical computer 110, and the classical computer 110 executes calculations according to the calculation target information, but 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 then inputs the calculation target information into the classical computer 110 using the storage medium or storage device.

[0135] Furthermore, in the above embodiment, the quantum circuit is executed by irradiating electromagnetic waves, but the present invention is not limited to this, and the quantum circuit may be executed by a different method.

[0136] In the above embodiment, the quantum computer 120 performs the calculations, but the present invention is not limited to this. For example, the calculations may be performed by a classical computer that simulates the behavior of a quantum computer.

[0137] 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 it is not necessary to transmit measurement results from the quantum computer 120 to the classical computer 110. In this case, it is also conceivable that the control device 121 of the quantum computer 120 will play the role of the classical computer 110 in the above description.

[0138] If a quantum computer exists that can replace part or all of the processing of the classical computer described in this embodiment, then part or all of the processing may be performed by the quantum computer.

[0139] It should be noted that in the above embodiments, unless there is a description of "only" such as "based on XX only," "depending only on XX," or "in the case of XX only," this specification assumes that additional information may also be taken into consideration. For example, the description "in the case of a, do b" does not necessarily mean "in the case of a, always do b," unless explicitly stated otherwise.

[0140] Furthermore, in the above embodiments, 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.

[0141] 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 identical to one 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 disclosed technology.

[0142] 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.

[0143] 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.

[0144] For example, the processing performed by the classical computer in each of the above embodiments may be distributed among multiple classical computers connected by a network. Alternatively, the processing performed by the quantum computer in each of the above embodiments may be distributed among multiple quantum computers connected by a network. In this case, a hybrid system is configured by at least one classical computer and at least one quantum computer.

[0145] All publications, patent applications, and technical standards mentioned in this specification are herein incorporated by reference to the same extent as if each individual publication, patent application, or technical standard was specifically and individually indicated to be incorporated by reference.

[0146] (Supplementary Notes) The following supplementary notes are provided regarding aspects of the present disclosure.

[0147] (Supplementary Note 1) A quantum information processing method executed by a classical computer in a hybrid system including a classical computer and a quantum computer, wherein the classical computer transmits to the quantum computer information relating 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 for performing quantum phase estimation; the quantum computer acquires measurement results of the eigenvalues ​​of the coefficient matrix by executing the quantum circuit and 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.

[0148] (Supplementary Note 2) The quantum circuit for performing the quantum phase estimation includes a first oracle quantum circuit O for outputting the position of a non-zero element of the coefficient matrix in the coefficient matrix. Ｆ and a second oracle quantum circuit O for outputting a component value present at a specified position in the coefficient matrix. Ｈ and the quantum circuit for performing the quantum phase estimation is configured to include the first oracle quantum circuit O Ｆ and the second oracle quantum circuit O Ｈ and (c) a quantum circuit in which the coefficient matrix is ​​embedded by incorporating the above.

[0149] (Supplementary Note 3) The quantum circuit for performing the quantum phase estimation includes a first oracle quantum circuit O for outputting the position of a non-zero element of the coefficient matrix in the coefficient matrix. Ｆ and a modified second oracle quantum circuit O including, as elements, rotation gates corresponding to the respective components of the coefficient matrix. Ｈ ｍｏｄ and the quantum circuit for performing the quantum phase estimation is configured to include the first oracle quantum circuit O Ｆ and the modified second oracle quantum circuit O Ｈ ｍｏｄand (c) a quantum circuit in which the coefficient matrix is ​​embedded by incorporating the above.

[0150] (Supplementary Note 4) The model representing the target system is N=2 ｎ The classical computer generates a model representing the target system having M=2 variables. ｍ By coarse-graining the quantum state |ψ〉 into a system having M<N variables, the initial state |ψ ｍ > is classically calculated, and the initial state |ψ of the quantum state |ψ> is calculated. ｍ and generating a quantum circuit for performing the quantum phase estimation based on the quantum state |ψ>, and the quantum computer ｍ >, a quantum state of nm quantum bits and a state in which nm quantum bit strings are superimposed is added to generate a state in which a solution of the coarse-grained model is embedded in the target system, and the quantum circuit is executed to obtain measurement results of the eigenvalues ​​of the coefficient matrix.

[0151] (Supplementary Note 5) The target system is a system having a repeating structure, there are L unit structures constituting the repeating structure, and one unit structure has K mass points, the target system is a system having K×L=N mass points, and the first oracle quantum circuit O Ｆ is the 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 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 a spring connecting 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), and H Δｌ≠０，ｘｙrepresents the components of the coefficient matrix at the connection points between different unit structures, and H －１，ｘｙ =-H ＋１，ｙｘ The first oracle quantum circuit O Ｆ ｓｕｂ is expressed by the following formula (3A), and the second oracle quantum circuit O Ｈ ｓｕｂ is expressed by the following formula (4A): (1A) (2A) (3A) (4A)

[0152] (Supplementary Note 6) A quantum information processing program executed by a classical computer in a hybrid system including a classical computer and a quantum computer, wherein the classical computer transmits to the quantum computer information relating to a coefficient matrix when an equation of motion of a target system is expressed in matrix form, and a quantum circuit for performing quantum phase estimation, the quantum circuit being generated based on a quantum state |ψ> corresponding to an eigenstate of the target system; the quantum computer acquires measurement results of the eigenvalues ​​of the coefficient matrix by executing the quantum circuit, and 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.

[0153] (Supplementary Note 7) A hybrid system including a classical computer and a quantum computer, wherein the classical computer transmits to the quantum computer information relating 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, the quantum circuit being for performing quantum phase estimation; the quantum computer acquires measurement results of the eigenvalues ​​of the coefficient matrix by executing the quantum circuit and 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.

[0154] (Supplementary Note 8) A hybrid system including a plurality of classical computers and a plurality of quantum computers, wherein one or more of the plurality of classical computers transmit to the quantum computer information relating 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, the quantum circuit being for performing quantum phase estimation; one or more of 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; and one or more of the plurality of classical computers calculates the eigenfrequency of the target system based on the measurement results of the eigenvalues.

[0155] The disclosure of Japanese Patent Application No. 2023-116311, filed on July 14, 2023, is incorporated herein by reference in its entirety. All documents, patent applications, and technical standards described herein are incorporated herein by reference to the same extent as if each individual document, patent application, and technical standard was specifically and individually indicated to be incorporated by reference.

Claims

1. A quantum information processing method executed by a classical computer in a hybrid system including a classical computer and a quantum computer, wherein the classical computer transmits to the quantum computer information relating 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 for performing quantum phase estimation; the quantum computer obtains measurement results of the eigenvalues ​​of the coefficient matrix by executing the quantum circuit, and 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.

2. The quantum circuit for performing the quantum phase estimation includes a first oracle quantum circuit O for outputting the position in the coefficient matrix of a non-zero element of the coefficient matrix. Ｆ A second oracle quantum circuit O for outputting a component value at a specified position in the coefficient matrix. Ｈ and a quantum circuit for performing the quantum phase estimation is configured to include the first oracle quantum circuit O Ｆ and the second oracle quantum circuit O Ｈ The quantum information processing method according to claim 1 , wherein the coefficient matrix is ​​embedded in the quantum circuit by incorporating:

3. The quantum circuit for performing the quantum phase estimation includes a first oracle quantum circuit O for outputting the position in the coefficient matrix of a non-zero element of the coefficient matrix. Ｆ A modified second oracle quantum circuit O Ｈ ｍｏｄ and a quantum circuit for performing the quantum phase estimation is configured to include the first oracle quantum circuit O Ｆ and the modified second oracle quantum circuit O Ｈ ｍｏｄ The quantum information processing method according to claim 1 , wherein the coefficient matrix is ​​embedded in the quantum circuit by incorporating:

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

5. The target system is a system having a repetitive structure, and there are L unit structures constituting the repetitive structure, and one unit structure has K mass points, and the target system is a system having K×L=N mass points, and 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 a spring connecting the th mass point and 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 The first oracle quantum circuit O Ｆ ｓｕｂ is expressed by the following formula (3A), and the second oracle quantum circuit O Ｈ ｓｕｂ The quantum information processing method according to claim 2 , wherein is represented by the following formula (4A): (1A) (2A) (3A) (4A) 6. A quantum information processing program executed by a classical computer in a hybrid system including a classical computer and a quantum computer, wherein the classical computer transmits to the quantum computer information relating to a coefficient matrix when the 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 for performing quantum phase estimation; the quantum computer obtains measurement results of the eigenvalues ​​of the coefficient matrix by executing the quantum circuit, and 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. A quantum information processing program for causing a classical computer to execute processing.

7. A hybrid system including a classical computer and a quantum computer, wherein 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 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 obtains measurement results of eigenvalues ​​of the coefficient matrix by executing the quantum circuit and 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.

8. A hybrid system including a plurality of classical computers and a plurality of quantum computers, wherein one or more of the plurality of classical computers transmit to the quantum computer information relating 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, the quantum circuit being for performing quantum phase estimation; one or more of 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; and one or more of the plurality of classical computers calculates the eigenfrequency of the target system based on the measurement results of the eigenvalues.

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