JP2021028847A - Quantum information processing method, classic computer, quantum computer, quantum information processing program, and data structure for obtaining differential of energy - Google Patents

Abstract

To obtain a derivative of energy when performing quantum computation of energy of a system by using VQE(Variational-Quantum-Eigensolver).SOLUTION: A quantum computer 120 executes quantum computation using VQE in accordance with a Hamiltonian and initial information which are outputted from a classic computer 110, to generate a parameter representing a first quantum circuit. The classic computer 110 generates a parameter representing a second quantum circuit including a rotating gate in accordance with the parameter representing the first quantum circuit. Then, the quantum computer 120 executes quantum computation according to the parameter representing the second quantum circuit to output a measurement result of the quantum computation. The classic computer 110 computes a derivative of energy corresponding to the Hamiltonian in accordance with the measurement result, the Hamiltonian, and a derivative of the Hamiltonian to output the derivative of energy.SELECTED DRAWING: Figure 1

Description

The disclosed techniques relate to quantum information processing methods for determining the derivative of energy, classical computers, quantum computers, quantum information processing programs, and data structures.

Conventionally, variational quantum eigenvalue calculation (VQE: Variational-Quantum-Eigensolver) (hereinafter, simply referred to as "VQE") is known (see, for example, Non-Patent Document 1). VQE approximates the minimum eigenvalues of the Hamiltonian by variationally updating the parameters of the quantum circuit. The energy information corresponding to the Hamiltonian's smallest eigenvalues is, for example, useful information in quantum chemistry calculations.

In quantum chemistry calculations, many time-independent physical or chemical properties are often defined using energy derivatives. In this regard, a technique for calculating the derivative of energy by performing quantum phase estimation using quantum calculation by a quantum computer is known (see, for example, Non-Patent Document 2).

A. Peruzzo, J. McClean, P. Shadbolt, M.-H. Yung, X.-Q. Zhou, PJ Love, A. Aspuru-Guzik and JLO'Brien, “A variational eigenvalue solver on a photonic quantum processor , ”Nature Communications, 5, article number: 4213, 2014. I. Kassal and A. Aspuru-Guzik, “Quantum algorithm for molecular properties and geometry optimization”, J. Chem. Phys. 131, 224102 (2009);

However, the VQE disclosed in Non-Patent Document 1 does not consider the derivation of the derivative of energy. Further, the technique disclosed in Non-Patent Document 2 uses quantum phase estimation when calculating the derivative of energy, and calculates the derivative of energy when calculating energy using VQE. That is not disclosed.

The disclosed technology was made in view of the above circumstances, and quantum information for obtaining the energy differentiation, which can obtain the derivative of the energy when the energy of the system is quantum-calculated using VQE. It is an object of the present invention to provide processing methods, classical computers, quantum computers, quantum information processing programs, and data structures.

The quantum information processing method for obtaining the differentiation of the energy of the first aspect of the present disclosure in order to achieve the above object is a quantum information processing method executed by a hybrid system including a classical computer and a quantum computer. The classical computer outputs the Hamiltonian and the initial information of the parameters representing the quantum circuit, and the quantum computer outputs VQE (Variational-Quantum-Eigensolver) according to the Hamiltonian and the initial information output from the classical computer. ) Is executed, a parameter representing the first quantum circuit for calculating energy is generated, a parameter representing the first quantum circuit is output, and the classical computer is transmitted from the quantum computer. A parameter representing the second quantum circuit including the rotating gate is generated according to the output parameter representing the first quantum circuit, and a parameter representing the second quantum circuit is output, and the quantum computer outputs the parameter representing the second quantum circuit. The quantum calculation according to the parameter representing the second quantum circuit output from the classical computer is executed, the measurement result of the quantum calculation is output, and the classical computer outputs the measurement result output from the quantum computer. And, the derivative of the energy corresponding to the Hamiltonian is calculated according to the Hamiltonian and the derivative of the Hamiltonian, and the derivative of the energy is output.

The second aspect of the present disclosure is a quantum information processing method for obtaining the derivative of energy, and the Hamiltonian is a Hamiltonian of a substance.

A third aspect of the present disclosure is a quantum information processing method for obtaining the differentiation of energy, in which the classical computer inserts the rotating gate between a plurality of unitary gates included in the first quantum circuit. By doing so, a parameter representing the second quantum circuit is generated.

The fourth aspect of the present disclosure is a quantum information processing method for obtaining the derivative of energy, and the classical computer is expressed by the following equation (1) when calculating the derivative of the energy in the ground state. The rotating gates R ^± _{a and μ} to be formed are inserted between the plurality of unitary gates included in the first quantum circuit.

(1)
Here, a is an index for identifying an element of the parameter vector θ of the quantum circuit, a, b, c, ..., And μ is an index for identifying the Pauli operator.

The fifth aspect of the present disclosure is a quantum information processing method for obtaining the derivative of energy, and the classical computer is expressed by the following equation (2) when calculating the derivative of the energy in the excited state. The rotating gates R ^{(s), ±} _{a, and μ} are inserted between the plurality of unitary gates included in the first quantum circuit.

(2)
Here, a is an index for identifying the elements of the parameter vector θ of the quantum circuit, a, b, c, ..., μ is an index for identifying the Pauli operator, and s is the excited state. It is an index to represent.

The sixth aspect of the present disclosure is a quantum information processing method for obtaining the differentiation of energy, in which the classical computer and the quantum computer are connected via a computer network, and the classical computer and the quantum computer are connected to each other. Sends and receives information via the computer network.

A seventh aspect of the present disclosure is a quantum information processing method for obtaining a differential of energy, wherein a classical computer outputs Hamiltonian and initial information of parameters representing a quantum circuit, and is output from the quantum computer. Depending on the parameter representing the first quantum circuit generated by the quantum calculation using VQE (Variational-Quantum-Eigensolver) based on the Hamiltonian and the initial information, the parameter representing the second quantum circuit including the rotating gate is set. Generated and output the parameter representing the second quantum circuit, the measurement result of the quantum calculation according to the parameter representing the second quantum circuit output from the quantum computer, the Hamiltonian, and the Hamiltonian It is a quantum information processing method by a classical computer that executes a process that generates a derivative of energy corresponding to the Hamiltonian according to the derivative and outputs the derivative of the energy.

The eighth aspect of the present disclosure is a quantum information processing method for obtaining the differentiation of energy, in which the quantum computer responds to the Hamiltonian H and the initial information of the parameters representing the quantum circuit output from the classical computer. Quantum calculation using VQE (Variational-Quantum-Eigensolver) was executed, a parameter representing the first quantum circuit was generated, a parameter representing the first quantum circuit was output, and the parameter was output from the classical computer. A quantum computer that executes a process that executes a quantum calculation based on a parameter representing a second quantum circuit including a rotating gate corresponding to a parameter representing the first quantum circuit and outputs a measurement result of the quantum calculation. It is a quantum information processing method by.

A ninth aspect of the present disclosure is a classical computer, which outputs Hamiltonian and initial information of parameters representing a quantum circuit, and VQE (Variational-Quantum) based on the Hamiltonian and the initial information output from the quantum computer. -A parameter representing a second quantum circuit including a rotating gate is generated according to a parameter representing the first quantum circuit generated by quantum calculation using (Eigensolver), and a parameter representing the second quantum circuit is generated. The energy corresponding to the Hamiltonian according to the measurement result of the quantum calculation according to the parameter representing the second quantum circuit, the Hamiltonian, and the derivative of the Hamiltonian, which is output and output from the quantum computer. It is a classical computer that executes a process that generates a derivative of the above and outputs a derivative of the energy.

The tenth aspect of the present disclosure is a quantum computer, which performs quantum calculation using VQE (Variational-Quantum-Eigensolver) according to the initial information of parameters representing a Hamiltonian and a quantum circuit output from a classical computer. Generates a parameter representing the first quantum circuit for executing and calculating energy, outputs a parameter representing the first quantum circuit, and represents the first quantum circuit output from the classical computer. It is a quantum computer that executes a process that executes a quantum calculation based on a parameter representing a second quantum circuit including a rotating gate according to the parameter and outputs a measurement result of the quantum calculation.

The eleventh aspect of the present disclosure is a quantum information processing program, which outputs Hamiltonian and initial information of parameters representing a quantum circuit, and VQE (Variational) based on the Hamiltonian and the initial information output from a quantum computer. -Quantum-Eigensolver) generated by the quantum calculation, the parameter representing the second quantum circuit including the rotating gate is generated according to the parameter representing the first quantum circuit for calculating the energy, and the above A parameter representing the second quantum circuit is output, and the measurement result of the quantum calculation according to the parameter representing the second quantum circuit output from the quantum computer, the Hamiltonian, and the derivative of the Hamiltonian are used. Correspondingly, it is a quantum information processing program for causing a classical computer to execute a process of generating an derivative of energy corresponding to the Hamiltonian and outputting the derivative of the energy.

The twelfth aspect of the present disclosure is a quantum information processing program, in which a quantum using VQE (Variational-Quantum-Eigensolver) is used according to the initial information of a parameter representing a Hamiltonian and a quantum circuit output from a classical computer. The first quantum circuit, which is output from the classical computer, executes a calculation, generates a parameter representing a first quantum circuit for calculating energy, outputs a parameter representing the first quantum circuit, and outputs the parameter representing the first quantum circuit. A quantum information program for causing a quantum computer to perform a process of executing a quantum calculation and outputting the measurement result of the quantum calculation based on a parameter representing a second quantum circuit including a rotating gate corresponding to the parameter representing the above. Is.

The thirteenth aspect of the present disclosure is a data structure used for quantum calculation of a quantum computer, which includes a Hamiltonian and initial information of parameters representing a quantum circuit, and VQE (Variational) based on the Hamiltonian and the initial information. -Quantum-Eigensolver) is a data structure used in the process of generating the parameters of the first quantum circuit for calculating the energy of the ground state or the excited state by the quantum calculation by the quantum computer.

A fourteenth aspect of the present disclosure is a data structure relating to the configuration of a quantum circuit used in quantum computing of a quantum computer, including a plurality of unitary gates and a rotating gate inserted between the plurality of unitary gates. It is a data structure used in the process of measuring the measurement result of the quantum calculation by the quantum calculation by the quantum computer based on the quantum circuit including the plurality of unitary gates and the rotating gate.

According to the disclosed technique, when the energy of the system is quantum-calculated using VQE, the effect that the derivative of the energy can be obtained can be obtained.

It is a figure which shows an example of the schematic structure of the hybrid system 100 of this embodiment. FIG. 5 is a schematic block diagram of a computer that functions as a classical computer 110, a control device 121, and a user terminal 130. It is a figure which shows an example of the 2nd quantum circuit schematically. It is a figure which shows an example of the 2nd quantum circuit schematically. It is a figure which shows an example of the calculation process of the derivative of energy by the parameter which represents the state of a system. It is a figure which shows the tentative quantum circuit used for the simulation. It is a figure which shows an example of the simulation result.

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

<Hybrid system 100 according to the first embodiment>

FIG. 1 shows the hybrid system 100 according to the first embodiment. The hybrid system 100 of the present embodiment includes a classical computer 110, 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 to each other via a computer network such as an IP network as an example.

In the hybrid system 100 of the present embodiment, the quantum computer 120 performs a predetermined quantum calculation in response to a request from the classical computer 110, and outputs the calculation result of the quantum calculation to the classical computer 110. The classical computer 110 outputs a calculation result according to the quantum calculation to the user terminal 130. As a result, a predetermined calculation process is executed for the entire hybrid system 100.

The classical computer 110 includes a communication unit 111 such as a communication interface, a processing unit 112 such as a processor and a CPU (Central processing unit), and an information storage unit 113 including a storage device such as a memory and a hard disk or a storage medium. It is configured by executing a program to perform processing. The classical computer 110 may include one or more devices or servers. In addition, the program may include one or more programs, and may be recorded on a computer-readable storage medium to be a non-transient program product.

As an example, the quantum computer 120 generates an electromagnetic wave for irradiating at least one qubit of the qubit group 123 based on the information transmitted from the classical computer 110. Then, the quantum computer 120 executes the quantum circuit by irradiating at least one of the qubits in the qubit group 123 with the generated electromagnetic wave.

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 generation device 122 that generates electromagnetic waves in response to a request from the control device 121, and electromagnetic wave irradiation from the electromagnetic wave generation device 122. It includes a quantum bit group 123 that receives. In the present embodiment, the "quantum computer" does not mean that the operation by the classical bit is not performed at all, but means a computer that includes the operation by the quantum bit.

The control device 121 is a classical computer that performs operations using classical bits, and performs a part or all of the processes described in the present specification as alternatives to those performed by the classical computer 110. For example, the control device 121 stores or determines the quantum circuit in advance, and executes the quantum circuit U (θ) in the qubit group 123 in response to receiving the parameter θ of the quantum circuit U (θ). Quantum gate information may be generated.

The user terminal 130 is a classical computer that performs operations using classical bits. The user terminal 130 receives the information input from the user and executes the process according to the information.

The classical computer 110, the control device 121, and the user terminal 130 can be realized by, for example, the computer 50 shown in FIG. The computer 50 includes a CPU 51, a memory 52 as a temporary storage area, and a non-volatile storage unit 53. Further, the computer 50 has an input / output interface (I / F) 54 to which an external device, an output device, and the like are connected, and a read / write (R / W) unit 55 that controls reading and writing of data to the recording medium 59. Be prepared. Further, the computer 50 includes a network I / F 56 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 each other via the bus 57.

The hybrid system 100 of the first embodiment calculates the derivative of the energy in the ground state. The prerequisites will be described below.

[About VQE]

First, the VQE algorithm will be briefly described.

The quantum computer performs quantum computation based on the quantum circuit U (θ). The relationship between the quantum circuit U (θ) and the quantum state | ψ (θ)> is expressed by the following equation. Note that ψ (θ) represents a wave function.

The term of the following equation represents the state of the initialized n [qubit].

θ is an N-dimensional parameter vector representing a quantum circuit, as shown in the following equation. Further, in the following, θ _p (p = a, b, c, ...) Represents an element of the parameter vector θ of the quantum circuit U (θ). The parameter θ of the quantum circuit U (θ) is information representing the configuration of the quantum circuit. Therefore, the quantum computer executes the quantum calculation according to the parameter θ of the quantum circuit U (θ).

VQE optimizes the parameter θ of the quantum circuit U (θ) so that the energy E (θ) = <ψ (θ) | H | ψ (θ)> corresponding to the given Hamiltonian H is minimized. .. In the parameter θ of the optimum quantum circuit U (θ), the following equation (1) holds for all a.

(1)

Here, the optimum parameter of the quantum circuit U (θ) is θ ^* . When the expression of the following equation (2) is adopted, the above equation (1) is represented by the following equation (3).

(2)


(3)

Further, the higher-order partial derivative of the wave function ψ (θ) by the parameter θ of the quantum circuit U (θ) is expressed by the following equation (4).

(4)

Many of the time-independent physical or chemical properties are calculated based on the derivative of energy with the parameter x representing the state of the system. The parameter x representing the state of the system is, for example, a parameter representing the electric field, the magnetic field, the position coordinates of the atomic nucleus, and the like in the system. In this embodiment, as shown in the following equation, the parameter x representing the state of the system is represented by an M-dimensional vector. Note that x _q (q = i, j, k, ...) Represents an element of the parameter vector x representing the state of the system.

^{The optimum parameter θ *} of the Hamiltonian H and the quantum circuit U (θ) is a function of the parameter x representing the state of the system. Therefore, Hamiltonian H is represented as H (x). ^{The optimum parameter θ *} of the quantum circuit U (θ) is expressed as ^{θ * (x).} Therefore, the energy E of the system is expressed by the following equation (5).

(5)

Here, when the energy of the ground state is E ^* (x), it ^{is expressed as E *} (x) = E ^* (θ ^* (x), x). ^{In this embodiment, the derivative of E *} (θ ^* (x), x) is calculated by the parameter x representing the state of the system as shown in the following equation.

,

,

[Analytical representation of derivatives]

Next, the analytical representation of the derivative of energy will be described below. The derivative of the energy in the ground state is expressed by the following equations (6) to (8).

(6)


(7)


(8)

In the above equations (6) to (8), the following equation is assumed.

Further, the partial derivative with the parameter x of the optimum parameter θ ^* (x) can be obtained by solving the following equations (9) to (10).

(9)


(10)

In addition, γ in the above formula (10) is represented by the following formula (11).

(11)

[Calculation and measurement of derivatives in the ground state]

It is assumed that the hybrid system 100 of the present embodiment operates at n [qubit]. Hamiltonian H is decomposed into the sum of Pauli operators I, X, Y, and Z included in the set of Pauli operators shown in the following equation.

Therefore, Hamiltonian H is represented by the following equation (12).

(12)

_{In addition, h P} (x) in the above formula (12) is a coefficient shown in the following formula.

In order to calculate the derivative of energy, it is necessary to calculate the derivative of Hamiltonian H as shown in the following equation (13).

,

,


(13)

The derivative of Hamiltonian H as shown in the above equation (13) can be calculated by a classical computer. The calculation of the above equation (13) corresponds to the derivative _{of h P (x) in the above equation (12).}

[Quantum circuit representation format]

Next, the representation format of the quantum circuit will be described. In this embodiment, it is assumed that the quantum circuit U (θ) is represented by the product of unitary matrices as shown in the following equation (14).

(14)

Each unitary matrix _{U a (θ a)} is generated by generators _{G a} shown in the following equation. In addition, i represents an imaginary number.

Additional generators _{G a} is represented by the following equation (15).

(15)

[Measurement of second-order partial derivative]

Next, the measurement of the second-order partial derivative of the energy E by the parameter θ of the quantum circuit U (θ) will be described.

In order to obtain the derivative of the energy E by the parameter x representing the state of the system, it is necessary to obtain the information on the derivative of the energy E by the parameter θ of the quantum circuit U (θ) as shown in the following equation.

The first-order partial derivative of the energy E by the parameter θ of the quantum circuit U (θ) as shown in the following equation is described in Reference 1 (Y. Li and SC Benjamin, "Efficient Variational Quantum Simulator Incorporating Active Error Minimization". ", Phys. Rev. X 7, 021050 (2017).) And Reference 2 (K Mitarai, M Negoro, M Kitagawa, K Fujii," Quantum circuit learning ", Physical Review A 98, 032309, 2018). It can be calculated by the technology.

Therefore, the calculation of the second-order partial derivative of the energy E by the parameter θ of the quantum circuit U (θ) as shown in the following equation will be described below.

The above second-order partial derivative is expressed by the following equation (16).

(16)

_{| ∂ a} ψ (θ)> in the above equation (16) is expressed by the following equation (17).

(17)

_{Further, | ∂ a} ∂ _b ψ (θ)> in the above equation (16) is expressed by the following equation (18).

(18)

Here, the definition as shown in the following equation (19) is provided.

(19)

Here, the following equation (20) holds.

(20)

FIG. 3 shows an explanatory diagram for explaining the quantum circuit of the present embodiment. The quantum circuit shown in FIG. 3 is a quantum circuit for calculating the second-order partial derivative of the energy E by the parameter θ of the quantum circuit U (θ) shown in the above equation (20).

For U in the quantum circuit shown in FIG. 3, the following equation holds.

^{Further, R ±} _{a, μ} and R ^± _{b, ν} shown in FIG. 3 represent a rotating gate. The rotating gates R ^± _{a, μ} and R ^± _{b, ν} are represented by the following equation (21). In addition, "±" appearing as a subscript in the following equation is a code determined according to parity.

(21)

Note that a and b in the above equation (21) are indexes for identifying the element of the parameter θ of the quantum circuit U (θ) as shown in the above equation (15) and the like. Further, μ in the above equation (21) is an index related to a generator that generates _a unitary U a, and is set in advance, as shown in the above equation (15) and the like.

In this embodiment, the quantum computer 120 measures the quantity represented by the following equation based on the quantum circuit shown in FIG.

Therefore, the term of the following equation included in the above equation (20) is quantum-calculated by the quantum computer 120, and the calculation result is measured.

(22)

Therefore, the second-order partial derivative of the energy E represented by the above equation (20) can be obtained based on the calculation result of the quantum calculation of the above equation (22).

[Measurement of third-order partial derivative]

Next, the measurement of the third-order partial derivative of the energy E by the parameter θ of the quantum circuit U (θ) will be described.

The third-order partial derivative of the energy E according to the parameter θ of the quantum circuit U (θ) is expressed by the following equation (23).

(23)

FIG. 4 shows a quantum circuit for calculating the third-order partial derivative of the energy E by the parameter θ of the quantum circuit U (θ). ^{In addition, R ±} _{c, ρ} shown in FIG. 4 is expressed by the following equation.

In this embodiment, the quantum computer 120 measures the quantity represented by the following equation based on the quantum circuit shown in FIG.

Therefore, the term of the following equation included in the above equation (23) is quantum-calculated by the quantum computer 120, and the calculation result is measured.

(24)

Therefore, based on the calculation result of the quantum calculation of the above equation (24), the third-order partial derivative of the energy E shown in the above equation (23) can be obtained.

[Measurement of other partial derivatives]

Next, the calculation of the higher-order partial derivative of the energy E will be described. The derivative of energy E shown in the following equation (25A) is calculated by the same procedure as the above-mentioned procedure.

(25A)

The derivative represented by the above equation (25A) includes a derivative of energy E according to the parameter x representing the state of the system. Here, regarding the derivative of the energy E according to the parameter x, for example, by substituting the derivative as shown in the following equation into _{h Q represented by the above equation (20) and the above equation (23), the above} The derivative of equation (25A) can be calculated. Since the following equation corresponds to the Hamiltonian derivative, it can be calculated by the classical computer 110.

Further, for example, a derivative such as the following equation (25B) that appears in the above equation (8) can be calculated by the same procedure.

(25B)

[Outline of operation of the hybrid system 100 of this embodiment]

The hybrid system 100 of the present embodiment executes each of the above calculation processes by the classical computer 110 and the quantum computer 120. Specifically, the hybrid system 100 calculates the derivative of the energy E according to the following procedures (A) to (F).

(A) The quantum computer 120 of the hybrid system 100 executes VQE ^{to obtain the optimum parameter θ *} (x) of the quantum circuit U (θ).

(B) The classical computer 110 of the hybrid system 100 calculates the derivative of Hamiltonian H as shown in the above equation (13).

(C) The classical computer 110 of the hybrid system 100 sets the derivative of the energy E for the parameter x representing the state of the system according to the above equations (6) to (8).

(D) The quantum computer 120 of the hybrid system 100 obtains the derivative of the energy E by the parameter θ of the quantum circuit U (θ).

(E) The classical computer 110 of the hybrid system 100 has a quantum circuit U (θ) with a parameter x representing the state of the system as shown in the following equations according to the above equations (9), (10), and (11). Find the derivative of the optimum parameter θ ^{* of.}

The terms of the following equations included in the above equations (9), (10), and (11) are obtained in the above equation (D). Therefore, by substituting the terms of the following equation obtained in the above equation (D) into the above equations (9), (10), and (11), the quantum circuit U (θ) by the parameter x representing the state of the system ) Parameter θ ^* is calculated.

,

,

,

,

(F) The classical computer 110 of the hybrid system 100 substitutes each term calculated in the above (A) to (E) into the above equations (6) to (8) to obtain a parameter x representing the state of the system. Obtain the derivative of energy E.

[Operation of the hybrid system 100 of the first embodiment]

Next, the specific operation of the hybrid system 100 of the first embodiment will be described. In each device of the hybrid system 100, each process shown in FIG. 5 is executed.

First, in step S100, the user terminal 130 transmits the problem information input by the user to the classical computer 110. The problem information is information about a problem solved by quantum calculation, and includes, for example, information about a substance to be analyzed and information about a physical property value of the substance. Examples of information on the substance to be analyzed include molecular parameters of the substance, and examples of information on physical property values include the dielectric constant of the molecule to be analyzed.

Next, in step S102, the classical computer 110 receives the problem information transmitted from the user terminal 130. Then, in step S102, the classical computer 110 calculates the Hamiltonian H representing the energy state of the system of the molecule according to the above formula (12) based on the information about the molecule of the substance in the received problem information. _{In addition, h P} (x) in the above formula (12) is set according to the information about the molecule of the substance to be analyzed.

In step S104, the classical computer 110 calculates the derivative of Hamiltonian H based on the Hamiltonian H calculated in step S102. Specifically, the classical computer 110 calculates the derivative of Hamiltonian H represented by the above equation (13) by the existing library software for quantum chemistry calculation.

In step S106, the classical computer 110 outputs the initial information of the Hamiltonian H calculated in step S102 and the parameter θ representing the quantum circuit. Specifically, the Hamiltonian H calculated in step S102, the initial information of the parameters representing the quantum circuit U (θ), and the optimization method are transmitted to the quantum computer 120. Examples of the optimization method include the Nelder-Mead method and the like.

In step S106, the data transmitted from the classical computer 110 to the quantum computer 120 is a data structure used in the quantum calculation of the quantum computer, and includes a Hamiltonian and initial information of parameters representing a quantum circuit. This data structure is used in the process of generating the parameters of the first quantum circuit for calculating the energy of the ground state or excited state by quantum calculation using VQE based on Hamiltonian and initial information.

In step S108, the control device 121 receives the Hamiltonian H, the initial information, and the optimization method transmitted from the classical computer in step S106. Then, the control device 121 causes the quantum computer 120 to execute the quantum calculation using the VQE according to the Hamiltonian H, the initial information, and the optimization method.

Specifically, the quantum computer 120 generates an electromagnetic wave for irradiating at least one of the qubits 123 in the quantum bit group 123 under the control of the control device 121. Then, the quantum computer 120 is the optimum quantum circuit by irradiating at least one of the qubits of the quantum bit group 123 with the generated electromagnetic wave and executing the quantum circuit according to the initial information. Generate the ^{parameter θ *} that represents the quantum circuit of 1. The gate operation of each quantum gate included in the quantum circuit is converted into the corresponding electromagnetic wave waveform, and the generated electromagnetic wave is applied to the qubit group 123 by the electromagnetic wave generator 122. Then, the quantum computer 120 outputs a ^{parameter θ * representing the first quantum circuit.}

^{In step S110, the control device 121 transmits the parameter θ *} representing the first quantum circuit obtained in step S108 to the classical computer 110.

In step S112, the classical computer 110 receives the ^{parameter θ *} representing the first quantum circuit transmitted from the control device 121 in step S110. Then, the classical computer 110 generates a parameter representing the second quantum circuit including the rotating gate according to the ^{parameter θ * representing the first quantum circuit.}

Specifically, the classical computer 110 generates a second quantum circuit as shown in FIGS. 3 and 4 according to the ^{parameter θ * representing the first quantum circuit.} The second quantum circuit is a quantum circuit in which a rotating gate represented by the above equation (21) is inserted between a plurality of unitary gates included in the first quantum circuit corresponding to the ^{optimum parameter θ *.}

By inserting the rotating gate between the plurality of unitary gates included in the first quantum circuit, a second quantum circuit for calculating the derivative of the energy E is generated. When the second quantum circuit is executed by the quantum computer 120, the quantities represented by the above equations (22) and (24) are calculated.

In step S114, the classical computer 110 transmits to the quantum computer 120 a parameter representing the second quantum circuit generated in step S112.

In step S114, the data transmitted from the classical computer 110 to the quantum computer 120 is a data structure relating to the configuration of the quantum circuit used for the quantum calculation of the quantum computer 120, and is between the plurality of unitary gates and the plurality of unitary gates. Includes an inserted rotating gate. This data structure is used in the process of measuring the measurement result of a quantum calculation by a quantum calculation based on a quantum circuit including a plurality of unitary gates and a rotating gate.

In step S116, the control device 121 receives the parameter representing the second quantum circuit transmitted from the classical computer in step S114. Then, the control device 121 causes the quantum computer 120 to execute the quantum calculation according to the second quantum circuit. The quantum computer 120 executes a quantum calculation according to a parameter representing the second quantum circuit.

Specifically, the quantum computer 120 generates an electromagnetic wave for irradiating at least one of the qubits 123 in the quantum bit group 123 under the control of the control device 121. Then, the quantum computer 120 measures the information observed by executing the second quantum circuit by irradiating at least one qubit of the qubit group 123 with the generated electromagnetic wave. Then, the quantum computer 120 outputs the measurement result obtained by the quantum calculation.

For example, a bit string as shown in the table below is obtained as a measurement result. The table below shows the number of samples obtained when a quantum circuit is executed. In the table below, when the quantum circuit is executed, the information of "0000" is "10" times, the information of "0001" is "50" times, the information of "0010" is "14" times, "0011". It is shown as an example that the information of "2" is obtained "12" times and the information of "0100" is obtained "85" times.

In step S118, the control device 121 transmits the measurement result obtained in step S116 to the classical computer 110.

In step S120, the classical computer 110 receives the measurement result transmitted from the control device 121 in step S118. Then, the classical computer 110 statistically processes the measurement results to obtain the second-order partial derivative of the energy E according to the parameter θ shown in the above equation (20) and the energy E according to the parameter θ shown in the above equation (23). Calculate with the third-order partial derivative of. Specifically, the classical computer 110 calculates the expected value of the partial derivative by statistically processing the obtained bit string. Further, the classical computer 110 calculates the first-order partial derivative of the energy E by the parameter θ by using the technique disclosed in Reference 1 above. Further, the classical computer 110 calculates a derivative as shown in the above formula (25A) and the above formula (25B).

In step S122, the classical computer 110 includes each of the derivative of Hamiltonian H calculated in step S104 and the derivative of energy E according to the parameter θ according to the measurement result of the quantum calculation obtained in step S120. Corresponds to, the derivative of the energy E with the parameter x representing the state of the system corresponding to the Hamiltonian H is calculated.

Specifically, in step S122, the classical computer 110 includes the Hamiltonian H calculated in step S102, the derivative of Hamiltonian H calculated in step S104, and each derivative calculated in step S120. Is substituted into the above equation (6), the above equation (7), and the above equation (8) to calculate each of the derivatives of the energy E by the parameter x representing the state of the system.

In step S124, the classical computer 110 obtains the physical property value of the problem information received in step S102 based on each of the derivatives of the energy E by the parameter x representing the state of the system obtained in step S122. calculate. As a result, the physical property value of the molecule of the substance corresponding to the problem information transmitted from the user terminal 130 can be obtained.

In step S126, the classical computer 110 transmits the calculation result of the physical characteristic value obtained in step S124 to the user terminal 130.

In step S128, the user terminal 130 receives the calculation result of the physical characteristic value transmitted from the classical computer 110 in step S124.

As described above, in the hybrid system of the first embodiment, the classical computer outputs the Hamiltonian H and the initial information of the parameters representing the quantum circuit. Then, the quantum computer executes the quantum calculation using VQE according to the Hamiltonian and the initial information output from the classical computer, and sets the parameter representing the first quantum circuit for calculating the energy of the ground state. Generate and output the parameters representing the first quantum circuit. Then, the classical computer generates a parameter representing the second quantum circuit including the rotating gate according to the parameter representing the first quantum circuit output from the quantum computer, and outputs a parameter representing the second quantum circuit. To do. Then, the quantum computer executes the quantum calculation according to the parameter representing the second quantum circuit output from the classical computer, and outputs the measurement result of the quantum calculation. Then, the classical computer calculates the derivative of the energy corresponding to the Hamiltonian according to the measurement result output from the quantum computer and the derivative of the Hamiltonian, and outputs the derivative of the energy. This makes it possible to obtain the energy derivative when quantum computing the energy of the system using VQE.

In addition, by appropriately dividing the roles between the classical computer and the quantum computer, when the energy of the system is quantum-calculated using VQE, the derivative of the energy E by the parameter x representing the state of the system can be efficiently obtained. Can be done.

Specifically, the classical computer calculates the derivatives of Hamiltonian H and Hamiltonian H, and the quantum computer quantum-calculates the derivative of VQE and the energy E according to the parameter θ of the quantum circuit. As a result, the derivative of the energy E with the parameter x representing the state of the system can be efficiently obtained.

Further, in the present embodiment, a shallow quantum circuit as shown in FIGS. 3 and 4 is used to calculate the derivative of the energy E by the parameter x representing the state of the system. Such a shallow quantum circuit is useful when using a NISQ (Noisy Intermediate-Scale Quantum Computer) device. Therefore, according to the present embodiment, it is possible to efficiently obtain the derivative of the energy E by the parameter x representing the state of the system while suppressing the error of the quantum calculation.

<Hybrid system 100 according to the second embodiment>

Next, the second embodiment will be described. Since the configuration of the hybrid system according to the second embodiment has the same configuration as that of the first embodiment, the same reference numerals are given and the description thereof will be omitted.

The hybrid system 100 of the second embodiment calculates the derivative of the energy in the excited state.

Techniques for calculating the energy of the excited state using VQE are disclosed in References 3 to 6 below.

Reference 3: KM Nakanishi, K. Mitarai, and K. Fujii, “Subspace-search variational quantum eigensolver for excited states”, (2018), arXiv: 1810.09434.
Reference 4: S. Endo, T. Jones, S. McArdle, X. Yuan, and S. Benjamin, “Variational quantum algorithms for discovering Hamiltonian spectra”, (2018), arXiv: 1806.05707.
Reference 5: O. Higgott, D. Wang, and S. Brierley, “Variational Quantum Computation of Excited States”, (2018), arXiv: 1805.08138.
Reference 6: JR McClean, ME Kimchi-Schwartz, J. Carter, and WA de Jong, “Hybrid quantum-classical hierarchy for mitigation of decoherence and determination of excited states”, Phys. Rev. A 95, 042308 (2017).

In the second embodiment, a case where the derivative of the energy in the excited state is calculated by using the technique disclosed in Reference 4 or Reference 5 will be described as an example.

Assuming that the ground state of a given Hamiltonian is H ₀ (x), the r-th excited state Hamiltonian H _r (x) is expressed by the following equation (26). In the following equation (26), it is assumed that _{β s is sufficiently large.} Further, the indexes r = 1, 2, ... Representing the excited state.

(26)

In the above equation (26), the ground state is expressed by the following equation.

^{Θ (0) and} (x) in the above equation represent the optimum parameters of the quantum circuit U (θ) in the ground state. In the first embodiment, the optimum parameter of the quantum circuit U (θ) in the ground state is ^{represented by θ *} (x), but in the second embodiment, the optimum parameter of the quantum circuit U (θ) in the ground state is optimal. The parameters are ^{represented by θ (0)} (x). Further, in the second embodiment, it is assumed that the following equation is established. ^{The U (r)} (θ) of the following equation has the same structure as the U (θ) of the first embodiment.

The quantum computer 120 of the hybrid system 100 of the second embodiment needs to calculate the inner product of two quantum states. Therefore, the quantum computer 120 of the second embodiment is a quantum computer capable of calculating the inner product of two quantum states.

The expected value in the state of Hamiltonian H _r (x) | ψ ^(r) (θ)> is expressed by the following equation.

The optimum energy in the r-th excited state is defined by the following equation.

The hybrid system 100 of the second embodiment calculates the derivative ^{of the energy E *} of the excited state by the parameter x representing the state of the system. Incidentally, for the Hamiltonian H _r of the r th excited state, energy E r th excited state _r ^* corresponds to the energy of the ground state. Therefore, the above equations (6), (7), and (8) can also be applied when calculating the derivative ^{of the excited energy E *.}

The above equation (6) corresponds to the first-order partial derivative of the energy E in the r-th excited state according to the parameter x representing the state of the system. Further, the above equation (7) corresponds to the second-order partial derivative of the energy E of the r-th excited state by the parameter x representing the state of the system. The first-order partial derivative of the energy E in the r-th excited state and the second-order partial derivative of the energy E in the r-th excited state are expressed by the following equations.

,

However, classical computer 110 is unable to compute the derivative of the Hamiltonian H _r of the excited state. Derivative of the Hamiltonian H _r of the excited state is represented by the following equation (27).

(27)

When the above equation (27) is substituted for the above equation (6), the following equation appears. The quantum computer 120 of the hybrid system 100 of the second embodiment quantum-calculates the following equation.

[Measurement of inner product]

The inner product of the quantum states as shown in the following equation is expanded into the form shown in the following equation (28).

(28)

^{Φ (s)} _{(a, μ} ) in the above formula (28) follows the above formula (19). Each term in Σ in the above equation (28) is calculated by the following relational expression.

(29)

The quantum computer 120 of the second embodiment quantum-calculates the left side of the above equation (29) and the first and second terms on the right side of the above equation (29). Further, the classical computer 110 of the second embodiment has the third term on the right side of the above equation (29) based on the calculation result of the quantum calculation of the first term and the second term on the left side and the right side of the above equation (29). To calculate.

In order to calculate the left side of the above equation (29), it is necessary to calculate the quantum state of the following equation.

The quantum state represented by the above equation is represented by the quantum circuit represented by the following equation (30A) and can be easily generated.

(30A)

The above formula (30A) corresponds to, for example, inserting a rotary gate between a plurality of unitary gates. For example, the rotating gates R ^{(s), +} _{a, and μ} shown in the following equation are inserted between the a-th unitary gate and the a-1st unitary gate.

(30B)

The quantum computer 120 measures the left side of the above equation (29) by executing a quantum circuit in which a rotating gate is inserted between a plurality of unitary gates.

The above method can be extended to other terms. For example, when the following equation (31) corresponding to the above equation (6) is expanded, a term such as the following equation (32) appears.

(31)

(32)

When the above formula (32) is quantum-calculated, the following formula (33) is used.

(33)

The calculation of the above formula (32) can be performed by calculating all the terms on the right side of the above formula (33) using the quantum computer 120.

In order to calculate the quantum state of each of the above equations, in the second embodiment, the rotating gates R ^{(s), ±} _{a, μ} and R ^{(r), ±} _{a, μ} shown in the following equations are between the unitary gates. Will be inserted.

[Operation of the hybrid system 100 of the second embodiment]

Next, the specific operation of the hybrid system 100 of the second embodiment will be described. Similar to the first embodiment, in each device of the hybrid system 100 of the second embodiment, each process shown in FIG. 5 is executed.

Each process of steps S100 to S110 is executed in the same manner as in the first embodiment.

In step S112, the classical computer 110 of the second embodiment generates a parameter representing the second quantum circuit including the rotating gate according to the ^{parameter θ * representing the first quantum circuit.}

Specifically, the classical computer 110 of the second embodiment has a rotating gate represented by the above equation (30B) between a plurality of unitary gates included in the first quantum circuit corresponding to the ^{optimum parameter θ *.} Insert to generate a second quantum circuit.

Each process of steps S114 to S126 is executed in the same manner as in the first embodiment.

As described above, in the hybrid system of the second embodiment, when the classical computer calculates the derivative of the energy of the excited state, the rotating gate corresponding to the excited state s is included in the first quantum circuit. Insert between multiple unitary gates. As a result, when the energy of the system is quantum-calculated using VQE, the derivative of the energy of the excited state can be obtained.

Next, an embodiment will be described. In this example, a numerical simulation was performed using an electron Hamiltonian of hydrogen molecules. In this example, the existing open source library PySCF (Reference 6 (Q. Sun, TC Berkelbach, NS Blunt, GH Booth, S. Guo, Z. Li, J. Liu, JD McClain, ER Sayfutyarova, S) See Sharma, S.Wouters, and GK Chan, Wiley Interdisciplinary Reviews: Computational Molecular Science 8, e1340 (2017).) And OpenFermion (Reference 7 (JR McClean, KJ Sung, ID Kivlichan, Y. Cao,). C. Dai, ES Fried, C. Gidney, B. Gimby, P. Gokhale, T. Hner, T. Hardikar, V. Havlek, O. Higgott, C. Huang, J. Izaac, Z. Jiang, X. Liu , S. McArdle, M. Neeley, T. O'Brien, B. O'Gorman, I. Ozdan, MD Radin, J. Romero, N. Rubin, NPD Sawaya, K. Setia, S. Sim, DS Steiger, Hamiltonian was calculated using M. Steudtner, Q. Sun, W. Sun, D. Wang, F. Zhang, and R. Babbush, (2017), arXiv: 1710.07629.). The simulation was performed using Qulacs (Qulacs, "https://github.com/qulacs/qulacs.").

FIG. 6 is a quantum circuit used for numerical simulation. Ry and Rx represent a y-axis rotating gate and an x-axis rotating gate, respectively. In FIG. 7, using the quantum circuit of FIG. 6 and the Hamiltonian of the hydrogen molecule, this method is numerically simulated as the distance between hydrogen atoms as the parameter x of the Hamiltonian, and the second-order and third-order differentials of energy are obtained to obtain the energy curve. This is a drawing of a quadratic approximation curve and a cubic approximation curve of. In FIG. 7, "Full CI" represents a theoretical value, "Harmonic approx." Represents a quadratic approximation curve, "3rd-oder approx." Represents a cubic approximation curve, and "Enegy minimum" represents a quadratic approximation curve. Represents the minimum value of energy. As shown in FIG. 7, it can be seen that the approximate curve is obtained with high accuracy.

The technique of the present disclosure is not limited to the above-described embodiment, and various modifications and applications are possible without departing from the gist of the present invention.

For example, in each of the above embodiments, information may be transmitted and received between the classical computer 110 and the quantum computer 120. For example, the transmission / reception of parameters representing a quantum circuit, the transmission / reception of measurement results, and the like between the classical computer 110 and the quantum computer 120 may be sequentially transmitted / received each time a predetermined calculation is completed, or all calculations may be performed. Transmission and reception may be performed after the completion of.

Further, in each of the above embodiments, the case where the problem information is transmitted from the user terminal 130 to the classical computer 110 and the classical computer 110 calculates the Hamiltonian H according to the problem information has been described as an example, but the present invention is limited to this. is not it. For example, if the user who operates the user terminal 130 can express the problem as a Hamiltonian, the classical computer 110 may receive the Hamiltonian H as the problem information. The user terminal 130 may transmit the problem information to the storage medium or storage device accessible to the classical computer 110 or the classical computer 110 via a computer network such as an IP network, but the problem information is stored in the storage medium or storage device. It may be handed over to the operator of the classical computer 110, and the operator may input the problem information into the classical computer 110 using the storage medium or the storage device.

Further, in each of the above embodiments, the problem information includes information on the substance to be analyzed and information on the physical property value of the substance, and the physical property value is calculated based on the derivative of the energy E corresponding to the substance to be analyzed. The case where this is done has been described as an example, but the present invention is not limited to this. For example, information about a predetermined optimization problem may be given as problem information. In this case, the hybrid system 100 calculates the derivative of the energy E with the parameter x representing the state of the system for a given optimization problem. For example, when the traveling salesman problem, which is an example of an optimization problem, is given as problem information, a cost function representing the sum of the distances between the places to be visited is set as the energy function E, and the places to be visited are to be visited. The derivative of the cost function with the parameter x representing the distance between them is calculated.

Further, in each of the above embodiments, as shown in the above equations (21) and (30B), the case where the angle of the rotating gate is π / 4 has been described as an example, but the present invention is not limited to this. It can be any angle. For example, the angle of the rotating gate may be π / 3. When changing the angle of the rotating gate, the above formula (21) and the above formula (30B) are transformed into an appropriate form according to the angle of the rotating gate.

Further, in each of the above embodiments, the case where the quantum circuit is executed by irradiation with electromagnetic waves has been described as an example, but the present invention is not limited to this, and the quantum circuit may be executed by a different method.

Further, in each of the above embodiments, it is assumed that the classical computer 110 and the quantum computer 120 are managed by different organizations, but even if the classical computer 110 and the quantum computer 120 are integrally managed by the same organization. Good. In this case, it is not necessary to transmit the quantum calculation information from the classical computer 110 to the quantum computer 120 and the measurement result from the quantum computer 120 to the classical computer 110. Further, in this case, it is conceivable that the control device 121 of the quantum computer 120 plays the role of the classical computer 110 in the above description.

In each of the above embodiments, unless there is a description of "only" such as "based on XX only", "according to XX only", and "in the case of XX only", the present specification. Note that it is assumed that additional information can also be considered in. As an example, the description "b in the case of a" does not necessarily mean "always b in the case of a" except when explicitly stated.

Further, even if some method, program, terminal, device, server or system (hereinafter referred to as "method") performs an operation different from the operation described in the present specification, each aspect of the disclosed technology is described. It is intended to be the same operation as any of the operations described in the present specification, and the existence of an operation different from the operation described in the present specification describes the method and the like in each aspect of the technique of the present disclosure. It is not out of the range of.

Further, although described as an embodiment in which the program is pre-installed in the specification of the present application, it is also possible to provide the program by storing it in a computer-readable recording medium.

100 Hybrid system 110 Classical computer 111 Communication unit 112 Processing unit 113 Information storage unit 120 Quantum computer 121 Control device 122 Electromagnetic wave generator 123 Qubit group 130 User terminal

Claims (14)

A quantum information processing method executed by a hybrid system including a classical computer and a quantum computer.
The classical computer outputs the Hamiltonian and the initial information of the parameters representing the quantum circuit.
The first quantum computer for calculating energy by executing quantum calculation using VQE (Variational-Quantum-Eigensolver) according to the Hamiltonian and the initial information output from the classical computer. Generate a parameter representing the quantum circuit, output the parameter representing the first quantum circuit, and output the parameter.
The classical computer generates a parameter representing a second quantum circuit including a rotating gate according to a parameter representing the first quantum circuit output from the quantum computer, and a parameter representing the second quantum circuit. Output,
The quantum computer executes a quantum calculation according to a parameter representing the second quantum circuit output from the classical computer, and outputs a measurement result of the quantum calculation.
The classical computer calculates the derivative of the energy corresponding to the Hamiltonian according to the measurement result output from the quantum computer, the Hamiltonian, and the derivative of the Hamiltonian, and obtains the derivative of the energy. Output,
A quantum information processing method for obtaining the derivative of energy including processing. The Hamiltonian is a substance Hamiltonian,
The quantum information processing method for obtaining the derivative of energy according to claim 1. The classical computer generates a parameter representing the second quantum circuit by inserting the rotating gate between a plurality of unitary gates included in the first quantum circuit.
The quantum information processing method for obtaining the derivative of energy according to claim 1 or 2. When calculating the derivative of the energy in the ground state, the classical computer uses a plurality of unitaries including the ^{rotating gates R ±} _{a and μ represented by the following equation (1) in the first quantum circuit.} Insert between the gates,
The quantum information processing method for obtaining the derivative of energy according to claim 3.






(1)
Here, a is an index for identifying an element of the parameter vector θ of the quantum circuit, a, b, c, ..., And μ is an index for identifying the Pauli operator. ^{The classical computer includes the rotating gates R (s), ±} _{a, μ} represented by the following equation (2) in the first quantum circuit when calculating the derivative of the energy in the excited state. Insert between multiple unitary gates,
The quantum information processing method for obtaining the derivative of energy according to claim 3.






(2)
Here, a is an index for identifying the elements of the parameter vector θ of the quantum circuit, a, b, c, ..., μ is an index for identifying the Pauli operator, and s is the excited state. It is an index to represent. The classical computer and the quantum computer are connected via a computer network.
The classical computer and the quantum computer transmit and receive information via the computer network.
The quantum information processing method for obtaining the derivative of energy according to any one of claims 1 to 5. Classic computer,
Outputs the Hamiltonian and the initial information of the parameters representing the quantum circuit,
A second including a rotating gate according to a parameter representing a first quantum circuit generated by a quantum calculation using VQE (Variational-Quantum-Eigensolver) based on the Hamiltonian and the initial information output from a quantum computer. A parameter representing the second quantum circuit is generated, and a parameter representing the second quantum circuit is output.
The measurement result of the quantum calculation according to the parameter representing the second quantum circuit output from the quantum computer, and the derivative of the energy corresponding to the Hamiltonian according to the Hamiltonian and the derivative of the Hamiltonian. And output the derivative of the energy,
A quantum information processing method for finding the derivative of the energy that executes processing. Quantum computer
Quantum calculation using VQE (Variational-Quantum-Eigensolver) is executed according to the initial information of Hamiltonian H and the parameter representing the quantum circuit output from the classical computer, and the parameter representing the first quantum circuit is generated. Then, the parameter representing the first quantum circuit is output, and
Quantum calculation is executed based on the parameter representing the second quantum circuit including the rotation gate corresponding to the parameter representing the first quantum circuit output from the classical computer, and the measurement result of the quantum calculation is output. To do,
A quantum information processing method for finding the derivative of the energy that executes processing. Outputs the Hamiltonian and the initial information of the parameters representing the quantum circuit,
A second including a rotating gate according to a parameter representing a first quantum circuit generated by a quantum calculation using VQE (Variational-Quantum-Eigensolver) based on the Hamiltonian and the initial information output from a quantum computer. A parameter representing the second quantum circuit is generated, and a parameter representing the second quantum circuit is output.
The measurement result of the quantum calculation according to the parameter representing the second quantum circuit output from the quantum computer, and the derivative of the energy corresponding to the Hamiltonian according to the Hamiltonian and the derivative of the Hamiltonian. And output the derivative of the energy,
A classic computer that performs processing. The first quantum circuit for calculating energy by executing quantum calculation using VQE (Variational-Quantum-Eigensolver) according to the initial information of the Hamiltonian and the parameters representing the quantum circuit output from the classical computer. Is generated, and the parameter representing the first quantum circuit is output.
Quantum calculation is executed based on the parameter representing the second quantum circuit including the rotation gate corresponding to the parameter representing the first quantum circuit output from the classical computer, and the measurement result of the quantum calculation is output. To do,
A quantum computer that performs processing. Outputs the Hamiltonian and the initial information of the parameters representing the quantum circuit,
Depending on the parameter representing the first quantum circuit for calculating energy, which is generated by quantum calculation using VQE (Variational-Quantum-Eigensolver) based on the Hamiltonian and the initial information output from the quantum computer. Then, a parameter representing the second quantum circuit including the rotating gate is generated, and a parameter representing the second quantum circuit is output.
The measurement result of the quantum calculation according to the parameter representing the second quantum circuit output from the quantum computer, and the derivative of the energy corresponding to the Hamiltonian according to the Hamiltonian and the derivative of the Hamiltonian. And output the derivative of the energy,
A quantum information processing program that allows a classical computer to perform processing. The first quantum circuit for calculating energy by executing quantum calculation using VQE (Variational-Quantum-Eigensolver) according to the initial information of the Hamiltonian and the parameters representing the quantum circuit output from the classical computer. Is generated, and the parameter representing the first quantum circuit is output.
Quantum calculation is executed based on the parameter representing the second quantum circuit including the rotation gate corresponding to the parameter representing the first quantum circuit output from the classical computer, and the measurement result of the quantum calculation is output. To do,
A quantum information program that allows a quantum computer to perform processing. A data structure used for quantum computation in a quantum computer.
With Hamiltonian,
Initial information of parameters representing quantum circuits and
Including
The parameters of the first quantum circuit for calculating the energy of the ground state or the excited state are generated by the quantum calculation by the quantum computer using the VQE (Variational-Quantum-Eigensolver) based on the Hamiltonian and the initial information. Used for processing,
data structure. It is a data structure related to the configuration of a quantum circuit used in quantum computing of a quantum computer.
With multiple unitary gates
A rotating gate inserted between multiple unitary gates,
Including
It is used in the process of measuring the measurement result of the quantum calculation by the quantum calculation by the quantum computer based on the quantum circuit including the plurality of unitary gates and the rotating gate.
data structure.