Quantum computing device, quantum computing method, and program

Abstract

A quantum computing device according to one aspect of the present disclosure simulates a composite system of a first quantum system and a second quantum system, the quantum computing device comprising: an approximation calculation unit that calculates a first quantum state representing an approximation of a ground state of a local Hamiltonian of the first quantum system and a second quantum state representing an approximation of a ground state of a local Hamiltonian of the second quantum system; a formularization unit that formulates a formula to virtually obtain a density matrix that minimizes the expected value of the Hamiltonian of the composite system using the first quantum state and the second quantum state; an optimal solution calculation unit that calculates an optimal solution to the formula using a dual virtual distillation method for the first quantum state and the second quantum state, a measurement related to the product of the Pauli operators acting on the first quantum system, and a measurement related to the product of the Pauli operators acting on the second quantum system; and a density matrix calculation unit that calculates the density matrix using the formula and the optimal solution.

Description

Quantum computing device, quantum computing method, and program

[0001] The present disclosure relates to a quantum computing device, a quantum computing method, and a program.

[0002] A known quantum error suppression method is called the generalized quantum subspace expansion method (Non-Patent Document 1). The generalized quantum subspace expansion method is a generalized quantum error suppression method that combines a quantum error suppression method called the virtual distillation method and a quantum error suppression method called the quantum subspace expansion method. Since the virtual distillation method is suitable for stochastic errors and the quantum subspace expansion method is suitable for coherent errors, the generalized quantum subspace expansion method can efficiently remove both types of errors.

[0003] Because virtual distillation is a method that uses a copy of the quantum state, the generalized quantum subspace expansion also requires a copy of the quantum state. Therefore, the generalized quantum subspace expansion imposes a large overhead on current NISQ (Noisy Intermediate-Scale Quantum) computers, which have a limited number of qubits. In contrast, it is conceivable that a method called dual virtual distillation can be combined with the generalized quantum subspace expansion to eliminate the need for a copy of the quantum state.

[0004] On the other hand, because it is still difficult to realize large-scale quantum systems, there is a need to simulate quantum systems that are larger than actual quantum systems. In this simulation, it is thought that by using a method that combines the dual virtual distillation method and the generalized quantum subspace expansion method, it will be possible to perform simulations that suppress calculation errors, including quantum errors.

[0005] Yoshioka, Nobuyuki, Hideaki Hakoshima, Yuichiro Matsuzaki, Yuuki Tokunaga, Yasunari Suzuki, and Suguru Endo. "Generalized quantum subspace expansion." Physical Review Letters 129, no. 2 (2022): 020502.

[0006] The present disclosure has been made in consideration of the above points, and provides a technique that enables simulation of a composite system of different quantum systems while suppressing calculation errors.

[0007] A quantum computing device according to one aspect of the present disclosure is a quantum computing device that simulates a composite system of a first quantum system and a second quantum system, and includes: an approximation calculation unit that calculates a first quantum state that represents an approximation to the ground state of a local Hamiltonian of the first quantum system, and a second quantum state that represents an approximation to the ground state of a local Hamiltonian of the second quantum system; a formulation unit that uses the first quantum state and the second quantum state to formulate an equation for virtually obtaining a density matrix that minimizes the expectation value of the Hamiltonian of the composite system; an optimal solution calculation unit that calculates an optimal solution to the equation using a dual virtual distillation method for the first quantum state and the second quantum state, a measurement related to the product of Pauli operators acting on the first quantum system, and a measurement related to the product of Pauli operators acting on the second quantum system; and a density matrix calculation unit that calculates the density matrix using the equation and the optimal solution.

[0008] A technique is provided that enables the simulation of composite systems of different quantum systems while suppressing computational errors.

[0009] Fig. 1 is a diagram showing an example of the configuration of a quantum computing device according to the present embodiment; Fig. 2 is a diagram showing an example of the hardware configuration of a control device according to the present embodiment; Fig. 3 is a diagram showing an example of the functional configuration of a control device according to the present embodiment; Fig. 4 is a flowchart showing an example of a density matrix calculation process; Fig. 5 is a flowchart showing an example of an optimal solution calculation process;

[0010] An embodiment of the present invention will be described below.

[0011] <Problem formulation> Two different quantum systems are called "quantum system A" and "quantum system B." Quantum system A and quantum system B may each be any quantum system. Quantum system A and quantum system B may each be, for example, a quantum system realized by a superconducting circuit, an ion trap, a photon, a quantum dot, or the like.

[0012] In this case, we would like to simulate a composite system of quantum systems A and B (hereinafter also referred to as "quantum system A+B") while suppressing calculation errors, including quantum errors. Note that quantum system A+B is a larger system than the actual quantum systems A and B.

[0013] As a conventional method for simulating a composite system of quantum systems A and B, a method is known that can virtually simulate quantum entanglement between quantum systems A and B by also including classical processing of the measurement results of quantum systems A and B (e.g., References 1 and 2). Hereinafter, we propose a method that can simulate a composite system of quantum systems A and B while suppressing calculation errors, including quantum errors, by incorporating a procedure similar to the above conventional method into a method that combines the dual virtual distillation method (Reference 3) and the generalized quantum subspace expansion method (Non-Patent Document 1).

[0014] <Preparation> Hamiltonian H of quantum system A+B, which is a composite system of quantum system A and quantum system B （Ａ＋Ｂ） is as follows:

[0015] Here, the following symbols represent tensor products:

[0016] In the text of this specification, the symbol representing the tensor product will be represented by (x).

[0017] H （Ａ） (×) I （Ｂ） is the local Hamiltonian of the quantum system A (hereinafter also referred to as the local Hamiltonian), I （Ａ） (×) H （Ｂ） is the local Hamiltonian of quantum system B, I （Ａ） is the identity operator of quantum system A, I （Ｂ） is the identity operator of the quantum system B. H ｉｎｔ （ＡＢ） is the interaction Hamiltonian between quantum systems A and B.

[0018] Also, the Pauli operator P acting on the quantum system A β （Ａ） and the Pauli operator P acting on the quantum system B β（Ｂ） Using the tensor product of these, we can obtain the Hamiltonian H （Ａ＋Ｂ） is as follows:

[0019] Here, h β is a complex coefficient, and β is a label that identifies each Pauli operator.

[0020] Furthermore, the local Hamiltonian H （Ａ） (×) I （Ｂ） Let ρ be the approximation of the ground state of (i.e., the approximation of the quantum state that represents that ground state). Ａ , local Hamiltonian I （Ａ） (×) H （Ｂ） Let ρ be the approximate ground state of Ｂ In addition, these approximate states ρ Ａ and ρ Ｂ can be obtained by, for example, a VQE (Variational Quantum Eigensolver) method.

[0021] <Formulation> Based on the above preparation, the Hamiltonian H of the quantum system A+B is expressed by the following formula (1): （Ａ＋Ｂ） The density matrix ρ that minimizes the expectation value (energy) of ＤＣＧＳＥ The purpose is to virtually obtain the density matrix. The density matrix is ​​a matrix representation of the density operator that represents the quantum state.

[0022] Here, the following are the (approximate) dual quantum states of quantum system A and quantum system B, respectively.

[0023] In the following text of this specification, the above dual quantum states will be referred to as "ρ Ａ － ", "ρ Ｂ － " will be expressed as ".

[0024] α ｉ is a complex number, and α = (α １ , ..., α Ｎ ) where N is the number of elements of vector α. C ｉis an operator acting on quantum systems A and B, and the Pauli operator P γ （Ａ） and the Pauli operator P acting on the quantum system B γ （Ｂ） Using the tensor product of

[0025] Here, g γ （ｉ） is a complex coefficient. Also, γ is a label that identifies each Pauli operator. Note that the asterisk symbol "*" represents a complex conjugate, and the dagger symbol "†" represents a Hermitian conjugate.

[0026] The density matrix ρ shown in the above equation (1) ＤＣＧＳＥ generally represents the state of quantum entanglement between quantum systems A and B. In this case, the Hamiltonian H （Ａ＋Ｂ） minimize the expected value (energy) of α=(α １ , ..., α Ｎ ) to obtain the density matrix ρ ＤＣＧＳＥ Ask for.

[0027] Here, (ρ Ａ ρ Ａ － +ρ Ａ － ρ Ａ ) / 2 and (ρ Ｂ ρ Ｂ － +ρ Ｂ － ρ Ｂ ) / 2 represent terms corresponding to the dual virtual distillation method in quantum systems A and B, respectively. In addition, in the above formula (1), as in References 1 and 2, a quantum entangled state is expressed by taking a linear combination of the tensor product of these terms. This eliminates the need to copy the quantum state while suppressing calculation errors, including quantum errors, and enables the simulation of a composite system of quantum systems A and B (i.e., a quantum system larger than either quantum system A or quantum system B).

[0028] Hereinafter, the above formula (1) will be formulated, and the density matrix ρＤＣＧＳＥ A quantum computing device 100 for calculating the following will be described.

[0029] <Configuration Example of Quantum Computing Device 10> A configuration example of the quantum computing device 10 according to this embodiment will be described with reference to Fig. 1. Fig. 1 is a diagram showing a configuration example of the quantum computing device 10 according to this embodiment.

[0030] As shown in FIG. 1, a quantum computing device 10 according to this embodiment includes a control device 100 and a quantum processor 200.

[0031] The control device 100 transmits a control signal to the quantum processor 200 and obtains a calculation result from the quantum processor 200. In this way, quantum calculation is performed. The control device 100 is realized by, for example, a classical computer or the like.

[0032] The quantum processor 200 configures a quantum two-level system called a quantum bit (physical quantum bit), and performs physical operations such as initialization, gate operation (unitary transformation), and measurement on the physical quantum bit in response to a control signal from the control device 100. The quantum system for realizing the quantum bit is not particularly limited, and any quantum system may be used. For example, a quantum system realized by a superconducting circuit, an ion trap, a photon, a quantum dot, or the like may be used.

[0033] Hereinafter, it is assumed that the quantum processor 200 is composed of a quantum processor 200A using a quantum system A and a quantum processor 200B using a quantum system B.

[0034] <Example of Hardware Configuration of Control Device 100> An example of a hardware configuration of the control device 100 according to this embodiment will be described with reference to Fig. 2. Fig. 2 is a diagram showing an example of a hardware configuration of the control device 100 according to this embodiment.

[0035] 2, the control device 100 according to this embodiment includes an input device 101, a display device 102, an external I / F 103, a communication I / F 104, a random access memory (RAM) 105, a read only memory (ROM) 106, an auxiliary storage device 107, and a processor 108. Each of these pieces of hardware is connected to each other via a bus 109 so as to be able to communicate with each other.

[0036] The input device 101 is, for example, a keyboard, a mouse, a touch panel, a physical button, etc. The display device 102 is, for example, a display, a display panel, etc. Note that the control device 100 does not necessarily have to include at least one of the input device 101 and the display device 102, for example.

[0037] The external I / F 103 is an interface with an external device such as a recording medium 103a. Examples of the recording medium 103a include a CD (Compact Disc), a DVD (Digital Versatile Disk), an SD memory card (Secure Digital memory card), and a USB (Universal Serial Bus) memory card.

[0038] The communication I / F 104 is an interface for transmitting and receiving various signals to and from the quantum processor 200. The RAM 105 is a volatile semiconductor memory (storage device) that temporarily stores programs and data. The ROM 106 is a non-volatile semiconductor memory (storage device) that can store programs and data even when the power is turned off. The auxiliary storage device 107 is a non-volatile storage device (storage device) such as an HDD (Hard Disk Drive), an SSD (Solid State Drive), or a flash memory. The processor 108 is an arithmetic device such as a CPU (Central Processing Unit).

[0039] 2 is an example, and the hardware configuration of the control device 100 is not limited to this. For example, the control device 100 may have multiple auxiliary storage devices 107 or multiple processors 108, may not have some of the hardware shown in the figure, or may have various hardware other than the hardware shown in the figure.

[0040] <Example of functional configuration of control device 100> An example of the functional configuration of the control device 100 according to this embodiment will be described with reference to Fig. 3. Fig. 3 is a diagram showing an example of the functional configuration of the control device 100 according to this embodiment.

[0041] As shown in Fig. 3, the control device 100 according to this embodiment includes a ground state approximation unit 110, a formulation unit 120, an optimal solution calculation unit 130, and a density matrix calculation unit 140. These units are realized, for example, by processing executed by a processor 108 of one or more programs installed in the control device 100. The control device 100 according to this embodiment also includes a storage unit 150. The storage unit 150 is realized, for example, by a storage area of ​​the auxiliary storage device 107 or the like. Note that the storage unit 150 may also be realized, for example, by a storage area of ​​a storage device communicably connected to the control device 100.

[0042] The ground state approximation unit 110 calculates the local Hamiltonian H （Ａ） (×) I （Ｂ） Approximation of the ground state of ρ Ａ and the local Hamiltonian I （Ａ） (×) H （Ｂ） Approximation of the ground state of ρ Ｂ The ground state approximation unit 110 calculates these approximate states ρ Ａ and ρ Ｂ is stored in the storage unit 150. Here, the ground state approximation unit 110 stores, for example, the local Hamiltonian H （Ａ） (×) I （Ｂ） is used as input and approximated state ρ Ａ Similarly, the ground state approximation unit 110 can obtain, for example, the local Hamiltonian I （Ａ） (×) H （Ｂ） is used as input and approximated state ρＢ The approximate state ρ Ａ and ρ Ｂ Quantum processor 200A and quantum processor 200B are also utilized when calculating

[0043] The formulation unit 120 calculates the approximate state ρ Ａ and ρ Ｂ The above equation (1) is formulated using the following equation.

[0044] The optimal solution calculation unit 130 calculates the Hamiltonian H （Ａ＋Ｂ） minimize the expected value (energy) of α=(α １ , ..., α Ｎ ) to the optimal solution α （０） = (α １ （０） , ..., α Ｎ （０） ) where the optimum solution calculation unit 130 includes a first matrix element calculation unit 131, a second matrix element calculation unit 132, and a solution calculation unit 133.

[0045] The first matrix element calculation unit 131 calculates the element H of the (i, j) component of the matrix H for all pairs of (i, j). ｉｊ is calculated by the following formula (2), where 1≦i≦N and 1≦j≦N.

[0046] Here, Tr represents a trace, and γ′ is a label that identifies each Pauli operator. At this time, the equation of the part that is the target of the trace is calculated by the quantum processor 200.

[0047] The second matrix element calculation unit 132 calculates the element S of the (i, j) component of the matrix S for all pairs of (i, j). ｉｊ is calculated by the following formula (3).

[0048] The part of the equation that is the target of tracing is calculated by the quantum processor 200.

[0049] The solution calculation unit 133 solves the generalized eigenvalue equation H·α=E·S·α to obtain the minimum eigenvalue E=E （０） α corresponding to（０） is calculated as the optimal solution.

[0050] The density matrix calculation unit 140 calculates the optimal solution α （０） Using the density matrix ρ ＤＣＧＳＥ That is, the density matrix calculation unit 140 calculates α=α in the above equation (1). （０） By doing so, the density matrix ρ ＤＣＧＳＥ Furthermore, the density matrix calculation unit 140 calculates the density matrix ρ ＤＣＧＳＥ is output to a predetermined destination. ＤＣＧＳＥ The output destination is not limited to a specific output destination, and can be any output destination, such as the storage unit 150, a program, a display device 102 such as a display, or another device or equipment connected to the control device 100 so as to be able to communicate with the control device 100.

[0051] The storage unit 150 stores the local Hamiltonian H （Ａ） (×) I （Ｂ） Approximation of the ground state of ρ Ａ and the local Hamiltonian I （Ａ） (×) H （Ｂ） Approximation of the ground state of ρ Ｂ and remember.

[0052] <density matrix ρ ＤＣＧＳＥ Calculation process of density matrix ρ ＤＣＧＳＥ The calculation process of the density matrix ρ will be described with reference to FIG. ＤＣＧＳＥ 4 is a flowchart showing an example of a calculation process of Step S101 or Steps S101 to S102 in FIG.

[0053] The ground state approximation unit 110 calculates the local Hamiltonian H （Ａ） (×) I （Ｂ） Approximation of the ground state of ρ Ａ and the local Hamiltonian I （Ａ） (×) H （Ｂ） Approximation of the ground state of ρ Ｂ (Step S101). Ａ and ρ Ｂ is stored in the storage unit 150. In addition, the approximate state ρＡ and ρ Ｂ Quantum processor 200A and quantum processor 200B are also utilized when calculating

[0054] The formulation unit 120 calculates the approximate state ρ Ａ and ρ Ｂ The above equation (1) is formulated using (step S102).

[0055] The optimal solution calculation unit 130 calculates the Hamiltonian H （Ａ＋Ｂ） minimize the expected value (energy) of α=(α １ , ..., α Ｎ ) to the optimal solution α （０） (Step S103) Details of this step will be described later.

[0056] The density matrix calculation unit 140 calculates the optimal solution α （０） Using the above equation (1), the density matrix ρ ＤＣＧＳＥ (Step S104). Note that this density matrix ρ ＤＣＧＳＥ is output to a predetermined output destination.

[0057] <optimal solution α （０） Calculation process of the optimal solution α in step S103 of FIG. （０） The calculation process of the optimal solution α （０） 10 is a flowchart showing an example of a calculation process.

[0058] The first matrix element calculation unit 131 of the optimal solution calculation unit 130 calculates the element H of the (i, j) component of the matrix H for all pairs of (i, j). ｉｊ is calculated by the above formula (2) (step S201). At this time, the first matrix element calculation unit 131 calculates H for each pair of (i, j) by the following steps 1-1 to 1-5. ｉｊ Calculate.

[0059] Step 1-1: The first matrix element calculation unit 131 calculates the approximate state ρ Ａ, and the quantum processor 200A is used to calculate the product P of the Pauli operators for all pairs of (β, γ, γ′). γ （Ａ） P β （Ａ） P γ' （Ａ） is measured and determined.

[0060] Step 1-2: The first matrix element calculation unit 131 calculates Tr[P γ （Ａ） P β （Ａ） P γ' （Ａ） (ρ Ａ ρ Ａ － +ρ Ａ － ρ Ａ ) / 2].

[0061] Step 1-3: The first matrix element calculation unit 131 calculates the approximate state ρ Ｂ , and the quantum processor 200B is used to calculate the product P of the Pauli operators for all pairs of (β, γ, γ′). γ （Ｂ） P β （Ｂ） P γ' （Ｂ） is measured and determined.

[0062] Step 1-4: The first matrix element calculation unit 131 calculates Tr[P γ （Ｂ） P β （Ｂ） P γ' （Ｂ） (ρ Ｂ ρ Ｂ － +ρ Ｂ － ρ Ｂ ) / 2].

[0063] Step 1-5: The first matrix element calculation unit 131 calculates Tr[P γ（Ａ） P β （Ａ） P γ' （Ａ） (ρ Ａ ρ Ａ － +ρ Ａ － ρ Ａ ) / 2] × Tr[P γ （Ｂ） P β （Ｂ） P γ' （Ｂ） (ρ Ｂ ρ Ｂ － +ρ Ｂ － ρ Ｂ ) / 2] with weight h β g γ' （ｉ）* g γ （ｊ） Then, add these together for all pairs of (β, γ, γ') to get H ｉｊ This virtually expresses the quantum entanglement between quantum systems A and B.

[0064] By the above steps 1-1 to 1-5, H is calculated for each pair (i, j). ｉｊ Since this H ｉｊ A matrix H having the following as its (i, j) element is obtained.

[0065] The second matrix element calculation unit 132 of the optimal solution calculation unit 130 calculates the element S of the (i, j) component of the matrix S for all pairs of (i, j). ｉｊ is calculated by the above formula (3) (step S202). At this time, the second matrix element calculation unit 132 calculates S for each pair of (i, j) by the following steps 2-1 to 2-5. ｉｊ Calculate.

[0066] Step 2-1: The second matrix element calculation unit 132 calculates the approximate state ρ Ａ γ′) and calculates the product P of the Pauli operators for all pairs of (γ, γ′) using the quantum processor 200A. γ （Ａ） P γ' （Ａ）is measured and determined.

[0067] Step 2-2: The second matrix element calculation unit 132 calculates Tr[P γ （Ａ） P γ' （Ａ） (ρ Ａ ρ Ａ － +ρ Ａ － ρ Ａ ) / 2].

[0068] Step 2-3: The second matrix element calculation unit 132 calculates the approximate state ρ Ｂ γ′) and calculates the product P of the Pauli operators for all pairs of (γ, γ′) using the quantum processor 200B. γ （Ｂ） P γ' （Ｂ） is measured and determined.

[0069] Step 2-4: The second matrix element calculation unit 132 calculates Tr[P γ （Ｂ） P γ' （Ｂ） (ρ Ｂ ρ Ｂ － +ρ Ｂ － ρ Ｂ ) / 2].

[0070] Step 2-5: The second matrix element calculation unit 132 calculates Tr[P γ （Ａ） P γ' （Ａ） (ρ Ａ ρ Ａ － +ρ Ａ － ρ Ａ ) / 2] × Tr[P γ （Ｂ） P γ' （Ｂ） (ρ Ｂ ρ Ｂ － +ρＢ － ρ Ｂ ) / 2] with weight g γ' （ｉ）* g γ （ｊ） Then, these are multiplied for all pairs of (γ, γ') to obtain S ｉｊ This virtually expresses the quantum entanglement between quantum systems A and B.

[0071] By the above steps 2-1 to 2-5, S ｉｊ Since this S ｉｊ A matrix S having the (i, j) component as an element is obtained.

[0072] The solution calculation unit 133 of the optimal solution calculation unit 130 solves the generalized eigenvalue equation H·α=E·S·α to obtain the minimum eigenvalue E=E （０） α corresponding to （０） is calculated as the optimal solution (step S203). （０） corresponds to a local solution within the trial wave function of the above formula (1). Note that the generalized eigenvalue method can be solved by a known method, and can be easily solved by using an existing library, etc.

[0073] <Summary> As described above, the quantum computing device 10 according to this embodiment can suppress computational errors, including quantum errors, while eliminating the need to copy quantum states, and can realize a simulation of a composite system of quantum systems A and B (i.e., a quantum system that is larger than either quantum system A or quantum system B). Therefore, by using the quantum computing device 10 according to this embodiment, it becomes possible to accurately simulate large-scale quantum systems that are currently difficult to realize.

[0074] The present invention is not limited to the above-described specifically disclosed embodiments, and various modifications, changes, and combinations with known technologies are possible without departing from the scope of the claims.

[0075] [References] Reference 1: Eddins, Andrew, Mario Motta, Tanvi P. Gujarati, Sergey Bravyi, Antonio Mezzacapo, Charles Hadfield, and Sarah Sheldon. "Doubling the size of quantum simulators by entanglement forging." PRX Quantum 3, no. 1 (2022): 010309. Reference 2: Yuan, Xiao, Jinzhao Sun, Junyu Liu, Qi Zhao, and You Zhou. "Quantum simulation with hybrid tensor networks." Physical Review Letters 127, no. 4 (2021): 040501. Reference 3: Huo, Mingxia, and Ying Li. "Dual-state purification for practical quantum error mitigation." Physical Review A 105, no. 2 (2022): 022427.

[0076] 10 Quantum computing device 100 Control device 101 Force input device 102 Display device 103 External I / F 103a Recording medium 104 Communication I / F 105 RAM 106 ROM 107 Auxiliary memory device 108プロセッサ109 バス110 Base state approximation part 120 Formatization part 130 Optimum solution calculation part 131 1st row and column element calculation part 132 2nd row and column element calculation part 133 Solution calculation part 140 Density row and column calculation part 150 Memory part 200 Quantum プロセッサ

Claims

1. A quantum computing device for simulating a composite system of a first quantum system and a second quantum system, comprising: an approximation calculation unit that calculates a first quantum state representing an approximation to the ground state of a local Hamiltonian of the first quantum system and a second quantum state representing an approximation to the ground state of a local Hamiltonian of the second quantum system; a formulation unit that uses the first quantum state and the second quantum state to formulate an equation for virtually obtaining a density matrix that minimizes the expectation value of the Hamiltonian of the composite system; an optimal solution calculation unit that calculates an optimal solution of the equation using a dual virtual distillation method for the first quantum state and the second quantum state, a measurement related to the product of Pauli operators acting on the first quantum system, and a measurement related to the product of Pauli operators acting on the second quantum system; and a density matrix calculation unit that calculates the density matrix using the equation and the optimal solution.

2. The formulation unit defines the first quantum state as ρ Ａ , the second quantum state is ρ Ｂ , the first quantum state ρ Ａ The dual quantum state of Ａ － , the second quantum state ρ Ｂ The dual quantum state of Ｂ － , the density matrix is ​​ρ ＤＣＧＳＥ As, ρ ＤＣＧＳＥ =Σ ｉｊ α ｉ ＊ α ｊ C ｉ † (ρ Ａ ρ Ａ － +ρ Ａ － ρ Ａ ) / 2)(×)((ρ Ｂ ρ Ｂ － +ρ Ｂ － ρ Ｂ ) / 2) C ｊ (where the Pauli operator acting on the first quantum system is P γ （Ａ） , the Pauli operator acting on the second quantum system is P γ （Ｂ） , the complex coefficients are g γ （ｉ） As C ｉ =Σ γ g γ （ｉ） P γ （Ａ） P γ （Ｂ） ) and the optimal solution calculation unit formulates the equation as an optimal solution α=α （０） The quantum computing device of claim 1 , which calculates:

3. α = (α １ , ..., α Ｎ ), the optimal solution calculation unit calculates H ｉｊ =Tr[C ｉ † (ρ Ａ ρ Ａ － +ρ Ａ － ρ Ａ ) / 2)(×)((ρ Ｂ ρ Ｂ － +ρ Ｂ － ρ Ｂ ) / 2) C ｊ H （ＡＢ） ](However, H （ＡＢ） is the Hamiltonian of the composite system) as an element of the (i, j) component of the N × N matrix H, and S ｉｊ =Tr[C ｉ † (ρ Ａ ρ Ａ － +ρ Ａ － ρ Ａ ) / 2)(×)((ρ Ｂ ρ Ｂ － +ρ Ｂ － ρ Ｂ ) / 2) C ｊ ] as the (i, j) element of the N × N matrix S, and solving the generalized eigenvalue equation H α = E S α, the minimum eigenvalue E = E （０） α corresponding to （０） The quantum computing device according to claim 2 , wherein the quantum computing device calculates the optimal solution as follows:

4. The optimal solution calculation unit is ｉｊ =Tr[C ｉ † (ρ Ａ ρ Ａ － +ρ Ａ － ρ Ａ ) / 2)(×)((ρ Ｂ ρ Ｂ － +ρ Ｂ － ρ Ｂ ) / 2) C ｊ H （ＡＢ） ]=Σ β，γ，γ' h β g γ' （ｉ）* g γ （ｊ） Tr[P γ （Ａ） P β （Ａ） P γ' （Ａ） (ρ Ａ ρ Ａ － +ρ Ａ － ρ Ａ ) / 2] × Tr [P γ （Ｂ） P β （Ｂ） P γ' （Ｂ） (ρ Ｂ ρ Ｂ － +ρ Ｂ － ρ Ｂ ) / 2], and then the first quantum state ρ Ａ The dual virtual distillation method is applied to P by a quantum processor realized in the first quantum system. γ （Ａ） P β （Ａ） P γ' （Ａ） By measuring the calculated result, Tr[P γ （Ａ） P β （Ａ） P γ' （Ａ） (ρ Ａ ρ Ａ － +ρ Ａ － ρ Ａ ) / 2], and calculating the second quantum state ρ Ｂ The dual virtual distillation method is applied to P by a quantum processor realized in the second quantum system. γ （Ｂ） P β （Ｂ） P γ' （Ｂ） By measuring the calculated result, Tr[P γ （Ｂ） P β （Ｂ） P γ' （Ｂ） (ρ Ｂ ρ Ｂ － +ρ Ｂ － ρ Ｂ ) / 2], and Tr[P γ （Ａ） P β （Ａ） P γ' （Ａ） (ρ Ａ ρ Ａ － +ρ Ａ － ρ Ａ ) / 2] and Tr[P γ （Ｂ） P β （Ｂ） P γ' （Ｂ） (ρ Ｂ ρ Ｂ － +ρ Ｂ － ρ Ｂ ) / 2] and the product β g γ' （ｉ）* g γ （ｊ） Then, by multiplying by and adding up for all (β, γ, γ'), H ｉｊ The quantum computing device of claim 3 , which calculates:

5. The optimal solution calculation unit is ｉｊ =Tr[C ｉ † (ρ Ａ ρ Ａ － +ρ Ａ － ρ Ａ ) / 2)(×)((ρ Ｂ ρ Ｂ － +ρ Ｂ － ρ Ｂ ) / 2) C ｊ ]=Σ γ，γ' g γ' （ｉ）* g γ （ｊ） Tr[P γ （Ａ） P γ' （Ａ） (ρ Ａ ρ Ａ － +ρ Ａ － ρ Ａ ) / 2] × Tr [P γ （Ｂ） P γ' （Ｂ） (ρ Ｂ ρ Ｂ － +ρ Ｂ － ρ Ｂ ) / 2], and then the first quantum state ρ Ａ The dual virtual distillation method is applied to P by a quantum processor realized in the first quantum system. γ （Ａ） P γ' （Ａ） By measuring the calculated result, Tr[P γ （Ａ） P γ' （Ａ） (ρ Ａ ρ Ａ － +ρ Ａ － ρ Ａ ) / 2], and calculating the second quantum state ρ Ｂ The dual virtual distillation method is applied to P by a quantum processor realized in the second quantum system. γ （Ｂ） P γ' （Ｂ） By measuring the calculated result, Tr[P γ （Ｂ） P γ' （Ｂ） (ρ Ｂ ρ Ｂ － +ρ Ｂ － ρ Ｂ ) / 2], and Tr[P γ （Ａ） P γ' （Ａ） (ρ Ａ ρ Ａ － +ρ Ａ － ρ Ａ ) / 2] and Tr[P γ （Ｂ） P γ' （Ｂ） (ρ Ｂ ρ Ｂ － +ρ Ｂ － ρ Ｂ ) / 2] and the product γ' （ｉ）* g γ （ｊ） Then, by multiplying by and adding up for all (γ, γ'), S ｉｊ The quantum computing device according to claim 3 or 4, which calculates 6. A quantum computing method in which a quantum computing device that simulates a composite system of a first quantum system and a second quantum system executes the following steps: an approximation calculation procedure for calculating a first quantum state that represents an approximation to the ground state of a local Hamiltonian of the first quantum system, and a second quantum state that represents an approximation to the ground state of a local Hamiltonian of the second quantum system; a formulation procedure for formulating an equation for virtually obtaining a density matrix that minimizes the expectation value of the Hamiltonian of the composite system, using the first quantum state and the second quantum state; an optimal solution calculation procedure for calculating an optimal solution of the equation, using a dual virtual distillation method for the first quantum state and the second quantum state, a measurement related to the product of Pauli operators acting on the first quantum system, and a measurement related to the product of Pauli operators acting on the second quantum system; and a density matrix calculation procedure for calculating the density matrix, using the equation and the optimal solution.

7. A program for causing a quantum computing device that simulates a composite system of a first quantum system and a second quantum system to execute the following: an approximation calculation procedure for calculating a first quantum state that represents an approximation to the ground state of a local Hamiltonian of the first quantum system, and a second quantum state that represents an approximation to the ground state of a local Hamiltonian of the second quantum system; a formulation procedure for formulating an equation for virtually obtaining a density matrix that minimizes the expectation value of the Hamiltonian of the composite system, using the first quantum state and the second quantum state; an optimal solution calculation procedure for calculating an optimal solution of the equation, using a dual virtual distillation method for the first quantum state and the second quantum state, a measurement related to the product of Pauli operators acting on the first quantum system, and a measurement related to the product of Pauli operators acting on the second quantum system; and a density matrix calculation procedure for calculating the density matrix using the equation and the optimal solution.

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