Noise simulation program, information processing apparatus, and noise simulation method

Abstract

To improve accuracy of noise simulation of an individual quantum circuit while suppressing calculation cost.SOLUTION: The information processing apparatus 1 performs a noise simulation using a noise process of a quantum gate included in a quantum circuit. For example, after the processing by the quantum gate, the information processing apparatus 1 performs a noise simulation by causing a half of the quantum gate to act in the backward direction as a noise process, adding time evolution derived from residual interaction, and causing a half of the quantum gate to act in the forward direction.SELECTED DRAWING: Figure 2

Description

[Technical Field]

[0001] The present invention relates to a noise simulation program and the like. [Background technology]

[0002] Quantum errors occur in quantum bits during quantum circuit execution due to various factors. For example, quantum errors include probabilistic reversal errors resulting from interactions with degrees of freedom outside the quantum device, and coherent errors resulting from extraneous interactions within the quantum device. Quantum errors occurring in quantum bits propagate through quantum gates, causing statistical and systematic errors in the results of quantum computations. Therefore, in order to investigate the specific impact of quantum errors on the results of quantum computations, it is necessary to perform noise simulations to investigate the propagation of noise within quantum circuits.

[0003] One example of noise simulation is analysis using the quantum master equation. The quantum master equation is expressed by the following equation (1). In equation (1), the time evolution of the state ρ of an open quantum system is expressed by the Hamiltonian H and the relaxation operator L. i where ρ represents the state of the quantum device, H represents the internal interaction, and L i indicates the interaction with the outside world. i indicates the strength of the interaction.

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[0004] As another example of noise simulation, analysis using a quantum circuit model is known (see, for example, Non-Patent Document 1). Fig. 12 is a diagram showing a reference example of the arrangement of a noise model in a quantum circuit. For example, if a noise process N 1Q Just after the two quantum gates, the noise process N 2QBy applying , the state after the noise is applied is approximated, i.e., the effect of quantum errors on individual qubits is approximated. [Prior art documents] [Patent documents]

[0005] [Patent Document 1] Special Publication No. 2023-550324 [Patent Document 2] Japanese Patent Application Publication No. 2024-23156 [Patent Document 3] US Patent Application Publication No. 2023 / 0016817 [Non-patent literature]

[0006] [Non-Patent Document 1] William Berquist et al “Stochastic Approach For Simulating Quantum Noise Using Tensor Networks” Summary of the Invention [Problem to be solved by the invention]

[0007] However, conventional noise simulations have the problem that the calculation costs increase and the accuracy of the noise simulation of quantum circuits cannot be improved.

[0008] For example, in the analysis using the quantum master equation, H, L i , ρ increases exponentially with the number of quantum bits, so as the system becomes larger, the cost of matrix calculations involved in the integration increases.

[0009] Furthermore, there are problems with analysis using quantum circuit models. The action of noise occurs simultaneously with the action of quantum gates, and even if the noise is the same, its content changes depending on the quantum gates that act at the same time. For this reason, we consider the noise to be N1Q , N 2Q If we standardize it like this, we cannot incorporate the effects of coherent errors, which change the content due to interference with quantum gates. In other words, the accuracy of noise simulation of quantum circuits will not improve.

[0010] In one aspect, the present invention aims to improve the accuracy of noise simulation of individual quantum circuits while reducing calculation costs. [Means for solving the problem]

[0011] In one aspect, the noise simulation program is a noise simulation program that performs noise simulation using the noise process of a quantum gate included in a quantum circuit, and causes a computer to execute processing that performs noise simulation after processing by the quantum gate by operating the quantum gate half in the reverse direction as the noise process, adding time evolution resulting from residual interactions, and operating the quantum gate half in the forward direction. [Effects of the Invention]

[0012] According to one embodiment, it is possible to improve the accuracy of noise simulation for each quantum circuit while suppressing calculation costs. [Brief explanation of the drawings]

[0013] [Figure 1] FIG. 1 is a diagram showing an image of the arrangement of noise models in a quantum circuit according to an embodiment. [Figure 2] FIG. 2 is a diagram illustrating a noise process according to an embodiment. [Figure 3] FIG. 3 is a diagram illustrating an example of a functional configuration of the information processing device according to the embodiment. [Figure 4A] FIG. 4A is a diagram (1) for explaining a method for extracting a noise process according to an embodiment. [Figure 4B] FIG. 4B is a diagram (2) for explaining a method for extracting noise processes according to the embodiment. [Figure 4C]FIG. 4C is a diagram (3) for explaining a method for extracting noise processes according to the embodiment. [Figure 5] FIG. 5 is a diagram illustrating modeling of a noise process according to an embodiment. [Figure 6] FIG. 6 is a diagram illustrating an example of an overall flowchart of the noise simulation according to the embodiment. [Figure 7] FIG. 7 is a diagram illustrating an example of a flowchart of noise process extraction according to the embodiment. [Figure 8A] FIG. 8A is a diagram (1) showing an example of noise process extraction according to the embodiment. [Figure 8B] FIG. 8B is a diagram (2) showing an example of noise process extraction according to the embodiment. [Figure 8C] FIG. 8C is a diagram (3) showing an example of noise process extraction according to the embodiment. [Figure 8D] FIG. 8D is a diagram (4) showing an example of noise process extraction according to the embodiment. [Figure 9] FIG. 9 is a diagram illustrating an example of a result of a noise simulation according to the embodiment. [Figure 10] FIG. 10 is a diagram showing another example of the results of the noise simulation according to the embodiment. [Figure 11] FIG. 11 is a diagram illustrating an example of a computer that executes a noise simulation program. [Figure 12] FIG. 12 is a diagram showing a reference example of the arrangement of noise models in a quantum circuit. DETAILED DESCRIPTION OF THE INVENTION

[0014] Hereinafter, embodiments of the noise simulation program, information processing apparatus, and noise simulation method disclosed in the present application will be described in detail with reference to the accompanying drawings. However, the present invention is not limited to the embodiments. (Example)

[0015] (Image of noise model placement) First, noise simulation in a quantum circuit according to an embodiment will be described with reference to FIG. 1. FIG. 1 is a diagram showing an image of the arrangement of a noise model in a quantum circuit according to an embodiment. The noise simulation in a quantum circuit according to an embodiment uses an individual noise process for each quantum gate included in the quantum circuit to investigate the propagation of noise in the quantum circuit. In other words, the noise simulation analyzes the influence of noise using the individual noise process of the quantum gate. The noise here refers to quantum errors.

[0016] As shown in Figure 1, for example, noise simulation involves multiple quantum gates U acting on two qubits, each with its own noise process N A ,N C ,N E ,N F ,N G , N H Then, the noise simulation analyzes the effect of noise (quantum error) using the individual noise processes that have been placed. In addition, the noise simulation analyzes the effect of noise (quantum error) using the individual noise processes N B ,N D ,N I Then, the noise simulation analyzes the effect of noise (quantum error) using the individual noise processes that have been placed.

[0017] Note that the noise simulation in the quantum circuit according to the embodiment is performed by performing an analysis using a noise process that incorporates the characteristics of the quantum device. The noise process that incorporates the characteristics of the quantum device refers to the Pauli channel. The Pauli channel here refers to a noise process in which Pauli errors occur randomly for quantum bits according to a certain probability distribution. Simulations using the Pauli channel have already been implemented in simulation software such as Qulacs (arXiv:13524). Note that the Pauli channel will be described later.

[0018] (Explanation of noise process) 2 is a diagram for explaining a noise process according to an embodiment, showing the relationship between a quantum gate U and a noise process N that acts after the processing.

[0019] The noise process N according to the embodiment is performed by operating the quantum gate U (ideal quantum gate) in the opposite direction by half ((√U) -1 ), adding a time evolution V resulting from residual interaction or relaxation, and operating the quantum gate U only halfway in the forward direction (√U). The process of operating the quantum gate U only halfway in the reverse direction is represented by the symbol n1. The time evolution V resulting from residual interaction or relaxation is represented by the symbol n2. The process of operating the quantum gate U only halfway in the forward direction is represented by the symbol n3. Note that the noise process N has been described as a time evolution resulting from residual interaction or relaxation for the time evolution V, but is not limited to this and may be a time evolution resulting from both residual interaction and relaxation.

[0020] Here, residual interaction refers to unwanted interactions between quantum bits. Noise resulting from this interaction is, for example, a coherent error. Relaxation refers to external interactions. Noise resulting from this interaction is, for example, a stochastic reversal error.

[0021] Such a noise process N takes into account the interference between the quantum gate U and residual interactions or relaxation. That is, the noise process N obtains the mutually interfering components of U and V by inserting rotations resulting from residual interactions or relaxation in an ideal time evolution (n1, n3). This provides a better approximation than simply applying V as noise after U. In other words, by applying V to the state during U's processing rather than after U's processing, the noise process N makes it possible to model the action of noise that proceeds simultaneously with the action of the actual quantum gate U.

[0022] By applying such a noise process N to noise simulation, quantum devices can be simulated based on a noise model that is more faithful to their own performance, thereby improving the accuracy of the noise simulation.

[0023] In Figure 2, we have explained the case where U is divided into two halves, one in the backward direction and the other in the forward direction, but this is not limiting. For example, by applying the results of the Suzuki-Trotter decomposition (arXiv:math-ph / 0506007), U and V may be divided into even smaller parts.

[0024] (Functional configuration of information processing device) 3 is a diagram illustrating an example of the functional configuration of an information processing device according to an embodiment. The information processing device 1 illustrated in FIG. 3 is an example of a quantum device that performs noise simulation. The information processing device 1 includes an input unit 21, a storage unit 22, a noise process extraction unit 23, a noise action unit 24, and a measurement unit 25.

[0025] The input unit 21 inputs information about the quantum circuit and stores it in the storage unit 22. The information about the quantum circuit refers to, for example, a quantum circuit described in a circuit description format.

[0026] The storage unit 22 stores information input by the input unit 21. The storage unit 22 also stores intermediate information of the simulations performed by the noise process extraction unit 23 and the noise application unit 24, and information measured by the measurement unit 25.

[0027] The noise process extraction unit 23 extracts the noise process of the target quantum gate.

[0028] For example, the noise process extraction unit 23 selects one step of interest in a quantum circuit. The one step of interest includes the noise process of the target quantum gate to be modeled. The noise process extraction unit 23 then approximates the process at the selected step in the quantum circuit with a combination of quantum gates. That is, the noise process extraction unit 23 approximates "N" shown in the left diagram of FIG. 2 with a combination of quantum gates n1, n2, and n3 shown in the right diagram. The noise process extraction unit 23 then extracts only quantum gates related to the noise process of the target quantum gate from the approximated combination of quantum gates. The noise process extraction unit 23 then models the time evolution of the extracted quantum gate as the noise process of the target quantum gate. Here, the noise process extraction unit 23 uses the Pauli channel when modeling the noise process. That is, the noise process extraction unit 23 calculates the probability distribution of the occurrence probability of various Pauli errors for the quantum bit on which the noise process of the target quantum gate acts, and models it as a noise process having the probability distribution of the occurrence probability.

[0029] Furthermore, the noise process extraction unit 23 sequentially selects other quantum gates included in the selected step as target quantum gates and extracts only quantum gates related to the noise process of the target quantum gate.The noise process extraction unit 23 then models the time evolution of the extracted quantum gates as the noise process of the target quantum gate.The noise process extraction unit 23 then similarly models the noise processes of each quantum gate included in the other steps in the quantum circuit.In other words, the noise process extraction unit 23 models a noise process with an individual probability distribution of occurrence probability for each target quantum gate.

[0030] The noise application unit 24 applies a noise process to the target quantum gate. For example, the noise application unit 24 randomly generates a Pauli error in accordance with the distribution of the Pauli error occurrence probability of the noise process of the target quantum gate modeled by the noise process extraction unit 23.

[0031] The measurement unit 25 measures the quantum bits. For example, the measurement unit 25 applies a noise process to all target quantum gates in the quantum circuit and measures the quantum bits included in the quantum circuit. That is, the measurement unit 25 measures the quantum bits in order to analyze the effect that noise has on each quantum bit. That is, the measurement unit 25 examines the propagation of noise in the quantum circuit.

[0032] (Method of noise process extraction) 4A to 4C are diagrams illustrating a method for extracting a noise process according to an embodiment. For ease of explanation, only one noise process is modeled. Furthermore, the time evolution V will be described as the time evolution resulting from residual interactions, for example.

[0033] 4A, the noise process extraction unit 23 selects one step of interest in the quantum circuit. Here, the selected step is represented by the symbol G1. Step G1 includes the target quantum gate and the noise process N to be modeled.

[0034] 4B, the noise process extraction unit 23 approximates the process at one step selected in the quantum circuit with a combination of quantum gates. That is, the noise process extraction unit 23 approximates the process at one step selected in the quantum circuit with a combination of the target quantum gate G11, the reverse half of the target quantum gate G12, the time evolution G13 resulting from residual interactions, and the forward half of the target quantum gate G14.

[0035] As shown in FIG. 4C, the noise process extraction unit 23 extracts quantum gates related to the noise process N of the target quantum gate from the combination of approximated quantum gates. Here, the quantum gates shown in highlighting are extracted as quantum gates related to the noise process N. Then, the noise process extraction unit 23 models the time evolution of the extracted quantum gates as the noise process of the target quantum gate. The modeled noise process is indicated by the symbol N'. In other words, the noise process extraction unit 23 extracts the quantum gates related to the noise process N of the target quantum gate. 2Q is approximated by the noise process N' to be modeled.

[0036] In modeling, analysis is performed using a Pauli channel that incorporates the characteristics of the quantum device. The Pauli channel here refers to a noise process in which Pauli errors occur randomly for a quantum bit according to a certain probability distribution. That is, when performing modeling, the noise process extraction unit 23 calculates the probability distribution of the occurrence probability of a Pauli error in the noise process N'. In other words, by adjusting the probability distribution of the occurrence probability of a Pauli error, the noise process extraction unit 23 can incorporate the characteristics of the quantum error that occurs in the quantum system, and can therefore perform a noise simulation for the quantum circuit using this probability distribution.

[0037] (Modeling of noise processes) FIG. 5 is a diagram illustrating modeling of a noise process according to an embodiment. Here, bit flip errors and phase flip errors that occur in a quantum bit are described using Pauli operators. The Pauli I operator corresponds to the case where no error occurs. The Pauli X operator corresponds to a bit flip error, the Pauli Z operator corresponds to a phase flip error, and the Pauli Y operator corresponds to a phase flip error of a correlated bit. When performing modeling, the noise process extraction unit 23 calculates the probability of each error occurring. When the noise process N' to be modeled is one quantum bit, a total of four types of probabilities are calculated. When the noise process N' to be modeled is two quantum bits, a total of 16 types of probabilities are calculated.

[0038] N shown in Figure 5 2Q is the case of a noise process N' acting on two quantum bits. In this case, the noise process extraction unit 23 calculates the probability of all 16 types of Pauli errors that may occur in the two quantum bits by performing an analysis using the Pauli channel. As an example, p II indicates the probability that no error occurs for both qubits. p IX denotes the probability that no error occurs in the upper qubit, but a bit-flip error occurs in the lower qubit. p XYindicates the probability that a bit decision error occurs in the upper qubit and a correlated bit phase reversal error occurs in the lower qubit. More specifically, for example, p XY indicates the probability of occurrence of a Pauli error, which is expressed by the tensor product of the Pauli X operator and the Pauli Y operator.

[0039] In this way, when performing modeling, the noise process extraction unit 23 performs analysis using the Pauli channel to extract the noise process N 2Q The probability distribution of the simultaneous occurrence probability of Pauli errors in (N') is calculated. FIG. 5 shows the probability distribution table H0 of the calculation results. After that, the noise application unit 24 selects one error by performing probabilistic sampling according to this probability distribution table H0, and applies the noise process N 2Q Apply (N´).

[0040] (Overall flowchart of noise simulation) An example of an overall flowchart of the noise simulation according to the embodiment will now be described with reference to Fig. 6. Fig. 6 is a diagram showing an example of an overall flowchart of the noise simulation according to the embodiment. It is assumed that the information processing device 1 has input information about the quantum circuit, etc.

[0041] 6, the information processing device 1 initializes all quantum bits for the input quantum circuit (step S11). The information processing device 1 repeats steps S13 to S17 for each step in the quantum circuit (step S12).

[0042] The information processing device 1 selects one step and repeats steps S14 to S16 for each quantum gate in the selected step (step S13). The information processing device 1 selects one quantum gate and operates the selected target quantum gate (ideal quantum gate) (step S14). Then, the information processing device 1 extracts the noise process of the target quantum gate (step S15). The process of extracting the noise process will be described later.

[0043] Then, the information processing device 1 applies the extracted noise process (step S16). If there is an unselected quantum gate in the selected step, the information processing device 1 proceeds to step S13 (step S17). If there is no unselected quantum gate in the selected step, the information processing device 1 proceeds to step S12 (step S18).

[0044] If there are no unselected steps, the information processing device 1 measures all of the quantum bits for the quantum circuit (step S19), and then the information processing device 1 ends the noise simulation.

[0045] (Flowchart of noise process extraction) Fig. 7 is a diagram showing an example of a flowchart of noise process extraction according to an embodiment. The flowchart of Fig. 7 will be described with reference to Figs. 8A to 8D. Figs. 8A to 8D are diagrams showing an example of noise process extraction according to an embodiment.

[0046] The information processing device 1 calculates the ideal time evolution U for the target quantum gate (step S21). Here, as shown in FIG. 8A, the quantum gate U acting on two quantum bits is taken as the target quantum gate. For example, the information processing device 1 determines the set of quantum bits on which the Pauli error P acts for the target quantum gate U as S(=supp(P)). The information processing device 1 calculates √U, which indicates the hyperoperator expression of the ideal quantum gate U to the power of 1 / 2, and the inverse matrix of √U. √U is denoted by the symbol a3. The inverse matrix of √U is denoted by the symbol a1.

[0047] Returning to FIG. 7, the information processing device 1 calculates each noise component ΔV i Steps S23 to S25 are repeated for the set of supp(U) and the set of supp(ΔV i ) is not an empty set (step S23). That is, the information processing device 1 determines whether the set S of quantum bits on which the Pauli error P acts has a common part. The set supp(U) and the set supp(ΔV i) is an empty set (step S23; No), the information processing device 1 proceeds to step S26.

[0048] On the other hand, the set of supp(U) and supp(ΔV i ) is not an empty set (step S23; Yes), the information processing device 1 i (Step S24). Then, the information processing device 1 calculates the noise process V and the calculated V i (Step S25). The information processing device 1 calculates the product of the unprocessed noise component ΔV i If there is, the process proceeds to step S22 (step S26). Here, as shown in FIG. 8B, the information processing device 1 calculates the noise process V related to the Pauli error P. At this time, the information processing device 1 calculates E as shown in the following equation (2). j Calculate the product only for j such that S intersects with S. j are V1, V2, and V3 shown in Fig. 8B. The information processing device 1 then defines supp(V) as a set E of quantum bits on which the noise process V acts. The set E represents the union of E1, E2, and E3 shown in Fig. 8B.

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[0049] Returning to FIG. 7, the information processing device 1 calculates the unprocessed noise component ΔV i If there is no noise process N, the noise process N is calculated and approximated (step S27). Here, as shown in FIG. 8C, the information processing device 1 calculates the dimension of √U by using the tensor product with the identity operator, |E| Similarly, the information processing device 1 also adjusts the dimensions of the inverse matrices of the noise processes V and √U to 4. |E| The dimension of √U is 4. |E| The dimension of the inverse matrix of √U is 4. |E| The result is (√U´) -1 The dimension of the noise process V is expressed as 4 |E|The result of aligning the two is represented as V'. Then, the information processing device 1 calculates "(√U') -1 ·V´·√U´」

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[0050] Here, the contraction operation will be described in detail with reference to FIG. 8D. First, the information processing device 1 sets the number of quantum bits on which the quantum circuit operates to "n". As shown in equation (3), the information processing device 1 uses a hyper-operator N i Calculate.

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[0051] P i is an operator that represents a transition and is defined as the following formula (4). j (i) is the symbol that represents the jth digit of the binary notation of i. n ×2 n is the identity matrix of , where n is the number of qubits as shown above.

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[0052] The information processing device 1 detects the i-th noise N i Among the matrices representing

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[0053] Furthermore, the information processing device 1 calculates the Pauli Twaring approximation N^ of the condensed noise process N as shown in the following equation (5). That is, the calculated Pauli Twaring approximation N^ is the Pauli channel after approximation. Note that P here is the Pauli error.

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[0054] Then, the information processing device 1 calculates the Pauli error occurrence probability p P Calculate the p P There are 4 in total n This represents the probability that a specific Pauli error P occurs among the possible Pauli errors (n is the number of qubits). n We are calculating the sum of the expressions on the right side of the right-hand side Σ for the Pauli errors Q. The Pauli errors P and Q each refer to the tensor product of n Pauli operators acting on each quantum bit.

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[0055] In addition, in equation (6),<P,Q> SP is also called the symplectic inner product, and its value changes depending on the commutation relationship of the Pauli operators P and Q, as shown in equation (7).

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[0056] In this way, the information processing device 1 approximates and models the noise process of the target quantum gate with the noise process N, and calculates the occurrence probability p P Calculate the probability distribution of .

[0057] Returning to FIG. 7, the information processing device 1 ends the noise process extraction process.

[0058] (Noise simulation results) Next, the results of a noise simulation according to an embodiment will be described with reference to FIGS. 9 and 10. FIG. 9 is a diagram showing an example of the results of a noise simulation according to an embodiment. The left diagram in FIG. 9 shows the quantum circuit to be simulated and the simulation conditions. In FIG. 9, the information processing device 1 simulates the effect of noise on the quantum circuit to be simulated using three methods, and examines the approximation error from the strictly calculated time evolution. Here, the approximation error is defined by the diamond distance. The definition method using the diamond distance here is shown in "Benenti, G. & Strini, G. Computing the distance between quantum channels: Usefulness of the Fano representation. J. Phys. B: At. Mol. Opt. Phys. 43, 215508 (2010)."

[0059] The three methods are a case where noise is not taken into consideration at all (Control), a case where depolarization noise is used (Conventional), and a case where noise simulation according to the embodiment is used (Proposed). Note that the case where depolarization noise is used (Conventional) is a case where the noise simulation shown in FIG. 12 is used. That is, the noise simulation in this case is a case where a common noise process N 1Q After processing by two quantum gates, 2Q This is a method of applying the following.

[0060] The simulation conditions are a gate operation time of 0.5 μs, a relaxation rate of 1.0, and a resident ZZ interaction of 1 MHz. In other words, the relaxation strength is stronger than a predetermined value. In this case, the noise simulation according to the embodiment indicated by symbol e1 (Proposed) has a smaller approximation error than the cases where no noise consideration is made (Control) or where depolarization noise is used (Conventional).

[0061] FIG. 10 is a diagram showing another example of the results of noise simulation according to the embodiment. The left diagram of FIG. 10 shows the quantum circuit to be simulated and the simulation conditions. In FIG. 10, similar to FIG. 9, the information processing device 1 simulates the effect of noise on the quantum circuit to be simulated using three methods, and examines the approximation error from the strictly calculated time evolution. The three methods are as shown in FIG. 9.

[0062] The simulation conditions are a gate operation time of 0.5 μs, a relaxation rate of 0.1, and a resident ZZ interaction of 1 MHz. In other words, this is the case where the strength of relaxation is weaker than a predetermined value. In this case, when using the noise simulation according to the embodiment indicated by symbol e2 (Proposed), the approximation error is even smaller than that shown in FIG. 9 compared to when no noise consideration is made (Control) or when depolarization noise is used (Conventional). In other words, it can be confirmed that when the influence of relaxation is small and the resident ZZ interaction is stronger, errors due to residual interactions and relaxation can be better approximated.

[0063] In this way, the information processing device 1 can perform an evaluation in accordance with the characteristics of an actual quantum device in estimating the performance of quantum computing using noise simulation, compared to the depolarization noise (Conventional) introduced in the conventional noise model.

[0064] [Effects of the Example] According to the above embodiment, the information processing device 1 performs noise simulation using the noise process of a quantum gate included in a quantum circuit. For example, after processing by the quantum gate, the information processing device 1 performs noise simulation by operating the quantum gate halfway in the reverse direction as a noise process, adding time evolution due to residual interactions, and operating the quantum gate halfway in the forward direction. In this way, by sandwiching time evolution due to residual interactions between the time evolution of an ideal quantum gate, the information processing device 1 can improve the accuracy of the noise simulation compared to simply operating the noise process after the target quantum gate. Furthermore, the information processing device 1 can improve the accuracy of the noise simulation of each quantum circuit while suppressing computational costs, even when the number of qubits in the quantum circuit increases.

[0065] Furthermore, in the information processing device 1, the noise simulation process approximates a process in one step in a quantum circuit, including the noise process of a target quantum gate, using a combination of quantum gates included in that step. The noise simulation process then extracts a quantum gate related to the noise process of the target quantum gate from the approximated combination of quantum gates, and models the time evolution corresponding to the extracted quantum gate as the noise process of the target quantum gate. The noise simulation process then generates noise using the modeled noise process. In this way, the information processing device 1 can improve the accuracy of the noise simulation by modeling the noise process of the target quantum gate included in the one step of interest.

[0066] Furthermore, in the information processing device 1, the modeling process uses a Pauli operator to calculate the probability distribution of various Pauli errors occurring for quantum bits affected by the noise process of the target quantum gate. The noise generating process then randomly generates Pauli errors according to the calculated probability distribution. This allows the information processing device 1 to incorporate the characteristics of errors occurring in quantum circuits by adjusting the distribution of the Pauli error occurrence probability using a Pauli channel in the noise process.

[0067] Furthermore, in the modeling process in the information processing device 1, the noise process is modeled for each target quantum gate included in the quantum circuit. As a result, the information processing device 1 can improve the accuracy of the noise simulation by using a noise process for each quantum gate individually instead of a common noise process.

[0068] Furthermore, in the information processing device 1, the noise simulation process uses a noise process in which the time evolution due to residual interactions is replaced with the time evolution due to relaxation. By inserting the time evolution due to relaxation into the time evolution of an ideal quantum gate, the information processing device 1 can improve the accuracy of the noise simulation compared to simply applying the noise process after the target quantum gate. Furthermore, even if the number of qubits in a quantum circuit increases, the information processing device 1 can improve the accuracy of the noise simulation of each individual quantum circuit while suppressing computational costs.

[0069] Note that the components of the illustrated information processing device 1 do not necessarily have to be physically configured as shown. In other words, the specific manner in which the information processing device 1 is distributed and integrated is not limited to that shown, and all or part of the information processing device 1 can be functionally or physically distributed and integrated in any unit depending on various loads, usage conditions, etc. Also, the storage unit 22 may be connected to the information processing device 1 as an external device via a network.

[0070] The various processes described in the above embodiments can be realized by executing a prepared program on a computer such as a personal computer or a workstation. Therefore, an example of a computer that executes a noise simulation program that realizes the same functions as the information processing device 1 shown in Fig. 3 will be described below. Here, a noise simulation program that realizes the same functions as the information processing device 1 will be described as an example. Fig. 11 is a diagram showing an example of a computer that executes a noise simulation program.

[0071] 11, computer 200 includes a CPU (Central Processing Unit) 203 that executes various types of arithmetic processing, an input device 215 that accepts data input from a user, and a display device 209. Computer 200 also includes a drive device 213 that reads programs and the like from a storage medium, and a communication I / F (Interface) 217 ​​that transmits and receives data to and from other computers via a network. Computer 200 also includes a memory 201 that temporarily stores various types of information, and an HDD (Hard Disk Drive) 205. Memory 201, CPU 203, HDD 205, display control unit 207, display device 209, drive device 213, input device 215, and communication I / F 217 are connected via a bus 219.

[0072] The drive device 213 is, for example, a device for the removable disk 211. The HDD 205 stores a noise simulation program 205a and noise simulation processing related information 205b. The communication I / F 217 manages the interface between the network and the inside of the device, and controls the input and output of data from other computers. The communication I / F 217 can be, for example, a modem or a LAN adapter.

[0073] The display device 209 is a display device that displays a cursor, an icon, a toolbox, and data such as documents, images, and function information. The display device 209 can be, for example, a liquid crystal display or an organic EL (Electroluminescence) display.

[0074] The CPU 203 reads out the noise simulation program 205a, expands it in the memory 201, and executes it as a process. These processes correspond to the respective functional units of the information processing device 1. The noise simulation processing related information 205b includes, for example, information stored in the storage unit 22. For example, the removable disk 211 stores each piece of information such as the noise simulation program 205a.

[0075] It should be noted that noise simulation program 205a does not necessarily have to be stored in HDD 205 from the beginning. For example, the program may be stored in a "portable physical medium" such as a flexible disk (FD), CD-ROM, DVD disk, magneto-optical disk, or IC card that is inserted into computer 200. Computer 200 may then read and execute noise simulation program 205a from these.

[0076] Furthermore, the noise simulation described in the above embodiment can be applied to, for example, evaluating the calculation performance of a quantum computer. [Explanation of symbols]

[0077] 1. Information processing equipment 21 Input section 22 Memory section 23 Noise process extraction unit 24 Noise acting part 25 Measuring part

Claims

1. A noise simulation program that performs noise simulation using a noise process of a quantum gate included in a quantum circuit, After the processing by the quantum gate, noise simulation is performed by operating the quantum gate in half in the backward direction as the noise process, adding time evolution due to residual interactions, and operating the quantum gate in half in the forward direction. A noise simulation program that causes a computer to execute processing.

2. The noise simulation process includes: In the quantum circuit, a process in one step including the noise process of the target quantum gate is approximated by a combination of quantum gates included in the one step; extracting a quantum gate associated with the noise process of the target quantum gate from the combination of approximated quantum gates, and modeling the time evolution corresponding to the extracted quantum gate as the noise process of the target quantum gate; Generate noise using the modeled noise process 2. The noise simulation program according to claim 1.

3. The modeling process uses a Pauli operator to calculate a probability distribution of various Pauli errors occurring for a quantum bit of the target quantum gate on which the noise process acts; The noise generating process randomly generates the Pauli errors according to the calculated probability distribution.

3. The noise simulation program according to claim 2.

4. The modeling process models the noise process for each target quantum gate included in the quantum circuit.

3. The noise simulation program according to claim 2.

5. The process of performing the noise simulation performs the noise simulation using the noise process in which the time evolution due to the residual interaction is replaced with the time evolution due to relaxation.

2. The noise simulation program according to claim 1.

6. An information processing device that performs noise simulation using a noise process of a quantum gate included in a quantum circuit, a control unit that performs a noise simulation by applying, as the noise process, a process of operating the quantum gate only halfway in the reverse direction, a process of adding time evolution resulting from residual interactions, and a process of operating the quantum gate only halfway in the forward direction after processing by the quantum gate. An information processing device comprising:

7. A noise simulation method for performing noise simulation using a noise process of a quantum gate included in a quantum circuit, comprising: As the noise process, after the processing by the quantum gate, a process of operating the quantum gate in the reverse direction by half, a process of adding time evolution due to residual interaction, and a process of operating the quantum gate in the forward direction by half are applied to perform noise simulation. A noise simulation method characterized in that processing is executed by a computer.

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