Quantum error correction code evaluation program, quantum error correction code evaluation method, and information processing device

Abstract

The present invention reduces calculation load for evaluating quantum error correction code.　An information processing device (10) according to the present invention generates a first map (5) for converting an input state to an output state on the basis of input / output information (4) indicating a correspondence relationship between the input state in syndrome measurement for a second quantum error correction code (3) and the output state including influence of noise. The information processing device (10) generates a second map (6) in which an amount of influence received by noise is extracted from the first map (5), and generates a first quantum error correction code (8) made up of a plurality of the second quantum error correction codes (3). The information processing device (10) causes noise generated according to the second map (6) to act on each of the second quantum error correction codes (3) making up the first quantum error correction code (8), and evaluates performance of error correction by the first quantum error correction code (8) with respect to an quantum error occurring due to the influence of noise.

Description

Quantum error correcting code evaluation program, quantum error correcting code evaluation method, and information processing device

[0001] The present invention relates to a quantum error correcting code evaluation program, a quantum error correcting code evaluation method, and an information processing device.

[0002] The quantum bits (qubits) used in quantum computers are exposed to various noises. Quantum bits can easily lose their quantum properties due to quantum errors (physical errors) caused by noise. Therefore, it is important to establish quantum error correction technology.

[0003] Quantum error correction is a procedure for correcting a physical error that occurs in one of multiple quantum bits used for redundancy. That is, in quantum error correction, quantum states are made redundant, and the quantum state of one quantum bit (logical quantum bit) is represented by multiple quantum bits. When a physical error occurs in one of the redundant quantum bits, quantum error correction detects the location of the physical error and corrects the error.

[0004] If quantum errors can be correctly corrected by quantum error correction, the quantum state of the logical quantum bit can be protected from the effects of quantum errors. On the other hand, if quantum errors cannot be correctly corrected, the quantum state of the logical quantum bit will be in an incorrect state (logical error), making correct quantum computation difficult.

[0005] The specific method for quantum error correction is called quantum error correcting code. The performance of quantum error correcting code is evaluated by the probability of error correction failure. For example, for quantum error correcting code, the relationship between the probability of physical error occurrence under a certain noise model and the probability of logical error occurrence is investigated.

[0006] Noise models used to evaluate the performance of quantum error correcting codes include code capacity models, phenomenological models, and circuit-level models. However, analyses using these noise models cannot incorporate the effects of noise that continues to act continuously while quantum gates are being executed. Therefore, an analytical method using the quantum master equation has been developed.

[0007] The quantum master equation method calculates the time evolution of the quantum state of an open quantum system by solving a differential equation described by a Hamiltonian and a relaxation operator. By solving the above equation for multiple initial states, a complete-positive trace preserving (CPTP) map, which is the input-output relationship of the quantum state, can be obtained. Analysis using the quantum master equation makes it possible to incorporate the effects of noise resulting from relaxation and residual interactions more accurately than circuit-level models.

[0008] As a technology related to quantum error correction, for example, a simulation method has been proposed that enables efficient determination of whether or not a logical error has occurred. Also, a technology related to optimizing physical parameters in fault-tolerant quantum computing to reduce frequency congestion has been proposed. Furthermore, a technology has been proposed that performs quantum error correction of one or more physical qubits among multiple physical qubits based on the measurement of one flag qubit.

[0009] International Publication No. 2023-089831 Japanese Patent Application Publication No. 2021-192324 US Patent Application Publication No. 2021 / 0019223

[0010] While analyzing the effects of noise using the quantum master equation allows us to accurately incorporate the effects of noise, the computation time increases exponentially with the number of qubits in the quantum circuit being analyzed. Therefore, with conventional techniques, it is difficult to accurately incorporate the effects of noise and evaluate the performance of quantum error correction for large-scale systems.

[0011] In one aspect, the present application aims to reduce the computational burden for evaluating quantum error correcting codes.

[0012] One proposal provides a quantum error correcting code evaluation program that causes a computer to perform the following processes: the computer generates a first map that converts an input state to a syndrome measurement into an output state based on input / output information that indicates a correspondence between an input state and an output state including the influence of noise in a syndrome measurement for a second quantum error correcting code having the same configuration as a part of a first quantum error correcting code to be evaluated; the computer generates a second map that extracts an amount of influence caused by noise from the first map; the computer generates a first quantum error correcting code that is composed of a plurality of second quantum error correcting codes; and the computer applies noise generated in accordance with the second map to each of the second quantum error correcting codes that make up the first quantum error correcting code, thereby evaluating the error correction performance of the first quantum error correcting code for quantum errors that occur due to the influence of noise.

[0013] According to one aspect, the computational load for evaluating a quantum error correcting code can be reduced. These and other objects, features, and advantages of the present invention will become apparent from the following description taken in conjunction with the accompanying drawings illustrating preferred embodiments of the present invention.

[0014] 1 is a diagram illustrating an example of a quantum error correcting code evaluation method according to a first embodiment; FIG. 2 is a diagram illustrating an example of a computer system configuration; FIG. 3 is a diagram illustrating an example of classical computer hardware for evaluating quantum error correcting codes; FIG. 4 is a diagram illustrating an example of a surface code; FIG. 5 is a diagram illustrating an example of a syndrome measurement circuit; FIG. 6 is a diagram illustrating an example of a code capacity model; FIG. 7 is a diagram illustrating an example of a phenomenological model; FIG. 8 is a diagram illustrating an example of a circuit level model; FIG. 9 is a diagram illustrating an example of a continuous error; FIG. 10 is a diagram illustrating an example of a CPTP map showing the operation of a syndrome measurement circuit; FIG. 11 is a diagram illustrating an example of a [[4,2,2]] code; FIG. 12 is a diagram illustrating an example of a syndrome measurement circuit for a [[4,2,2]] code with a measurement qubit for X stabilizer measurement in the center; FIG. 13 is a diagram illustrating an example of a syndrome measurement circuit for a [[4,2,2]] code with a measurement qubit for Z stabilizer measurement in the center; FIG. 14 is a block diagram illustrating an example of functions of a classical computer; FIG. 15 is a diagram illustrating an example of a procedure for quantum error correcting code evaluation processing; FIG. 16 is a flowchart illustrating an example of a procedure for a CPTP map generation processing; FIG. 17 is a flowchart illustrating an example of a procedure for a 7-qubit noise model generation processing; FIG. 18 is a diagram illustrating an example of a Pauli channel; FIG. 1 is a diagram showing an example of a correction circuit for a 5-qubit repetition code. FIG. 2 is a diagram showing an example of a pulse schedule for operating an actual machine. FIG. 3 is a diagram showing an example of a calculated probability of occurrence of a Pauli error. FIG. 4 is a diagram showing an example of a surface code represented by a set of [[4,2,2]] codes with a measurement qubit for X stabilizer measurement in the center. FIG. 5 is a diagram showing an example of a surface code represented by a set of [[4,2,2]] codes with a measurement qubit for Z stabilizer measurement in the center. FIG. 6 is a diagram showing an example of a generated bit flip error. A flowchart showing an example of a processing procedure for surface code simulation. FIG. 7 is a diagram showing an example of a state in which logical errors occur. FIG. 8 is a diagram showing the relationship between a physical error rate and a logical error rate.

[0015] The present embodiment will be described below with reference to the drawings. Note that each embodiment can be implemented by combining multiple embodiments within a consistent range. [First Embodiment] FIG. 1 is a diagram showing an example of a quantum error correcting code evaluation method according to a first embodiment. FIG. 1 shows an information processing device 10 that implements the quantum error correcting code evaluation method. The information processing device 10 can implement the quantum error correcting code evaluation method by, for example, executing a quantum error correcting code evaluation program.

[0016] The information processing device 10 includes a storage unit 11 and a processing unit 12. The storage unit 11 is, for example, a memory or a storage device included in the information processing device 10. The processing unit 12 is, for example, a processor or an arithmetic circuit included in the information processing device 10.

[0017] The storage unit 11 stores input / output information 4 indicating the correspondence between input states and output states including the influence of noise in syndrome measurement for a second quantum error correcting code 3 having the same configuration as, for example, a part of a first quantum error correcting code 8 to be evaluated. The first quantum error correcting code 8 to be evaluated is, for example, a surface code. The second quantum error correcting code 3 is, for example, a [[4,2,2]] code having the same configuration as, for example, a part of the surface code.

[0018] The processing unit 12 evaluates the performance of the first quantum error correcting code 8 to be evaluated. For example, the processing unit 12 acquires input / output information 4 by a time evolution simulation in which syndrome measurement of the second quantum error correcting code 3 is performed on the quantum computer 1. For example, the processing unit 12 accepts input of actual machine information 2 related to noise generated in the quantum computer 1, and performs a precise time evolution simulation using the actual machine information 2. The actual machine information 2 is, for example, the value of a parameter included in a differential equation used in the time evolution simulation.

[0019] The processing unit 12 generates a first map 5 that converts an input state to the syndrome measurement into an output state based on the input / output information 4. For example, the processing unit 12 generates the first map 5 through analysis using a quantum master equation. The first map 5 is, for example, a CPTP map. The first map 5 is divided into a second map 6 that indicates the amount of influence of noise and a third map 7 that indicates a noise-free syndrome measurement. The second map 6 and the third map 7 are, for example, CPTP maps.

[0020] The processing unit 12 generates a second map 6 by extracting the amount of influence of noise from the first map 5. For example, the processing unit 12 generates the second map 6 by performing an operation opposite to that of syndrome measurement on the first map 5. In this case, the processing unit 12 may approximate the second map 6 to a Pauli channel 6a that indicates the process by which a stochastic Pauli error acts.

[0021] The processing unit 12 also generates a first quantum error correcting code 8 that is composed of a plurality of second quantum error correcting codes 3. The processing unit 12 then applies noise generated according to the second mapping 6 to each of the second quantum error correcting codes 3 that compose the first quantum error correcting code 8, and evaluates the error correction performance of the first quantum error correcting code 8 for quantum errors that occur due to the influence of the noise.

[0022] For example, when the second map 6 is approximated to a Pauli channel 6a, the processing unit 12 calculates, based on the Pauli channel 6a, the probability of occurrence of a Pauli error caused by noise generated in each of the plurality of second quantum error correcting codes 3. The processing unit 12 then evaluates the performance of the first quantum error correcting code 8 based on whether or not a logical error occurs when a Pauli error is caused in a quantum bit included in the first quantum error correcting code 8 at the calculated probability of occurrence of the Pauli error. For example, the processing unit 12 calculates a logical error rate in error correction by the first quantum error correcting code 8 as an index indicating the performance of the first quantum error correcting code 8.

[0023] According to this quantum error correcting code evaluation method, the processing unit 12 can obtain the second mapping 6 for the noise component occurring in the syndrome measurement of the second quantum error correcting code 3, based on the input / output information 4. The second quantum error correcting code 3 is smaller in scale than the first quantum error correcting code 8, and the calculation load for obtaining the second mapping 6 is small.

[0024] Furthermore, by using the second mapping 6, it is possible to easily apply noise to the second quantum error correcting code 3 that constitutes the first quantum error correcting code 8 with a small computational load. Therefore, the processing unit 12 can evaluate the error correction performance of the first quantum error correcting code 8 with a small computational load. In other words, the quantum error correcting code evaluation method according to the first embodiment can reduce the computational load for evaluating the first quantum error correcting code.

[0025] The input / output information 4 can be obtained by a time evolution simulation of syndrome measurement of the second quantum error correcting code 3. The second quantum error correcting code 3 is smaller in scale than the first quantum error correcting code 8, and the computational load for the time evolution simulation is also small. Therefore, a precise time evolution simulation is possible using a quantum master equation that more accurately incorporates the effects of noise resulting from relaxation and residual interactions. Therefore, an output state that includes the effects of noise resulting from relaxation and residual interactions can be obtained as the output state of the input / output information 4. As a result, the processing unit 12 can evaluate the first quantum error correcting code 8 with high accuracy, incorporating the effects of noise resulting from relaxation and residual interactions.

[0026] Furthermore, by approximating the second map 6 to the Pauli channel 6a, the processing unit 12 can easily cause a Pauli error due to the influence of generated noise to act on the first quantum error correcting code 8. As a result, the calculation load required for evaluating the first quantum error correcting code 8 is reduced. For example, the processing unit 12 can easily calculate the probability of occurrence of a Pauli error based on the Pauli channel 6a. As a result, the processing unit 12 can easily evaluate the first quantum error correcting code 8 based on whether or not a logical error occurs when a Pauli error is caused in a quantum bit included in the first quantum error correcting code 8 using the calculated probability of occurrence of a Pauli error.

[0027] Furthermore, when the surface code is the first quantum error correcting code 8 to be evaluated, the processing unit 12 uses the [[4,2,2]] code as the second quantum error correcting code 3, making it easy to generate a first quantum error correcting code 8 composed of multiple second quantum error correcting codes 3.

[0028] Second Embodiment The second embodiment is a computer system for evaluating the performance of surface codes with a low computational load. Surface codes are also called topological surface codes. In recent years, surface codes have attracted attention due to their high error correction performance and ease of implementation.

[0029] 2 is a diagram showing an example of the configuration of a computer system. The quantum computer system 300 includes a classical computer 310 and a quantum computer 320. The classical computer 310 is a conventional computer also known as a von Neumann computer. The classical computer 310 controls the quantum computer 320 to perform quantum calculations. The quantum computer 320 is a computer that applies the principles of quantum mechanics to calculations. The quantum computer 320 is a quantum gate-type computer that uses quantum devices such as superconducting circuits, ion traps, and diamonds.

[0030] A terminal device 400 and a classical computer 100 for evaluating quantum error correcting codes are connected to the classical computer 310 via a network 20. The terminal device 400 is a computer used by a user who requests quantum computing by the quantum computer system 300. The classical computer 100 is also a von Neumann-type computer, like the classical computer 310. The classical computer 100 performs an error correction simulation of the quantum error correcting code to be applied to quantum computing in the quantum computer system 300, and evaluates its reliability.

[0031] The classical computer 310 receives a quantum circuit from the terminal device 400. A quantum circuit indicates the order of operations on quantum bits by arranging elements such as gates. A quantum bit is a bit that can represent a superposition of the "0" state and the "1" state.

[0032] The classical computer 310 instructs the quantum computer 320 to control the quantum bits in accordance with the quantum circuit received from the terminal device 400. The classical computer 310 also acquires measurement results of each quantum bit from the quantum computer 320. The quantum computer 320 has multiple quantum bits and devices for manipulating each of the multiple quantum bits.

[0033] The classical computer 100 evaluates the performance of quantum error correction when quantum error correction using a surface code is applied to quantum computing in the quantum computer 320, for example, using parameters that indicate the characteristics of the quantum computer 320.

[0034] 3 is a diagram illustrating an example of classical computer hardware for evaluating quantum error correcting codes. The classical computer 100 is entirely controlled by a processor 101. A memory 102 and multiple peripheral devices are connected to the processor 101 via a bus 109. The processor 101 may be a multiprocessor. The processor 101 is, for example, a central processing unit (CPU), a micro processing unit (MPU), or a digital signal processor (DSP). At least some of the functions realized by the processor 101 executing a program may be realized by an electronic circuit such as an application specific integrated circuit (ASIC) or a programmable logic device (PLD).

[0035] The memory 102 is used as the main storage device of the classical computer 100. The memory 102 temporarily stores at least a portion of the OS (Operating System) program and application programs to be executed by the processor 101. The memory 102 also stores various data used in processing by the processor 101. As the memory 102, for example, a volatile semiconductor storage device such as a RAM (Random Access Memory) is used.

[0036] The peripheral devices connected to the bus 109 include a storage device 103 , a GPU (Graphics Processing Unit) 104 , an input interface 105 , an optical drive device 106 , a device connection interface 107 , and a network interface 108 .

[0037] The storage device 103 electrically or magnetically writes and reads data to and from a built-in recording medium. The storage device 103 is used as an auxiliary storage device for the classical computer 100. The storage device 103 stores the OS program, application programs, and various data. Note that the storage device 103 may be, for example, a hard disk drive (HDD) or a solid state drive (SSD).

[0038] The GPU 104 is an arithmetic unit that performs image processing. The GPU 104 is an example of a graphics controller. A monitor 21 is connected to the GPU 104. The GPU 104 displays an image on the screen of the monitor 21 in accordance with an instruction from the processor 101. The monitor 21 may be a display device using organic electroluminescence (EL) or a liquid crystal display device.

[0039] The input interface 105 is connected to a keyboard 22 and a mouse 23. The input interface 105 transmits signals sent from the keyboard 22 and the mouse 23 to the processor 101. The mouse 23 is an example of a pointing device, and other pointing devices can also be used. Examples of other pointing devices include a touch panel, a tablet, a touch pad, and a trackball.

[0040] The optical drive device 106 uses a laser beam or the like to read data recorded on an optical disc 24 or write data to the optical disc 24. The optical disc 24 is a portable recording medium on which data is recorded so that it can be read by reflected light. Examples of the optical disc 24 include a DVD (Digital Versatile Disc), a DVD-RAM, a CD-ROM (Compact Disc Read Only Memory), and a CD-R (Recordable) / RW (Rewritable).

[0041] The device connection interface 107 is a communication interface for connecting peripheral devices to the classical computer 100. For example, a memory device 25 or a memory reader / writer 26 can be connected to the device connection interface 107. The memory device 25 is a recording medium equipped with a function for communicating with the device connection interface 107. The memory reader / writer 26 is a device for writing data to a memory card 27 or reading data from the memory card 27. The memory card 27 is a card-type recording medium.

[0042] The network interface 108 is connected to the network 20. The network interface 108 transmits and receives data to and from other computers or communication devices via the network 20. The network interface 108 is a wired communication interface that is connected by a cable to a wired communication device such as a switch or a router. The network interface 108 may also be a wireless communication interface that is connected by radio waves to a wireless communication device such as a base station or an access point.

[0043] The classical computer 100 can realize the processing functions of the second embodiment with the hardware described above. Note that the information processing device 10 shown in the first embodiment can also be realized with hardware similar to that of the classical computer 100 shown in FIG.

[0044] The classical computer 100 realizes the processing functions of the second embodiment by executing a program recorded on, for example, a computer-readable recording medium. The program describing the processing to be executed by the classical computer 100 can be recorded on various recording media. For example, the program to be executed by the classical computer 100 can be stored in the storage device 103. The processor 101 loads at least a portion of the program in the storage device 103 into the memory 102 and executes the program. The program to be executed by the classical computer 100 can also be recorded on a portable recording medium such as the optical disk 24, the memory device 25, or the memory card 27. The program stored on the portable recording medium becomes executable after being installed on the storage device 103, for example, under the control of the processor 101. The processor 101 can also read and execute the program directly from the portable recording medium.

[0045] In such a system, a quantum error correcting code is evaluated by a classical computer 100. A surface code, for example, is used as the quantum error correcting code. Fig. 4 is a diagram showing an example of a surface code. The surface code 30 is a quantum error correcting code that arranges quantum bits in a two-dimensional square lattice and realizes quantum error correction by causing adjacent quantum bits to interact with each other.

[0046] The quantum bits that make up surface code 30 are shown as circular shapes. The open circles represent data quantum bits (e.g., data quantum bit 31) that write quantum information. The closed circles represent measurement quantum bits (e.g., measurement quantum bits 32 and 33) for error detection. Measurement quantum bits located at the center of the shaded rectangular area, such as measurement quantum bit 32, are used to measure the Z stabilizer. Measurement quantum bits located at the center of the open rectangular area, such as measurement quantum bit 33, are used to measure the X stabilizer.

[0047] The data qubit and the measurement qubit interact by running a quantum circuit called a syndrome measurement circuit. If an error occurs in a data qubit, the eigenvalue indicated by the measurement result of the adjacent measurement qubit flips from "+1" to "-1." The measurement result of the measurement qubit is called the syndrome.

[0048] FIG. 5 is a diagram showing an example of a syndrome measurement circuit. The syndrome measurement circuit 41 shown in FIG. 5 is a quantum circuit for measuring the Z stabilizer. In the syndrome measurement circuit 41, five quantum bits are set as operation targets. The first quantum bit in the syndrome measurement circuit 41 corresponds to the measurement quantum bit for measuring the Z stabilizer. The other four quantum bits in the syndrome measurement circuit 41 correspond to the four data quantum bits surrounding the measurement quantum bit. |ψ z 〉 represents the state of the measurement qubit. a >,|ψ b >,|ψ c >,|ψ d >,... represent the states of the data qubits.

[0049] In syndrome measurement circuit 41, the state of the measurement qubit is first initialized to |0> (a state in which the eigenvalue of Z is "1"). Then, CNOT gate operations are performed between the measurement qubit and each of the other four data qubits. In each CNOT gate, the data qubit is the control qubit and the measurement qubit is the target qubit.

[0050] The performance of a surface code is determined by the probability of failing to correct a quantum error (logical error probability P L ) where P is the probability of quantum error correction failure. The higher the physical error probability P, the higher the probability of quantum error correction failure. The physical error probability P depends on the noise generation state in the quantum computer 320. Therefore, as an index representing the performance of the surface code, the physical error probability P and the logical error probability P are calculated based on an idealized noise model. L The relationship can be investigated.

[0051] Noise models used to evaluate the performance of surface codes include a code capacitance model, a phenomenon theory model, and a circuit level model. Fig. 6 shows an example of a code capacitance model. Fig. 6 shows a code capacitance model that indicates the noise generation state in the syndrome measurement circuit 42 for X stabilizer measurement.

[0052] Five quantum bits are set as operation targets in the syndrome measurement circuit 42. The first quantum bit in the syndrome measurement circuit 42 corresponds to a measurement quantum bit for measuring the X stabilizer. The other four quantum bits in the syndrome measurement circuit 42 correspond to four data quantum bits surrounding the measurement quantum bit.

[0053] In the syndrome measurement circuit 42, a Hadamard gate is operated on the measurement qubit initialized to |0>. Then, a CNOT gate is operated between the measurement qubit and each of the other four data qubits. In each CNOT gate, the measurement qubit is the control qubit and the data qubit is the target qubit. Finally, a Hadamard gate is operated on the measurement qubit.

[0054] The code capacity model is a model in which quantum errors occur only in the data quantum bits. In Figure 6, error occurrence locations 43a to 43d are surrounded by dashed lines (the same applies to Figures 7 and 8). The code capacity model may be used if the analysis assumes quantum errors only in the data quantum bits, but in reality, quantum errors also occur in the measurement quantum bits due to the influence of noise. Therefore, the code capacity model cannot accurately evaluate the performance of the surface code.

[0055] 7 is a diagram showing an example of a phenomenological model. The phenomenological model is a model in which errors occur in the data quantum bits and syndrome measurement results. In the phenomenological model, the state of each quantum bit after gate operation becomes the error occurrence locations 44a to 44e.

[0056] Compared to the code capacity model, the phenomenological model can analyze the effects of noise on syndrome measurement results. However, noise occurs in various situations, such as gate operation and measurement, and the phenomenological model is insufficient to analyze the effects of such noise.

[0057] 8 is a diagram showing an example of a circuit-level model. The circuit-level model is a model in which an error occurs immediately after a quantum gate in a syndrome measurement circuit. In the circuit-level model, the parts where the quantum gates are located correspond to error occurrence locations 45a to 45f.

[0058] When the classical computer 100 evaluates the surface code using a circuit-level model, it applies a noise process that models actual noise immediately after each quantum gate that constitutes the syndrome measurement circuit 42. The classical computer 100 then performs a simulation of how the effects of noise propagate through the quantum gates. In this simulation, the classical computer 100 can apply the noise process even during waiting times when the quantum gates are not operating.

[0059] In the evaluation of surface codes using circuit-level models, the effects of noise can be approximately captured by applying a noise process after an ideal quantum gate, but in real quantum devices, noise continues to act continuously and in parallel with the execution of the quantum gate.

[0060] FIG. 9 is a diagram showing an example of a continuous error. In an actual quantum device, noise occurs continuously and simultaneously with the execution of a quantum gate, resulting in an error occurrence point 46 in a location other than the gate operation of the quantum gate. The error occurrence point 46 shown in FIG. 9 is just one example, and there are countless such error occurrence points. Evaluation using a circuit-level model cannot incorporate the effects of such noise that occurs continuously and simultaneously with the execution of a quantum gate.

[0061] Furthermore, for example, noise caused by residual interactions is one type of noise that cannot be captured by a circuit-level model. Fig. 10 is a diagram showing an example of residual interactions. As shown in Fig. 10, residual interactions 52a, 52b, and 52c exist between adjacent quantum bits. The influence of noise caused by such residual interactions 52a, 52b, and 52c cannot be captured by a circuit-level model.

[0062] Therefore, it is possible to perform an analysis using the quantum master equation. In the analysis using the quantum master equation, the Hamiltonian H and the relaxation operator L i The time evolution of the state ρ of the open quantum system is calculated by solving the differential equation described by the following. The differential equation used in the quantum master equation is as follows:

[0063]

[0064] γ in Equation (1) i is the relaxation rate, which is a value obtained from measurements of an actual device. By solving the differential equation shown in equation (1) for multiple initial states, a CPTP map, which is the input-output relationship of the quantum state, can be obtained.

[0065] A CPTP map is a map for representing quantum operations. The CPTP map gives the input-output relationship of quantum states. In other words, by using the CPTP map, the probability distribution of the output quantum state can be obtained from the input quantum state.

[0066] 11 is a diagram showing an example of a CPTP map illustrating the operation of the syndrome measurement circuit. The input state ρ to the syndrome measurement circuit is transformed by a CPTP map 51 to obtain the output state ε(ρ).

[0067] The properties of CPTP are complete positivity and trace preservation. Complete positivity means that negative probabilities do not appear in the output distribution. Trace preservation means that the sum of probabilities is preserved before and after input and output.

[0068] The CPTP map can be calculated based on the results of, for example, a rigorous time evolution simulation or an experiment using an actual quantum device.N By examining the input-output relationship for each of the density operators (quantum states) (N is the number of quantum bits), a CPTP mapping can be obtained.

[0069] The evaluation of surface codes using such quantum master equations can more accurately incorporate noise effects from relaxation and residual interactions than circuit-level models. However, the computation time increases exponentially with the number of qubits. Therefore, the evaluation of surface codes using quantum master equations is difficult to apply to large-scale systems.

[0070] As mentioned above, the challenge with evaluations using circuit-based models is that they cannot take into account the effects of quantum gates and noise acting simultaneously and continuously, while the challenge with evaluations based on quantum master equations is that the calculation time increases as the target system becomes larger.

[0071] Therefore, we focus on a portion of the surface code. For example, the classical computer 100 performs a detailed simulation of the portion of the surface code based on the quantum master equation. The classical computer 100 processes the CPTP map obtained from the simulation into a noise model that can be efficiently calculated in a large-scale simulation system. The classical computer 100 then uses the processed noise model to perform a quantum error correction simulation of the surface code.

[0072] For example, we focus on noise acting on the [[4,2,2]] code, which uses a common syndrome measurement circuit for the surface code and can be configured with fewer physical quantum bits. Hereinafter, the noise model for analyzing noise acting on the [[4,2,2]] code will be referred to as the 7-qubit noise model. Syndrome measurement for the [[4,2,2]] code can be performed using the same syndrome measurement circuit as the surface code.

[0073] 12 is a diagram showing an example of a [[4,2,2]] code. The [[4,2,2]] code 60 is a code with a code distance of "2" that encodes "2" logical quantum bits with "four" data quantum bits 60a, 60b, 60f, and 60g. The [[4,2,2]] code 60 uses three measurement quantum bits 60c to 60e. The measurement quantum bits 60c and 60e at both ends of the [[4,2,2]] code 60 are used for Z stabilizer measurement, and the central measurement quantum bit 60d is used for X stabilizer measurement.

[0074] In the example of Figure 12, the qubit number of each qubit that makes up the [[4,2,2]] code 60 is shown next to that qubit. Data qubit 60a has qubit number "1". Data qubit 60b has qubit number "2". Measurement qubit 60c has qubit number "3". Measurement qubit 60d has qubit number "4". Measurement qubit 60e has qubit number "5". Data qubit 60f has qubit number "6". Data qubit 60g has qubit number "7".

[0075] Of the quantum bits that make up the [[4,2,2]] code 60, data quantum bits 60a and 60f make up one gauge operator 60h, and data quantum bits 60a and 60b also make up one gauge operator 60i.

[0076] 13 is a diagram showing an example of a syndrome measurement circuit for a [[4,2,2]] code in which a measurement qubit for measuring the X stabilizer is located in the center. In a syndrome measurement circuit 70 for the [[4,2,2]] code 60, a Hadamard gate 70a is first arranged for a measurement qubit 60d for measuring the X stabilizer.

[0077] Next, two CNOT gates 70b and 70c are arranged. CNOT gate 70b uses data qubit 60b as a control qubit and measurement qubit 60e for Z stabilizer measurement as a target qubit. CNOT gate 70c uses measurement qubit 60d for X stabilizer measurement as a control qubit and data qubit 60a as a target qubit.

[0078] Next, two CNOT gates 70d and 70e are arranged. CNOT gate 70d uses data qubit 60g as a control qubit and measurement qubit 60e for Z stabilizer measurement as a target qubit. CNOT gate 70e uses measurement qubit 60d for X stabilizer measurement as a control qubit and data qubit 60f as a target qubit.

[0079] Next, two CNOT gates 70f and 70g are arranged. CNOT gate 70f uses measurement qubit 60d for X stabilizer measurement as the control qubit and data qubit 60b as the target qubit. CNOT gate 70g uses data qubit 60a as the control qubit and measurement qubit 60c for Z stabilizer measurement as the target qubit.

[0080] Next, two CNOT gates 70h and 70i are arranged. CNOT gate 70h uses measurement qubit 60d for X stabilizer measurement as the control qubit and data qubit 60g as the target qubit. CNOT gate 70i uses data qubit 60f as the control qubit and measurement qubit 60c for Z stabilizer measurement as the target qubit.

[0081] As the final gate operation, a Hadamard gate 70j is placed on measurement qubit 60d for measuring the X stabilizer. Then, measurements 70k to 70m are specified for three measurement qubits 60c to 60e of the [[4,2,2]] code, respectively.

[0082] By using this syndrome measurement circuit 70, an X stabilizer is obtained from the measurement result of measurement qubit 60d, and a Z stabilizer is obtained from the measurement results of measurement qubits 60c and 60e.

[0083] Such a syndrome measurement circuit 70 enables syndrome measurement of the [[4,2,2]] code 60. Fig. 13 shows an example of the [[4,2,2]] code 60 in which the measurement qubit 60d for measuring the X stabilizer is at the center, but the measurement qubit at the center may also be for measuring the Z stabilizer.

[0084] 14 is a diagram showing an example of a syndrome measurement circuit for a [[4,2,2]] code in which a measurement qubit for Z stabilizer measurement is located in the center. [[4,2,2]] code 61 has four data qubits 61a, 61b, 61f, and 61g and three measurement qubits 61c to 61e. Measurement qubits 61c and 61e at both ends of [[4,2,2]] code 61 are used for X stabilizer measurement, and the measurement qubit 61d in the center is used for Z stabilizer measurement.

[0085] In the syndrome measurement circuit 71 denoted by the [[4,2,2]] symbol 61, Hadamard gates 71a and 71b are arranged for the measurement quantum bits 61c and 61e for measuring the X stabilizer, respectively.

[0086] Next, two CNOT gates 71c and 71d are arranged. CNOT gate 71c uses data qubit 61b as a control qubit and measurement qubit 61d for Z stabilizer measurement as a target qubit. CNOT gate 71d uses measurement qubit 61c for X stabilizer measurement as a control qubit and data qubit 61a as a target qubit.

[0087] Next, two CNOT gates 71e and 71f are arranged. CNOT gate 71e uses measurement qubit 61e for X stabilizer measurement as the control qubit and data qubit 61b as the target qubit. CNOT gate 71f uses data qubit 61a as the control qubit and measurement qubit 61d for Z stabilizer measurement as the target qubit.

[0088] Next, two CNOT gates 71g and 71h are arranged. CNOT gate 71g uses data qubit 61g as a control qubit and measurement qubit 61d for Z stabilizer measurement as a target qubit. CNOT gate 71h uses measurement qubit 61c for X stabilizer measurement as a control qubit and data qubit 61f as a target qubit.

[0089] Next, two CNOT gates 71i and 71j are arranged. CNOT gate 71i uses measurement qubit 61e for X stabilizer measurement as the control qubit and data qubit 61g as the target qubit. CNOT gate 71j uses data qubit 61f as the control qubit and measurement qubit 61d for Z stabilizer measurement as the target qubit.

[0090] As the final gate operation, Hadamard gates 71k and 71l are placed on measurement qubits 61c and 61e for X stabilizer measurement, respectively. Measurements 71m to 71o are specified for the three measurement qubits 61c to 61e of the [[4,2,2]] code.

[0091] By using this syndrome measurement circuit 71, a Z stabilizer is obtained from the measurement result of measurement qubit 61d, and an X stabilizer is obtained from the measurement results of measurement qubits 61c and 61e.

[0092] The classical computer 100 treats the noise acting on such [[4,2,2]] codes 60 and 61 as a 7-qubit noise model, and performs a detailed simulation of the 7-qubit noise model based on the quantum master equation. This results in a CPTP map that represents the effect of errors in the 7-qubit noise model. A simulation of the scale of the 7-qubit noise model does not require a large amount of calculation.

[0093] The classical computer 100 processes the 7-bit noise model CPTP map into a noise model that can be efficiently calculated in a large-scale simulation system, and then uses the processed noise model to perform quantum error correction simulations on larger-scale surface codes.

[0094] 15 is a block diagram showing an example of functions of a classical computer. The classical computer 100 includes a CPTP map generation unit 110, a noise model generation unit 120, and a surface code simulation unit .

[0095] The CPTP map generator 110 obtains a CPTP map that reflects the noise characteristics of the quantum computer 320. For example, based on information about the actual quantum computer 320, a detailed simulation of the time evolution of the syndrome measurement circuit of the [[4,2,2]] code is performed, and the CPTP map is calculated from the input / output relationship.

[0096] The noise model generation unit 120 generates noise generated by a 7-qubit noise model based on the obtained CPTP mapping. The surface code simulation unit 130 performs a quantum error correction simulation of the entire surface code using the obtained 7-qubit noise. This allows, for example, the logical error rate when quantum error correction of quantum computation by the quantum computer 320 is performed using the surface code.

[0097] The function of each element shown in Fig. 15 can be realized, for example, by having the processor 101 execute a program module corresponding to that element. Fig. 16 is a diagram showing an example of the procedure for quantum error correcting code evaluation processing. The processing shown in Fig. 16 will be explained below in order of step number.

[0098] [Step S101] The CPTP map generation unit 110 generates a CPTP map for the syndrome measurement circuit of the [[4,2,2]] code based on actual machine information indicating the characteristics of the quantum computer 320. Details of the CPTP map generation process will be described later (see FIG. 17).

[0099] [Step S102] The noise model generation unit 120 generates a 7-qubit noise model based on the CPTP mapping. Details of the 7-qubit noise model generation process will be described later (see FIG. 18).

[0100] [Step S103] The surface code simulation unit 130 performs a surface code evaluation process by applying noise based on a 7-qubit noise model. The surface code evaluation process will be described in detail later (see FIG. 23).

[0101] By this process, it is possible to perform an evaluation that accurately reflects the influence of noise that actually occurs, even for a large-scale surface code. Fig. 17 is a flowchart showing an example of the procedure for the CPTP mapping generation process. The process shown in Fig. 17 will be explained below in order of step number.

[0102] [Step S201] The CPTP mapping generation unit 110 N (N is the number of quantum bits in the syndrome measurement circuit) density operators (quantum states) are set as initial states, and the process of step S202 is looped for each initial state.

[0103] [Step S202] The CPTP map generation unit 110 performs a detailed simulation (rigorous time evolution simulation) of the syndrome measurement circuit for the [[4,2,2]] code. Specifically, the CPTP map generation unit 110 sets an initial state for each quantum bit of the [[4,2,2]] code, calculates the change in the state of each quantum bit when gate operations are performed in accordance with the syndrome measurement circuit using time evolution simulation, and obtains the output quantum state.

[0104] The time evolution simulation is an analysis using a quantum master equation, and can be calculated by solving the differential equation shown in Equation (1). This calculation is performed by accurately incorporating the effects of noise resulting from relaxation and residual interactions in the quantum computer 320. For example, the relaxation rate γ i In the parameter, actual machine parameters that indicate the characteristics of the quantum computer 320 are set.

[0105] The CPTP map generation unit 110 can also instruct the quantum computer system 300 to execute quantum computation of the syndrome measurement circuit for the [[4,2,2]] code, and obtain an output state corresponding to the initial state as a result of quantum computation by the quantum computer 320. By using the computation results using the actual device, it is possible to obtain an output state that reflects the effects of all noise that occurs in the actual device.

[0106] [Step S203] The CPTP mapping generation unit 110 N When the calculation in step S202 is completed for all the initial states, the process proceeds to step S204. [Step S204] The CPTP map generation unit 110 calculates the input / output relationship of the syndrome measurement circuit for the [[4,2,2]] code. For example, the CPTP map generation unit 110 calculates the input / output relationship of the syndrome measurement circuit for the [[4,2,2]] code. N We calculate the CPTP mapping that obtains the output states corresponding to each of the three initial states.

[0107] In this way, the CPTP map of the syndrome measurement circuit for the [[4,2,2]] code is obtained. The obtained CPTP map accurately reflects the influence of noise generated in the quantum computer 320.

[0108] 18 is a flowchart showing an example of the procedure for generating a 7-qubit noise model. The process shown in FIG. 18 will be described below in order of step number. [Step S301] The noise model generation unit 120 performs an inverse operation of an ideal syndrome measurement circuit for the [[4,2,2]] code to obtain a CPTP map that extracts the noise components contained in the syndrome measurement circuit.

[0109] [Step S302] The noise model generation unit 120 approximates the CPTP map representing the noise component to a process (Pauli channel) in which stochastic Pauli errors act. This results in a Pauli channel in the syndrome measurement circuit for the [[4,2,2]] code. This Pauli channel is a formulation of the 7-qubit noise model.

[0110] FIG. 19 is a diagram showing an example of a Pauli channel. The CPTP map 72a acquired by the CPTP map generator 110 is represented as "ε(ρ)". The CPTP map 72a is expressed as the tensor product of a map 72b that indicates the influence of noise occurring when the syndrome measurement circuit is executed, and a map 72c that indicates the action of the syndrome measurement circuit when executed without noise. Here, the map 72b corresponding to noise is represented as "ε noise (ρ)" and the mapping 72c corresponding to the syndrome measurement circuit without noise is "U(ρ)". At this time, the mapping 72b corresponding to noise is "ε noise (ρ)" is expressed by the following formula:

[0111]

[0112] When equation (2) is converted into an approximate equation using the Pauli-twirling approximation, the following equation is obtained.

[0113]

[0114] B m is the mth (m is a natural number) Pauli operator. k is the kth Claus operator (k is a natural number). K is the total number of Pauli operators (4 N ) in equation (3). noise (ρ)" (ε is followed by ~) is the Pauli channel 72d.

[0115] Here, the Pauli-twirling approximation is a method of approximating the CPTP map with a process (Pauli channel 72d) in which the Pauli operator acts stochastically. In discussions of quantum error correction, the Pauli operator acting stochastically is called a Pauli error, which corresponds to a bit-flip error or phase-flip error that occurs in a quantum bit.

[0116] The Pauli-twirling approximation to the CPTP mapping “ε(ρ)” is as follows:

[0117]

[0118] p j is the jth (j is a natural number) Pauli operator "B jThe reason for using the Pauli-twirling approximation is as follows.

[0119] The syndrome measurement circuit is a quantum circuit that has the property of not causing a superposition of bit-flip errors or phase-flip errors, but only changing the type of error. Here, if the only quantum errors that occur are bit-flip errors and phase-flip errors, the classical computer 100 only needs to simulate the time evolution of errors represented by a vector of at most 2N dimensions by using the Pauli-twirling approximation.

[0120] Such a time evolution simulation is N This can be performed more efficiently than simulations of the time evolution of quantum states represented by n-dimensional vectors. By using the Pauli-twirling approximation in this way, computational efficiency is greatly improved. The fact that the Pauli-twirling approximation enables efficient simulations is known as the Gottesman-Knill theorem.

[0121] Based on equation (4), the Pauli error occurrence probability p for each quantum bit when the syndrome measurement circuit is executed on the quantum computer 320 is j Hereafter, the Pauli error occurrence probability p j The calculation method will be specifically explained below.

[0122] CPTP mapping ε with respect to noise noise Pauli transfer matrix ε ij The Pauli transfer matrix ε ij The diagonal terms of i The Pauli transfer matrix represents how the CPTP map transforms the Pauli operator into a linear combination of Pauli matrices.

[0123] The elements of the Pauli transfer matrix are represented by the weights of the linear combination, and can be calculated by the trace (the diagonal sum of the matrix) using the following formula:

[0124]

[0125] On the other hand, the CPTP map representing the Pauli channel has the following input-output relationship:

[0126]

[0127] From equation (6), it can be seen that if we ignore the non-diagonal terms of the obtained Pauli transfer matrix, the Pauli transfer matrix becomes a Pauli channel. In other words, expressing the CPTP map using a Pauli transfer matrix is ​​an operation equivalent to the Pauli-twirling approximation.

[0128] Next, the diagonal terms d of the Pauli transfer matrix i and the error probability p j Conversion relationship A ij is expressed as follows:

[0129]

[0130] [B in formula (7)] i , B j ] is called the commutation relation. Two Pauli operators B i , B j In contrast, [B i , B j ]=B i B j -B j , B i where the diagonal term d i A vector d with components and a Pauli error occurrence probability p j The following transformation relationship holds between the vector p having components:

[0131]

[0132] Therefore, the desired Pauli error occurrence probability is given by the following formula:

[0133]

[0134] In this way, the seven-qubit noise model allows the Pauli error occurrence probability of each qubit due to the influence of noise that occurs when implementing the syndrome measurement circuit for the [[4,2,2]] code to be accurately determined.

[0135] Note that, although the above example shows the procedure for calculating the Pauli error occurrence probability in the syndrome measurement circuit for the [[4,2,2]] code, the Pauli error occurrence probability can be calculated for other correction circuits using similar processing. Below, with reference to Figures 20 to 22, an example of calculating the Pauli error occurrence probability for a correction circuit for a 5-qubit repetition code will be described.

[0136] 20 is a diagram showing an example of a correction circuit for a five-qubit repetition code. In the correction circuit 73 for a five-qubit repetition code, the first, third, and fifth qubits are data qubits, and the second and fourth qubits are measurement qubits.

[0137] The noise model generating unit 120 executes a simulation assuming that the quantum computer 320 is made to execute the 5-qubit iterative code correction circuit 73, and calculates the CPTP mapping.

[0138] 21 is a diagram showing an example of a pulse schedule for operating an actual device. For example, the noise model generation unit 120 simulates gate operations of quantum bits using a pulse schedule 74. Each of ch0 to ch4 of the pulse schedule 74 corresponds to a quantum bit and indicates a gate operation for the corresponding quantum bit. Ch5 to ch8 correspond to a connection relationship between two quantum bits and indicate a gate operation for the two connected quantum bits. The solid lines indicate the values ​​of the real parts of the pulses for gate operation, and the dashed lines indicate the values ​​of the imaginary parts of the pulses for gate operation.

[0139] The noise model generation unit 120 calculates the CPTP map by simulating the operation of an actual device in accordance with the pulse schedule 74. The noise model generation unit 120 creates Pauli noise from the obtained CPTP map and calculates the probability of a Pauli error occurring for each quantum bit.

[0140] 22 is a diagram showing an example of the calculated probability of occurrence of a Pauli error. The horizontal axis of graph 75 shows the output state of the five quantum bits after the gate operation of the correction circuit 73. If no Pauli error occurs, the output state will be "IIIIII." However, a Pauli error occurs due to the influence of noise, and states other than "IIIIII" also occur. In the example of graph 75, a Pauli error correlated with the quantum bits occurs.

[0141] In this way, for a small-scale quantum circuit (e.g., a syndrome measurement circuit), it is possible to accurately calculate the probability of Pauli errors based on the CPTP map that reflects the noise when executed on a real device. By evaluating the surface code using the Pauli error probability calculated in this way, it is possible to accurately evaluate even a large-scale surface code that reflects the influence of noise on the real device.

[0142] 23 is a diagram showing an example of a surface code represented by a set of [[4,2,2]] codes with a measurement quantum bit for X stabilizer measurement at the center. As shown in FIG. 23, a surface code 62 can be tiled with [[4,2,2]] codes 60 with a measurement quantum bit for X stabilizer measurement at the center. Note that quantum bits are shared between adjacent [[4,2,2]] codes 60.

[0143] 24 is a diagram showing an example of a surface code represented by a set of [[4,2,2]] codes with a measurement qubit for Z stabilizer measurement at the center. As shown in FIG. 24, a surface code 62 can be tiled with [[4,2,2]] codes 61 with a measurement qubit for Z stabilizer measurement at the center.

[0144] 23 and 24, the surface code simulation unit 130 expresses the surface code 62 by tiling two types of [[4,2,2]] codes 60 and 61. The surface code simulation unit 130 then calculates the Pauli channel “ε” which indicates the noise process of the 7-qubit noise model. noise ” (ε is followed by ~) is applied to each quantum bit at the corresponding position on the surface symbol 62. Since multiple Pauli errors added by noise are commutative, “ε noise” (ε is followed by ~) can be applied in any order.

[0145] FIG. 25 is a diagram showing an example of a generated bit flip error. In the example of FIG. 25, it is assumed that a surface code 62 is covered with [[4,2,2]] codes 60 with a measurement qubit for measuring the X stabilizer in the center. The surface code simulation unit 130 calculates the Pauli channel "ε noise An error is generated in one of the quantum bits according to the Pauli error occurrence probability of each quantum bit that occurs when applying the Pauli X error (ε follows the - symbol). In the example of FIG. 25, in the [[4,2,2]] code 63, Pauli X errors (bit flip errors) have occurred in the first, third, and seventh quantum bits.

[0146] The surface code simulation unit 130 performs error detection and error correction processing (surface code simulation) for the generated error in accordance with an error detection and correction algorithm based on syndrome measurement of the surface code. If the error can be correctly corrected by the surface code simulation, the surface code simulation unit 130 determines that a logical error has not occurred based on the generated error. On the other hand, if the error cannot be correctly corrected by the surface code simulation, the surface code simulation unit 130 determines that a logical error has occurred.

[0147] 26 is a flowchart showing an example of a processing procedure for surface code simulation. The processing shown in FIG. 26 will be explained below in order of step number. [Step S401] The surface code simulation unit 130 performs the processing of steps S402 to S405 for a predetermined number of samples.

[0148] [Step S402] The surface code simulation unit 130 applies noise based on a 7-qubit noise model to each of the [[4,2,2]] codes spread across the surface code. By applying noise, a Pauli error occurs in a quantum bit within the [[4,2,2]] code with a Pauli error occurrence probability based on the Pauli channel. The state of the multiple quantum bits that make up the surface code after applying noise based on the 7-qubit noise model is one sample for attempting correction using the surface code.

[0149] [Step S403] The surface code simulation unit 130 simulates syndrome measurement for the surface code. For example, the surface code simulation unit 130 calculates the state measured by the measurement quantum bit after executing the syndrome measurement circuit of the surface code.

[0150] [Step S404] The surface code simulation unit 130 estimates the quantum bit in which a quantum error has occurred based on the state of the measured quantum bit and in accordance with an algorithm for detecting errors in the surface code.

[0151] [Step S405] The surface code simulation unit 130 performs quantum error correction processing on the quantum bit in which a quantum error is estimated to have occurred. [Step S406] When the surface code simulation unit 130 has completed the error correction trials using the surface code for a predetermined number of samples, it proceeds to step S407.

[0152] [Step S407] The surface code simulation unit 130 calculates the logical error rate, i.e., determines whether quantum error correction has been successful for each sample.

[0153] For example, the surface code simulation unit 130 determines that the quantum error correction has succeeded if the state of the logical bit represented by the surface code is consistent with the state in which no error occurs. Furthermore, the surface code simulation unit 130 determines that the quantum error correction has failed if the state of the logical bit represented by the surface code is not consistent with the state in which no error occurs, even after quantum error correction has been performed. The surface code simulation unit 130 then determines the value obtained by dividing the number of samples for which quantum error correction has failed by the total number of samples as the logical error rate.

[0154] In this way, even for large-scale surface codes, the logical error rate can be calculated while accurately reflecting the noise of the actual device. Below, we will show the results of a surface code simulation conducted for the case in which Pauli errors correlated with the data qubits occur in the seven-qubit noise model, and investigating the logical error probability.

[0155] 27 is a diagram showing an example of a logical error occurrence situation. For example, suppose that a surface code 62 is covered with a [[4,2,2]] code 60 in which a measurement quantum bit for X stabilizer measurement is placed at the center, and the surface code 62 is evaluated. In this case, if a Pauli error occurs in all data quantum bits in a vertical column, correction will fail. In other words, the data quantum bit in a vertical column in which a Pauli error occurred becomes the logical error source location 62a.

[0156] The logical error rate depends on the input state of the data quantum bit and the physical error rate. The results of the investigation of the logical error rate will be described with reference to FIG. 28. FIG. 28 is a diagram showing the relationship between the physical error rate and the logical error rate. Graph 76 shows the relationship between the error pattern generated on the X stabilizer measurement circuit and the logical error rate. The horizontal axis of graph 76 is the physical error rate (p), and the vertical axis is the logical error rate (p L ) The dotted line 76a of the graph 76 is "p L = p 2 The dotted line 76b is the line of "p L = p 3 " line.

[0157] The solid line 76c shows the relationship between the physical error rate and the logical error rate when the error pattern of the stabilizer measurement circuit is "XXII". The solid line 76d shows the relationship between the physical error rate and the logical error rate when the error pattern of the stabilizer measurement circuit is "IXXI". The solid line 76e shows the relationship between the physical error rate and the logical error rate when the error pattern of the stabilizer measurement circuit is "XIIX". The solid line 76f shows the relationship between the physical error rate and the logical error rate when the error pattern of the stabilizer measurement circuit is "XIII". The solid line 76g shows the relationship between the physical error rate and the logical error rate when the error pattern of the stabilizer measurement circuit is "XIXI". Each error pattern indicates that an X error has occurred in the quantum bit corresponding to "X".

[0158] The evaluation results of such surface codes reveal that some correlated errors induce logical errors, thereby increasing the probability of quantum error correction failure. For example, in graph 76, for error pattern "XXII," the degree of decrease in logical errors is smaller than that of other error patterns, even though the physical error rate decreases. This indicates that correlated errors between the first and second quantum bits in "XXII" induce logical errors.

[0159] In this way, the classical computer 100 can obtain an estimate of the quantum error correction performance using an actual quantum device using a noise model that can efficiently simulate even large-scale quantum error correction code systems. By being able to efficiently evaluate quantum error correction performance, it is possible to efficiently perform an evaluation that takes into account the effects of residual interactions (e.g., resident ZZ interactions) that exist between qubits where quantum gates are not acting.

[0160] The foregoing merely illustrates the principles of the present invention. Further, since numerous modifications and changes will be apparent to those skilled in the art, the present invention is not limited to the exact construction and application shown and described above, and all corresponding modifications and equivalents are deemed to be within the scope of the present invention as defined by the appended claims and their equivalents.

[0161] DESCRIPTION OF SYMBOLS 1 Quantum computer 2 Actual machine information 3 Second quantum error correcting code 4 Input / output information 5 First map 6 Second map 6a Pauli channel 7 Third map 8 First quantum error correcting code 10 Information processing device 11 Storage unit 12 Processing unit

Claims

1. Based on input-output information indicating the correspondence between the input state and the output state including the influence of noise in syndrome measurement for a second quantum error correction code having the same configuration as a part of the first quantum error correction code to be evaluated, generate a first mapping that converts the input state to the output state for the syndrome measurement, generate a second mapping that extracts the amount of influence received by the noise from the first mapping, generate the first quantum error correction code composed of a plurality of the second quantum error correction codes, and for each of the second quantum error correction codes constituting the first quantum error correction code, apply the noise generated according to the second mapping to evaluate the error correction performance of the first quantum error correction code against quantum errors generated by the influence of the noise. A quantum error correction code evaluation program for causing a computer to execute the process.

2. The quantum error correction code evaluation program according to claim 1, further causing the computer to execute a process of obtaining the input-output information by time evolution simulation when the syndrome measurement of the second quantum error correction code is executed in a quantum computer.

3. The quantum error correction code evaluation program according to claim 1, wherein in the process of generating the second mapping, the second mapping is generated by applying an operation reverse to the syndrome measurement to the first mapping.

4. The quantum error correction code evaluation program according to claim 1, wherein in the process of generating the second mapping, the second mapping is approximated to a Pauli channel indicating a process in which a probabilistic Pauli error acts.

5. The quantum error correction code evaluation program according to claim 4, wherein in the process of evaluating the performance of the first quantum error correction code, the occurrence probability of a Pauli error caused by the noise generated in each of the plurality of second quantum error correction codes is calculated based on the Pauli channel, and the performance of the first quantum error correction code is evaluated based on the presence or absence of a logical error when the Pauli error is generated in the qubits included in the first quantum error correction code with the calculated occurrence probability of the Pauli error.

6. In the process of generating the first mapping, a [[4, 2, 2]] code having the same configuration as a part of the surface code when the surface code is used as the first quantum error correction code to be evaluated is used as the second quantum error correction code. The quantum error correction code evaluation program according to claim 1.

7. Based on input / output information indicating the correspondence between the input state and the output state including the influence of noise in the syndrome measurement for a second quantum error correction code having the same configuration as a part of the first quantum error correction code to be evaluated, generate a first mapping that converts the input state to the output state for the syndrome measurement, generate a second mapping that extracts the amount of influence received from the noise from the first mapping, generate the first quantum error correction code composed of a plurality of the second quantum error correction codes, and apply the noise generated according to the second mapping to each of the second quantum error correction codes constituting the first quantum error correction code, and evaluate the error correction performance of the first quantum error correction code against the quantum error generated by the influence of the noise. A quantum error correction code evaluation method in which a computer executes the process.

8. Based on input / output information indicating the correspondence between the input state and the output state including the influence of noise in the syndrome measurement for a second quantum error correction code having the same configuration as a part of the first quantum error correction code to be evaluated, generate a first mapping that converts the input state to the output state for the syndrome measurement, generate a second mapping that extracts the amount of influence received from the noise from the first mapping, generate the first quantum error correction code composed of a plurality of the second quantum error correction codes, and apply the noise generated according to the second mapping to each of the second quantum error correction codes constituting the first quantum error correction code, and evaluate the error correction performance of the first quantum error correction code against the quantum error generated by the influence of the noise. An information processing apparatus having a processing unit for performing the process.

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