Crosstalk mitigation system and crosstalk mitigation method

Abstract

A relation table indicating the voltage and the state of quantum dots is generated on the basis of the resonance frequency of the quantum dots, the voltage dependency of the resonance frequency of the quantum dots, hardware constraints, and the distance function, and an optimal quantum circuit is selected so as to reduce crosstalk on the basis of a post-transpilation quantum circuit, the relation table, and the hardware constraints.

Description

Cross-talk mitigation system and cross-talk mitigation method 【0001】 The present invention relates to a cross-talk mitigation system and a cross-talk mitigation method. 【0002】 In recent years, the development of quantum computers has been accelerating. As characteristics of quantum computers, it can be mentioned that one qubit can take a superposition state of 0 and 1. Also, entanglement in which multiple qubits are quantum mechanically correlated is also a characteristic in quantum computers. By effectively utilizing the characteristics of qubits such as superposition states and entanglement, it is expected that quantum computers can execute calculations faster than conventional computers for prime factorization, inverse matrix calculation, etc. 【0003】 However, the state of qubits is affected by physical noise and changes unintentionally. Examples of noise sources include failures in quantum gate implementation and failures in quantum state preparation. If noise countermeasures are not executed, quantum computers cannot output correct answers. 【0004】 Quantum gates are implemented by irradiating qubits with microwaves. For example, in the method disclosed in Patent Document 1, the microwave pulse used to implement the quantum gate is optimized using a cost function defined using the Hamiltonian so that the noise is reduced. 【0005】 Among the hardware methods of quantum computers, in a quantum computer using a silicon semiconductor, the interval between quantum dots that can store qubits is on the order of several tens of nanometers, while the wavelength of microwaves is on the order of millimeters. Therefore, the microwaves irradiated for quantum gate implementation have the property of hitting all qubits. 【0006】 Therefore, in a quantum computer using a silicon semiconductor, adjusting the frequency of microwaves and the resonance frequency of qubits is also necessary to reduce failures in quantum gate implementation. 【0007】When implementing quantum gates that are not unit operators, such as X gates, it is necessary to match the microwave resonance frequency with the resonance frequency of the qubit to which the quantum gate is to be applied. If the difference between the microwave frequency and the qubit's resonance frequency is large, the implementation error of the quantum gate will increase. 【0008】 Conversely, if you want to idle a qubit, that is, if you want to apply a quantum gate corresponding to the unit operator to the qubit, you need to shift the microwave frequency and the qubit's resonance frequency. If the microwave frequency and the qubit's resonance frequency are close, the state of the qubit that you want to idle will change unintentionally. 【0009】 Crosstalk occurs when the relationship between the microwave frequency and the qubit's resonance frequency is not properly adjusted, causing the state of a qubit that is intended to be idle to change unintentionally, or when a quantum gate is intended to be applied to a qubit but the qubit does not resonate with the microwave, preventing the quantum gate from being implemented. 【0010】 To avoid crosstalk, it is necessary to adjust the microwave frequency and the qubit's resonance frequency. The Stark effect can be used to change the qubit's resonance frequency. The Stark effect is the phenomenon where the qubit's resonance frequency changes in response to the voltage applied to it. By appropriately adjusting the voltage of the quantum dot, crosstalk can be reduced. 【0011】 Furthermore, in quantum computers using silicon semiconductors, qubits can be moved from one quantum dot to another by shuttle. Shuttle can also be used to avoid crosstalk. However, shuttle also generates noise in the qubits, so it is desirable to minimize the number of shuttle operations. 【0012】 Japanese Patent Publication No. 2024-95690 【0013】 To adjust the resonance frequency of a qubit using the Stark effect, it is necessary to determine the relationship between the qubit's resonance frequency and the magnitude of crosstalk. 【0014】Generally, fidelity is a mathematical indicator that is easily measurable experimentally and represents how accurately a quantum gate has been implemented. The fidelity of an entire quantum circuit is often evaluated using the product of the fidelity of the individual fundamental gates that make up the quantum circuit. 【0015】 However, because fidelity has the mathematical property of not satisfying the triangle inequality, if the magnitude of crosstalk is taken as a function composed of the product of the fidelity of the basic gates, even if the voltage application method to the quantum dot is calculated so that the expected magnitude of crosstalk is kept within the range that satisfies the required accuracy, the actual magnitude of crosstalk may not fall within the range that satisfies the required accuracy. 【0016】 For example, consider the operation of idling one qubit for 500 nanoseconds. Idling for 500 nanoseconds is equivalent to idling for 250 nanoseconds twice in series. Therefore, as a method for evaluating the magnitude of crosstalk, instead of evaluating the fidelity of the 500-nanosecond idling operation, it is conceivable to evaluate it using the square of the fidelity of the 250-nanosecond idling operation. 【0017】 However, since fidelity does not satisfy the triangle inequality, even if the magnitude of crosstalk is evaluated using the square of the fidelity of the 250 nanosecond idling operation, and the voltage application method is calculated based on that to meet the required accuracy, the actual accuracy of the 500 nanosecond idling operation may be worse than expected. 【0018】 One way to avoid this is to calculate the accuracy for each quantum gate individually and then use that to calculate the voltage application method. However, since practical quantum computers capable of error correction are expected to be on the scale of several million qubits, changing the function used to evaluate accuracy for each quantum gate would increase the memory and computation time required for calculating that evaluation function on the classical computer. 【0019】For example, suppose we have two qubits, qubit A and qubit B. Qubit A is idled for 250 nanoseconds, then resonated with microwaves for 250 nanoseconds to perform a rotation gate in the X direction. Qubit B is to be resonated with microwaves for 500 nanoseconds to perform a rotation gate in the X direction. 【0020】 In this case, the method of calculating the accuracy for each quantum gate individually requires preparing and calculating functions that represent the accuracy of three types of operations: a 250-nanosecond idling operation, an operation of applying a rotation gate in the X direction by resonating with microwaves for 250 nanoseconds, and an operation of applying a rotation gate in the X direction by resonating with microwaves for 500 nanoseconds. 【0021】 On the other hand, if we can evaluate the operation of applying a rotation gate in the X direction by resonating with microwaves for 500 nanoseconds from the function that evaluates the accuracy of the operation of applying a rotation gate in the X direction by resonating with microwaves for 250 nanoseconds, then the functions that need to be prepared will only be functions that evaluate the accuracy of two types of operations: a 250-nanosecond idling operation and an operation of applying a rotation gate in the X direction by resonating with microwaves for 250 nanoseconds, thus reducing the number of necessary functions. 【0022】 However, as mentioned above, if we use the square of the fidelity of the operation that applies a rotation gate in the X direction by resonating with microwaves for 250 nanoseconds to evaluate the accuracy of the operation that applies a rotation gate in the X direction by resonating with microwaves for 500 nanoseconds, it may output a voltage application method that does not meet the required accuracy. 【0023】 Furthermore, since quantum computers capable of solving practical problems are expected to have millions of qubits, it is anticipated that some quantum computers will have hardware designs that control the voltage of multiple quantum dots with a single control line to accommodate this large-scale operation. 【0024】 For quantum computers, which are well-suited for such large-scale operations but lack the ability to individually control voltages, it is necessary to calculate the voltage application method while also considering hardware constraints. 【0025】Furthermore, if voltage application alone is insufficient to keep the crosstalk magnitude within the required accuracy range, shuttles will be used to reduce the crosstalk. However, in this case, reducing crosstalk requires considering three factors simultaneously: the quantum circuit, the shuttle method, and the voltage application method. 【0026】 The objective of the present invention is to reduce crosstalk in a crosstalk mitigation system by simultaneously considering three factors: quantum circuits, a shuttle method, and a voltage application method. 【0027】 A crosstalk mitigation system according to one aspect of the present invention is a crosstalk mitigation system for mitigating crosstalk in a quantum computer, comprising: a distance function generation unit that generates a distance function for evaluating the magnitude of the crosstalk from a shift in the resonance frequency using a CPU; a relation table generation unit that generates a relation table showing the voltage and state of a quantum dot based on the resonance frequency of the quantum dot, the voltage dependence of the resonance frequency of the quantum dot, hardware constraints, and the distance function using a CPU; and an optimal quantum circuit selection unit that selects an optimal quantum circuit that reduces the crosstalk based on a transpiled quantum circuit after the CPU has transpiled a user-desired quantum circuit that the user wishes to execute so that it can be executed by the hardware, the relation table, and the hardware constraints. 【0028】 According to one aspect of the present invention, in a crosstalk mitigation system, crosstalk can be reduced by simultaneously considering three factors: a quantum circuit, a shuttle method, and a voltage application method. 【0029】This is a block diagram showing an example configuration of a crosstalk mitigation system. This is a block diagram showing an example configuration of a crosstalk mitigation system. This is a block diagram showing an example hardware configuration of a crosstalk mitigation system. This is a diagram showing an example program for describing the quantum circuit desired by the user. This is a flowchart showing an example procedure for the distance function generation unit. This is a diagram showing an example of the relationship between resonance frequency deviation and fidelity. This is a diagram showing an example of the relationship between resonance frequency deviation and the Frobenius norm. This is a diagram showing an example of data in the region of resonance frequency deviation that satisfies the required accuracy. This is a diagram showing an example of quantum dot resonance frequency information input to the quantum dot voltage-state relationship table generation unit. This is a diagram showing an example of voltage dependence information of the quantum dot resonance frequency input to the quantum dot voltage-state relationship table generation unit. This is a diagram showing an example of hardware constraint information input to the quantum dot voltage-state relationship table generation unit. This is a flowchart showing an example procedure for the quantum dot voltage-state relationship table generation unit. This is a diagram showing an example of the voltage-state relationship table for quantum dot 1. This is a diagram showing an example of the voltage-state relationship table for quantum dot 2. This is a diagram showing an example of a state table for a pair of quantum dots that take the same voltage value. This is a diagram showing an example of a quantum circuit after transpilation. This is a diagram showing an example of hardware constraint information input to the optimal quantum circuit selection unit. This is a flowchart showing an example of the procedure for the optimal quantum circuit selection unit. This is a diagram showing an example of a state table for sets of quantum dots that take the same voltage value. This is a diagram showing an example of the time series of the ideal state and the corresponding re-transformed circuit. This is a diagram showing an example of candidate bit arrangements. This is an example of the voltage value of a quantum dot that matches the ideal state. This is a diagram showing an example of the evaluation result of the cost function. This is a diagram showing an example of updated hardware constraint information generated by the optimal quantum circuit selection unit. This is a diagram showing an example of qubit arrangement, shuttle procedure and voltage schedule. This is a flowchart showing an example of the procedure for the crosstalk magnitude visualization data generation unit. This is a diagram showing an example of the distance function and approximate distance function. This is a diagram showing an example of the resonance frequency and gate operation information for each step. This is a diagram showing an example of the crosstalk magnitude visualization data animation. 【0030】 This embodiment is applied to a crosstalk mitigation system. Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings. 【0031】 Figures 1A and 1B are block diagrams showing an example configuration of the crosstalk mitigation system in this embodiment. 【0032】 The crosstalk mitigation system includes a distance function generation unit 101, a distance function information storage unit 102, a quantum dot resonance frequency information storage unit 103, a quantum dot voltage dependence information storage unit 104, a hardware constraint information storage unit 105, a quantum dot voltage-state relationship table generation unit 106, a quantum dot voltage-state relationship table information storage unit 107, a user-desired quantum circuit information storage unit 108, a quantum circuit transpiler 109, a quantum circuit information storage unit 110 after transpiler, an optimal quantum circuit selection unit 111, a frequently occurring circuit schedule pattern information storage unit 112, an executed quantum circuit / voltage schedule information storage unit 113, a crosstalk magnitude visualization data generation unit 114, a crosstalk magnitude visualization data information storage unit 115, a display device 205, and an input device 206. 【0033】 The crosstalk mitigation system is implemented on a computer having a CPU, memory, communication device, and input / output device. The processing unit is executed by the CPU, and each storage unit is located in memory. The communication device is used in some of the processing of the above unit where it is necessary to send and receive data between the CPU and the quantum computer. 【0034】 The distance function generation unit 101 generates a distance function and stores the generated distance function in the distance function information storage unit 102. 【0035】 The quantum dot voltage-state relationship table generation unit 106 obtains the distance function from the distance function information holding unit 102, the quantum dot resonance frequency from the quantum dot resonance frequency information holding unit 103, the voltage dependence of the quantum dot resonance frequency from the quantum dot resonance frequency voltage dependence information holding unit 104, and the hardware constraints from the hardware constraint information holding unit 105, and calculates the voltage value corresponding to the state in which no crosstalk occurs for each quantum dot. 【0036】Furthermore, considering hardware constraints, quantum dots that always take the same voltage value are grouped together to generate a quantum dot voltage-state relationship table. The generated quantum dot voltage-state relationship table is stored in the quantum dot voltage-state relationship table information holding unit 107. 【0037】 The quantum circuit transpiler 109 acquires the user's desired quantum circuit from the user's desired quantum circuit information storage unit 108 and converts it into an equivalent quantum circuit that has been decomposed into quantum gates called basic gates that can be executed in hardware. The converted quantum circuit is stored in the transpiler's quantum circuit information storage unit 110. 【0038】 The optimal quantum circuit selection unit 111 acquires hardware constraints from the hardware constraint information holding unit 105, the quantum dot voltage / state relationship table from the quantum dot voltage / state relationship table information holding unit 107, the quantum circuit after transpilation from the transpilation quantum circuit information holding unit 110, and the frequently occurring circuit schedule pattern from the frequently occurring circuit schedule pattern information holding unit 112. 【0039】 Then, if the quantum circuit after transpilation matches a frequently occurring circuit schedule pattern, the matching frequently occurring circuit schedule pattern is stored in the execution quantum circuit / voltage schedule information holding unit 113. On the other hand, if the quantum circuit after transpilation does not match a frequently occurring circuit schedule pattern, the quantum circuit after transpilation, the shuttle schedule, and the voltage application schedule are optimized to reduce crosstalk, and the optimal quantum circuit after transpilation, the shuttle schedule, and the voltage application schedule are stored in the execution quantum circuit / voltage schedule information holding unit 113 and the frequently occurring circuit schedule pattern information holding unit 112. 【0040】The crosstalk magnitude visualization data generation unit 114 acquires the distance function from the distance function information holding unit 102, acquires the resonance frequency of the quantum bit from the resonance frequency information holding unit 103 of the quantum dot, acquires the voltage dependence of the resonance frequency of the quantum dot from the voltage dependence information holding unit 104 of the resonance frequency of the quantum dot, acquires the execution quantum circuit / voltage schedule from the execution quantum circuit / voltage schedule information holding unit 113, and generates data for visualizing the three pieces of information of the resonance frequency of each quantum bit, the presence or absence of the gate operation, and the magnitude of the crosstalk at the same time. The generated visualization data is stored in the crosstalk magnitude visualization data information holding unit 115. 【0041】 FIG. 2 is a diagram showing an example of the hardware configuration of the crosstalk mitigation system 201 in the present embodiment. 【0042】 The crosstalk mitigation system 201 includes a CPU 202, a memory 203, an external storage device 204, a display device 205, an input device 206, an external medium input / output device 207, and a communication device 208. 【0043】 The CPU 202 executes various processes by executing a program stored in the memory 203. The memory 203 functions as a work area for the CPU 202 and stores programs and data necessary for program execution. 【0044】 Specifically, programs that constitute the distance function generation unit 101, the voltage / state relation table generation unit 106 of the quantum dot, the quantum circuit transpiler 109, the optimal quantum circuit selection unit 111, and the crosstalk magnitude visualization data generation unit 114 are stored. At the same time, the data stored in the distance function information holding unit 102, the resonance frequency information holding unit 103 of the quantum dot, the voltage dependence information holding unit 104 of the resonance frequency of the quantum dot, the hardware constraint condition information holding unit 105, the voltage / state relation table information holding unit 107 of the quantum dot, the user execution desired quantum circuit information holding unit 108, the quantum circuit information holding unit 110 after the transpiler, the frequent circuit schedule pattern information holding unit 112, the execution quantum circuit / voltage schedule information holding unit 113, and the crosstalk magnitude visualization data information holding unit 115 is stored. 【0045】The external storage device 204 stores various types of data. The external storage device is, for example, a hard disk drive device or a solid state drive device, etc. 【0046】 Specifically, the data stored in the external storage device includes the distance function information holding unit 102, the resonance frequency information holding unit 103 of the quantum dot, the voltage dependency information holding unit 104 of the resonance frequency of the quantum dot, the hardware constraint condition information holding unit 105, the voltage - state relationship table information holding unit 107 of the quantum dot, the user - desired quantum circuit information holding unit 108, the quantum circuit information holding unit 110 after transpilation, the frequent circuit schedule pattern information holding unit 112, the executed quantum circuit - voltage schedule information holding unit 113, and the visualization data information holding unit 115 of the magnitude of crosstalk. 【0047】 Alternatively, at least a part of the programs that constitute the distance function generation unit 101, the voltage - state relationship table generation unit 106 of the quantum dot, the quantum circuit transpiler 109, the optimal quantum circuit selection unit 111, and the visualization data generation unit 114 of the magnitude of crosstalk are also stored in the external storage device. When executing various processes, the CPU 202 can read them into the memory 203 and execute the programs. 【0048】 Also, each program may be stored in the memory 203 or the external storage device 204 in advance, or may be introduced from another device into the memory 203 or the external storage device 204 via an available medium as needed. The available medium refers to, for example, a removable storage medium attached to the external medium input / output device 207, or a communication medium such as a network, a carrier wave propagating through the network, or a digital signal. 【0049】 The display device 205 displays the processing results of the program, etc. The display device 205 is, for example, a display. The input device 206 receives execution instructions for the process and input of information necessary for the process from the user. The input device 206 is, for example, a keyboard and a mouse, etc. 【0050】The external media input / output device 207 performs input and output of data stored in the external media and the external storage device 204. The external media is a portable storage medium that can be attached to and detached from the external media input / output device 207, and the external media output device 207 is a drive device that can read from and write to the external media. 【0051】 The communication device 208 is used to transmit the execution quantum circuit and voltage schedule stored in the execution quantum circuit and voltage schedule information holding unit 113 to the quantum computer via the network. The communication device 208 is assumed to be a network interface card or the like. 【0052】 A first embodiment of the crosstalk mitigation system 201 is shown, using the example program for describing the user's desired quantum circuit shown in Figure 3 as an example. 【0053】 Figure 3 shows an example of the source code for a user-desired quantum circuit in the crosstalk mitigation system 201 of this embodiment. Assume that the crosstalk mitigation system 201 receives source code 301, which describes a quantum program that the user wishes to process using a quantum computer, as input. The source code 301 is stored in the user-desired quantum circuit information storage unit 108. 【0054】 Quantum programs are written in programming languages ​​such as Python, as illustrated in source code 301. However, the quantum programs written in source code 301 can also be visually represented in circuit form, as illustrated in circuit diagram 302. For the sake of clarity, the following explanation will describe the examples using the quantum program in circuit form. 【0055】 Figure 4 is a flowchart showing an example of the procedure of the distance function generation unit 101. 【0056】The following process is implemented by a program executed by the CPU 202 of the crosstalk mitigation system 201 on memory 203. This program calculates a distance function for each basic gate based on the Hamiltonian from a predetermined metric that satisfies the triangle inequality by the CPU 202 executing the distance function generation unit 101 (step 401). Then, it calculates the range of acceptable resonance frequency deviations from the calculated distance function and outputs it to the distance function information holding unit 102 (step 402). 【0057】 The procedure shown in Figure 4 is illustrated as an example of crosstalk evaluation for a single-qubit idling operation when microwaves are incident in the x-direction. 【0058】 Here, it is predetermined that the Frobenius norm will be used as the metric for comparing two matrices U and V, as shown in (Equation 1). Here, d in Equation 1 is the size of matrices U and V. 【0059】 In the case of one qubit, d = 2. Let's assume the Hamiltonian is given by (equation 2). 【0060】 γ represents the gyromagnetic ratio, B0 is the magnetic flux density in the z direction applied to the qubit, h is the reduced Planck constant, B1 is the amplitude of the microwave, ω1 is the angular frequency of the microwave, and φ1 is the phase of the microwave. The first term of the Hamiltonian represents the Zeeman splitting due to the z-direction magnetic field, and the second term represents the interaction with the microwave. 【0061】 If we want to perform an idle operation on a single qubit, the ideal state is one where no microwaves hit it. The Hamiltonian in the absence of microwaves corresponds to the Hamiltonian when B1 = 0 in (Equation 2). The time evolution operator U of the quantum state in the absence of microwaves is given by (Equation 3). 【0062】 On the other hand, in silicon semiconductor quantum computers, the spacing between quantum dots is shorter than the wavelength of microwaves, making it difficult to selectively target only specific quantum dots with microwaves. Consequently, microwaves also hit the qubits that are intended to be idled, but the time evolution operator V of the quantum state when microwaves are hitting it is given by (Equation 4). 【0063】 The difference between the case where microwaves are applied and the case where they are not is evaluated using metrics such as the Frobenius norm, as exemplified in (Equation 1). To evaluate the difference between the two time evolution operators, it is necessary to specify the value of the time parameter t. 【0064】 The microwave irradiation time depends on the type of quantum gate other than the unit gate. For example, if you have a qubit that you want to operate an X gate on, the rotation angle of the X gate is 180 degrees, so you need to irradiate it with microwaves for the amount of time it takes for the quantum state to rotate 180 degrees in the X direction. In the case of a √X gate, the rotation angle is 90 degrees, so the microwave irradiation time for implementing a √X gate is half the time for implementing an X gate. 【0065】 Thus, the microwave irradiation time depends on the quantum gate to be implemented. Therefore, the time parameter t of the two time evolution operators described in (Equation 3) and (Equation 4) also needs to be changed according to the type of quantum gate. 【0066】 However, in quantum computers with error correction capabilities capable of solving practical problems, the number of qubits is on a massive scale, reaching millions of qubits. Therefore, if we were to use a method that involves calculating two time evolution operators for each qubit and each quantum gate—that is, for each time parameter value corresponding to each quantum gate—and comparing the differences between the two time evolution operators, the time required for evaluating crosstalk would become very long. 【0067】The part that calculates the time evolution operator from the Hamiltonian is particularly computationally intensive. Therefore, one way to shorten the crosstalk evaluation time is to set a reference time and a corresponding quantum gate, and estimate the crosstalk of other quantum gates from the magnitude of the crosstalk of that reference quantum gate. 【0068】 For example, if we use the √X gate as a reference, the X gate can be considered as if the √X gate were applied twice in a row. Therefore, if we can calculate the crosstalk of the √X gate, we can estimate the crosstalk of the X gate. 【0069】 In quantum computing, fidelity, which is easily measurable experimentally, is often used as a measure to compare actual implementation results with ideal implementation results. The fidelity of a basic gate composition operation is often estimated using the power of the fidelity of each basic gate. 【0070】 However, since fidelity is a metric that does not satisfy the triangle inequality, the relationship between the fidelity of a composition operation when estimated directly and strictly and when estimated from the powers of the fidelity of the basic gates can be reversed. 【0071】 Figure 5 shows the relationship between the estimated fidelity of an X-direction rotation gate with a rotation angle of π / 4 and the shift in resonance frequency. Line 501 shows the result when the fidelity of an X-direction rotation gate with a rotation angle of π / 4 is calculated directly as a function of the shift in resonance frequency. Line 502 shows the result when an X-direction rotation gate with a rotation angle of π / 4 is considered as if an X-direction rotation gate with a rotation angle of π / 8 were applied twice in succession, and the fidelity of the X-direction rotation gate with a rotation angle of π / 4 is estimated by the square of the fidelity of the X-direction rotation gate with a rotation angle of π / 8. 【0072】 As shown in Figure 5, the relative magnitudes of lines 501 and 502 can be reversed depending on the value of the resonance frequency shift. Therefore, if the fidelity of a π / 4 X-direction rotation gate is estimated by the square of the fidelity of a π / 8 X-direction rotation gate, then, for example, when the resonance frequency shift is 0.001 GHz, the actual fidelity will be worse than the estimated fidelity. 【0073】If fidelity is used, it becomes difficult to set a reference time value. In order to set a reference time and the corresponding quantum gate, and then estimate the crosstalk of other quantum gates from the magnitude of the crosstalk of that reference quantum gate, it is necessary to use a different evaluation metric. 【0074】 For the relative magnitudes of the two time evolution operators to remain consistent even when the resonant frequency shift takes on an arbitrary value, the evaluation metric used to compare the two time evolution operators must satisfy the triangle inequality. Furthermore, since the required precision is often given in terms of fidelity values ​​that are easily measurable experimentally, an evaluation metric that clearly shows its relationship to fidelity is preferable. 【0075】 An example of a metric that satisfies these two properties is the Frobenius norm shown in (Equation 1). However, in the embodiments of the present invention, the metric may be any metric that satisfies the triangle inequality, and is not limited to the Frobenius norm. 【0076】 Figure 6 shows the relationship between the estimated Frobenius norm and the deviation of the resonance frequency for an X-direction rotating gate with a rotation angle of π / 4. 【0077】 Line 601 shows the result when the Frobenius norm of an X-direction rotation gate with a rotation angle of π / 4 is calculated directly as a function of the shift in the resonance frequency. Line 602 shows the result when an X-direction rotation gate with a rotation angle of π / 4 is considered to be the result of applying an X-direction rotation gate with a rotation angle of π / 8 twice in succession, and the Frobenius norm of the X-direction rotation gate with a rotation angle of π / 8 is estimated to be twice the Frobenius norm of the X-direction rotation gate with a rotation angle of π / 8. 【0078】 Unlike fidelity, due to the property of satisfying the triangle inequality, even when the Frobenius norm of a composition operation is estimated using the sum-product of the Frobenius norms of the base gates, the value estimated using the sum-product of the Frobenius norms of the base gates will never be lower than the exact value of the Frobenius norm of the composition operation. Therefore, it is not possible for the estimation result to be more accurate than the actual result. 【0079】In addition, the Frobenius norm, as shown in (Equation 1), includes the Hilbert-Schmidt inner product of two matrices. Since this Hilbert-Schmidt inner product is also a term included in fidelity, it has the advantage of being easy to see its relationship with fidelity. 【0080】 By evaluating crosstalk using metrics that satisfy the triangle inequality, such as the Frobenius norm, it becomes possible to set a reference time and its corresponding quantum gate, and then estimate the crosstalk of other quantum gates from the magnitude of the crosstalk of that reference quantum gate. 【0081】 This allows us to determine the greatest common denominator (GCD) of the rotation angles of quantum gates that can be implemented in hardware. By using the quantum gate with the rotation angle corresponding to this GCD as the reference gate, and the microwave irradiation time required to implement the reference gate as the reference time, the crosstalk of the quantum gates that can be implemented in hardware can be estimated from the crosstalk of the reference gate. As a result, the time required to estimate the crosstalk of each quantum gate can be reduced. 【0082】 An example of information stored in the distance function information storage unit 102 is a table of data showing the relationship between the Frobenius norm and the resonance frequency deviation at the reference gate. 【0083】 Figure 7 shows an example of data in the region of resonance frequency deviation that satisfies the required accuracy, generated by the quantum dot voltage-state relationship table generation unit 106. 【0084】 The data 701 in the region of resonance frequency deviation that satisfies the required precision includes a state label 702 and an acceptable range of resonance frequency deviation 703. Here, the "idling" state represents a state in which, even when microwaves are applied, the resonance frequency of the qubit is appropriately deviated from the microwave frequency, and the fidelity of the unit gate at reference time is greater than or equal to the required precision. The "operable" state represents a state in which the resonance frequency of the qubit is sufficiently close to the microwave frequency, and the fidelity of the reference gate is greater than or equal to the required precision. 【0085】Figure 8 shows an example of quantum dot resonance frequency information held by the quantum dot resonance frequency information holding unit 103 and input to the quantum dot voltage / state relationship table generation unit 106. The quantum dot resonance frequency information 801 includes the dot number label 802 and the resonance frequency 803 of each dot. 【0086】 Figure 9 shows an example of voltage dependence information for the resonance frequency of a quantum dot, which is held by the quantum dot resonance frequency voltage dependence information holding unit 104 and input to the quantum dot voltage-state relationship table generation unit 106. The quantum dot resonance frequency voltage dependence information 901 includes the dot number label 902 and the voltage dependence 903 of the resonance frequency of each dot. 【0087】 Figure 10 shows an example of hardware constraint information held by the hardware constraint information holding unit 105 and input to the quantum dot voltage / state relationship table generation unit 106. The hardware constraint information includes data 1001 of the range of voltages that can be applied, dot arrangement 1004, and a table 1005 of sets of quantum dots to which the same voltage is applied. 【0088】 The data 1001 for the range of voltages that can be applied includes the dot number label 1002 and the range of voltages that can be applied 1003. The table 1005 for pairs of quantum dots to which the same voltage is applied includes the pair number label 1006 and the dot number pair 1007. 【0089】 Figure 11 is a flowchart showing an example of the procedure of the quantum dot voltage-state relation table generation unit 106. The process shown below is implemented by a program executed on the memory 203 by the CPU 202 of the crosstalk mitigation system 201. 【0090】 In this program, the CPU 202 executes the quantum dot voltage / state relationship table generation unit 106, thereby obtaining distance function information from the distance function information storage unit 102, quantum dot resonance frequency information from the quantum dot resonance frequency information storage unit 103, voltage dependence information of the quantum dot resonance frequency from the quantum dot resonance frequency voltage dependence information storage unit 104, and hardware constraint information from the hardware constraint information storage unit 105 (step 1101). 【0091】 The quantum dot voltage-state relationship table generation unit 106 calculates a threshold for the distance function corresponding to a predetermined required accuracy from the distance function information. Then it calculates the region of resonance frequency deviation where the value of the distance function is less than or equal to that threshold (step 1102). 【0092】 Next, the allowable voltage for each dot is calculated using the results calculated in step 1102, the quantum dot resonance frequency information, the voltage dependence information of the quantum dot resonance frequency, and the hardware constraint information (step 1103). 【0093】 Next, using the allowable voltage data for each dot calculated in step 1103 and the information on sets of quantum dots that take the same voltage value due to hardware constraints, as described in the hardware constraint information, a relationship table between the voltage and state of the dots is generated for sets of quantum dots that take the same voltage value due to hardware constraints (step 1104). 【0094】 Then, a relationship table between the voltage and state of quantum dots is generated for pairs of quantum dots that have the same voltage value, and the generated table data is stored in the quantum dot voltage-state relationship table information holding unit 107 (step 1105). 【0095】 The procedure shown in Figure 11 is illustrated using an example of quantum dot resonance frequency information (801), an example of voltage dependence information of quantum dot resonance frequency (901), an example of data on the range of voltages that can be applied (1001), an example of dot arrangement (1004), and an example of a table of sets of quantum dots to which the same voltage is applied (1005). 【0096】 Figure 7 shows an example of the execution result of step 1102. In Figure 7, the relationship between the Frobenius norm and the deviation of the resonance frequency is determined using a 1-qubit gate with a rotation angle of π / 8 as the reference gate, and the range of the deviation of the resonance frequency that is below the threshold of the Frobenius norm corresponding to a fidelity of 99.9% is listed as table data. 【0097】Figure 12 illustrates the calculation results of the allowable voltage for each quantum dot in step 1103. The voltage-state relationship table 1201 for a single quantum dot includes the state number label 1202, state 1203, minimum voltage 1204, and maximum voltage 1205. 【0098】 The Stark effect is a phenomenon in which the resonance frequency of a quantum bit changes linearly with respect to the applied voltage. In the case of example 901 of the voltage dependence information for quantum dot resonance frequency, it is shown that the resonance frequency of the quantum bit in dot 1 shifts by 100 MHz when a voltage of 1 volt is applied. In the case of example 801 of the quantum dot resonance frequency information, the resonance frequency of dot 1 is 20.009 GHz, so when a voltage of 1 volt is applied, the resonance frequency of the quantum bit becomes 20.010 GHz. 【0099】 From the information of the region of resonance frequency deviation that satisfies the required accuracy calculated in step 1102, the resonance frequency information of the quantum dot, and the voltage dependence information of the resonance frequency of the quantum dot, the voltage value that should be applied for the quantum dot to enter an idling state or an operable state can be calculated, and a voltage-state relationship table 1201 for one quantum dot can be generated. Figure 12 shows an example of a voltage-state relationship table for only one quantum dot, but a similar calculation can be used to generate a voltage-state relationship table for each quantum dot included in the quantum computer. 【0100】 Figure 13 shows an example of the calculation result of the allowable voltage for a quantum dot different from that in Figure 12. The voltage-state relationship table 1301 for a single quantum dot includes the state number label 1302, state 1303, minimum voltage 1304, and maximum voltage 1305. 【0101】 In step 1104, a table of voltage-state relationships for quantum dots is generated from the table 1005 of quantum dot pairs with the same voltage applied and the voltage-state relationship table 1201 of each quantum dot, for pairs of quantum dots that take the same voltage value due to hardware constraints. 【0102】For example, looking at set 1 listed in column 1008 of example table 1005, which shows sets of quantum dots with the same voltage applied, we can see that there is a constraint that dot 1 and dot 2 must have the same voltage value. Therefore, the states of dot 1 and dot 2 must be considered simultaneously. 【0103】 Table example 1005, showing a set of quantum dots with the same voltage applied, corresponds to the hardware constraint in dot arrangement example 1004 where vertical columns always have the same voltage applied. However, the present invention can also be implemented under other hardware constraints, such as horizontal rows having the same voltage applied. 【0104】 Figure 14 shows an example of a state table for sets of quantum dots with the same voltage value, which is held by the quantum dot voltage / state relationship table information holding unit 107 and input to the optimal quantum circuit selection unit 111. The state table 1401 for sets of quantum dots with the same voltage value includes a state number label 1402, the states 1403 and 1404 of each quantum dot constituting the set of quantum dots, and the minimum voltage 1405 and maximum voltage 1406. 【0105】 Given that the voltage-state relationship table 1201 for dot 1 and the voltage-state relationship table 1301 for dot 2 are provided, the state table 1401 for pair 1 is generated by joining the tables. A similar operation is performed for all pairs of quantum dots that have the same voltage value, and a voltage-state relationship table is generated for all pairs. 【0106】 In step 1105, a table of the relationship between the voltage and state of quantum dots for the set of quantum dots that take the same voltage value generated in step 1104 is stored in the quantum dot voltage-state relationship table information holding unit 107. 【0107】 Figure 15 shows an example of a transpiled quantum circuit that is held by the transpiled quantum circuit information holding unit 110 and input to the optimal quantum circuit selection unit 111. 【0108】The user-desired quantum circuit 302, held in the user-desired quantum circuit information holding unit 108, is decomposed by the quantum circuit transpiler 109 into a quantum circuit composed only of fundamental gates that can be physically implemented in hardware. Furthermore, for fundamental gates implemented using microwaves, since the phase of the microwaves irradiated differs for each fundamental gate, only one type of fundamental gate can be executed at the same time. Therefore, the quantum circuit transpiler 109 modifies the user-desired quantum circuit 302 so that only one type of fundamental gate is executed at the same time. 【0109】 For example, if the user's desired quantum circuit is given by circuit 302, the first step 303 is an instruction to apply an X gate to qubit q0 and a Y gate to qubit q1. However, the microwaves used to implement the X gate and the microwaves used to implement the Y gate have different phases. Therefore, in hardware that can only irradiate with one type of microwave at a time, step 303 cannot be implemented. 【0110】 Therefore, a quantum circuit transpiler is used to convert the user's desired quantum circuit so that it can be implemented in hardware. An example of the conversion of quantum circuit 302 is given by circuits 1501 and 1502. Both circuits 1501 and 1502 are converted so that only one type of gate is applied at the same time. 【0111】 Figure 16 shows an example of a transpiled quantum circuit held by the hardware constraint information holding unit 105 and input to the optimal quantum circuit selection unit 111. The hardware constraint information includes dot connection graph and voltage value information 1601, and qubit arrangement 1602. 【0112】 In the dot connection graph and voltage value information example 1601, there are four quantum dots 1, 2, 3, and 4, and it is shown that dots 1 and 2, 1 and 3, 2 and 4, and 3 and 4 are connected to each other. Furthermore, in this hardware, it is assumed that the voltage of dots in the same column is the same, so it is shown that dots 1 and 2 have the same voltage value of 0mV, and dots 3 and 4 also have the same voltage value of 0mV. 【0113】In qubit arrangement example 1602, it is shown that at the initial time of the quantum circuit 302, qubit q0 is located at dot 1 and qubit q1 is located at dot 2. 【0114】 Figure 17 is a flowchart showing an example of the procedure of the optimal quantum circuit selection unit 111. The process described below is implemented by a program executed on the memory 203 by the CPU 202 of the crosstalk relaxation system 201. 【0115】 When the CPU 202 executes the optimal quantum circuit selection unit 111, it obtains the dot connection graph, initial voltage value, and initial arrangement of qubits from the hardware constraint information holding unit 105, the state table of sets of quantum dots with the same voltage applied from the quantum dot voltage / state relationship table information holding unit 107, and the quantum circuit after transpilation from the transpilation quantum circuit information holding unit 110 (step 1701). 【0116】 It is determined whether the quantum circuit after transpilation is included in the frequently occurring circuit schedule pattern information holding unit 112 (step 1702). 【0117】 If the quantum circuit after transpilation is included in the frequently occurring circuit schedule pattern information holding unit 112, the voltage schedule, qubit arrangement, and shuttle procedure stored in the frequently occurring circuit schedule pattern information holding unit 112 are output and the process ends (step 1703). 【0118】 On the other hand, if the quantum circuit after transpilation is not included in the frequently occurring circuit schedule pattern information holding unit 112, in the first step of the quantum circuit after transpilation, the ideal state of whether each qubit should resonate with microwaves and the corresponding re-transformed quantum circuit are listed in descending order of the number of operable qubits (step 1704). 【0119】 For each re-conversion circuit listed in step 1704, candidate bit configurations are listed in descending order of the number of shuttle operations (step 1705). Next, for each candidate bit configuration listed in step 1705, the voltage value of the quantum dot that matches the ideal state listed in step 1704 is searched for (step 1706). 【0120】 Each candidate state calculated up to step 1706 is evaluated using a cost function. The state with the smallest cost function value is then used as the input state for the next step of the quantum circuit (step 1707). 【0121】 The operations from step 1704 to step 1707 are repeated step by step for each transpiled quantum circuit (step 1708). Once the final step of a transpiled quantum circuit is reached, the calculation for that transpiled quantum circuit is completed (step 1709). 【0122】 The operations from step 1704 to step 1709 are performed on all transpiled quantum circuits of the user-desired quantum circuits held in the transpiled quantum circuit information holding unit 110 (step 1710). This operation is terminated when it has been performed on all quantum circuits (step 1711). Finally, the cost function value is calculated for each transpiled quantum circuit, and the voltage schedule, qubit arrangement, and shuttle procedure with the smallest cost function value is stored in the execution quantum circuit / voltage schedule information holding unit 113 and the frequently occurring circuit schedule pattern information holding unit 112, and the process is terminated (step 1712). 【0123】 Figure 18 shows an example of a state table for sets of quantum dots with the same voltage value, which is held by the quantum dot voltage / state relationship table information holding unit 107 and input to the optimal quantum circuit selection unit 111. The state table 1801 for sets of quantum dots with the same voltage value includes a state number label 1802, the states 1803 and 1804 of each quantum dot constituting the set of quantum dots, and the minimum voltage 1805 and maximum voltage 1806. 【0124】 An example of an embodiment of the optimal quantum circuit selection unit 111 is shown, assuming that the quantum circuits after transpilation of the user's desired quantum circuit are circuits 1501 and 1502, the dot connection graph and initial voltage value are 1601, the initial arrangement of qubits is 1602, and the state tables of sets of quantum dots that take the same voltage value are given in tables 1401 and 1801. 【0125】In this embodiment, the CPU 202 first executes the optimal quantum circuit selection unit 111, and in step 1701, it obtains circuits 1501 and 1502 as quantum circuits after transpilation from the quantum circuit information holding unit 110, the dot connection graph, initial voltage value 1601 and initial qubit arrangement 1602 from the hardware constraint information holding unit 105, and tables 1401 and 1801 as state tables of pairs of quantum dots with the same voltage applied from the quantum dot voltage / state relationship table information holding unit 107. 【0126】 In step 1702, it is determined whether circuits 1501 and 1502 are included in the frequently occurring circuit schedule pattern information holding unit 112. In this embodiment, the explanation will proceed assuming that circuits 1501 and 1502 were not included in the frequently occurring circuit schedule pattern information holding unit 112. 【0127】 If circuits 1501 and 1502 are not included in the frequently occurring circuit schedule pattern information holding unit 112, step 1704 is executed as the next step after step 1702. Below, an embodiment of steps 1704 to 1707 is shown for circuit 1501. 【0128】 Figure 19 shows an example of a re-transformed circuit corresponding to the time series of the ideal state, generated by the optimal quantum circuit selection unit 111 in step 1704. The re-transformed circuit 1901 corresponding to the time series of the ideal state includes state number 1902, qubit states 1903 and 1904, and re-transformed circuit 1905. 【0129】 The first step of circuit 1501 is the operation of applying an X gate to both qubit q0 and qubit q1, as illustrated in step 1503. In order to implement step 1503, both qubit q0 and qubit q1 must resonate with microwaves. In other words, the quantum dot containing qubits q0 and qubit q1 must be operable. 【0130】However, depending on the voltage and state relationship of the quantum dots, it may be impossible to simultaneously operate both quantum dots containing qubit q0 and qubit q1. In this case, it is necessary to further divide step 1503 into two steps: in the first step, an X gate is applied to q0 and q1 is idled, and in the second step, q0 is idled and an X gate is applied to q1. 【0131】 In step 1704, the time series of ideal states that can implement step 1503 of circuit 1501 and the corresponding re-transformed quantum circuits are listed in descending order of the number of simultaneously operable states. 【0132】 In step 1503, making both qubits operable simultaneously minimizes the time required to implement step 1503. Therefore, the first candidate 1906 for the re-transformed circuit 1901 corresponding to the ideal state time series describes a circuit that applies an X gate to two qubits that are simultaneously operable. 【0133】 Depending on the voltage and state relationship of the quantum dots, it may be impossible to simultaneously operate both quantum dots that store qubit q0 and qubit q1. Therefore, in step 1704, the optimal quantum circuit selection unit 111 lists quantum circuit patterns 1907 and 1908, in which one qubit is operable and the other qubit is in an idle state. 【0134】 In step 1705, candidate bit arrangements are listed in descending order of the number of shuttle operations from the initial qubit arrangement 1602. 【0135】 Figure 20 shows an example of a candidate bit arrangement generated by the optimal quantum circuit selection unit 111 in step 1705. The candidate bit arrangement 2001 includes candidate number 2002, the number of shuttle operations 2003, and the arrangement after shuttle operations 2004. 【0136】If the number of shuttle operations from the initial qubit configuration 1602 is 0, the bit configuration after shuttle operations will be the same as the initial configuration, as exemplified by candidate 2005 in the first row of candidate bit configuration 2001. There are two types of bit configurations that can be reached from the initial qubit configuration 1602 in one shuttle operation, as exemplified by candidate 2006 in the second row of candidate bit configuration 2001 and candidate 2007 in the third row. 【0137】 Shuttling can also cause errors in the state of the qubits. Therefore, it is desirable to minimize the number of shuttling operations. Thus, in step 1705, the candidate bit arrangements generated by the optimal quantum circuit selection unit 111 can be listed in order of the number of shuttling operations being smallest. 【0138】 In step 1706, for each candidate state, the voltage value of the quantum dot that matches the ideal state is searched for. 【0139】 Figure 21 shows an example of a quantum dot voltage value that matches the ideal state, generated by the optimal quantum circuit selection unit 111 in step 1706. The voltage value 2101 of the quantum dot that matches the ideal state includes candidate number 2102, bit arrangement number 2103, time series number 2104, and voltage value 2105. Bit arrangement number 2103 corresponds to candidate number 2002 of candidate bit arrangement 2001. Time series number 2104 corresponds to candidate number 1902 of the re-converted circuit 1901 that corresponds to the time series of the ideal state. 【0140】 In step 1706, the voltage values ​​of quantum dots that match the ideal state are searched from state tables 1401 and 1801 of quantum dot pairs that have the same voltage value, in descending order of the number of shuttle operations and the number of qubits that can be operated simultaneously, among the combinations of the re-converted circuit 1901 corresponding to the time series of the ideal state generated in step 1704 and the candidate bit arrangement 2001 generated in step 1705. 【0141】When implementing step 1503 of circuit 1501, the ideal state time series and bit configuration combination that results in the shortest microwave irradiation time and the minimum number of shuttle operations is the pattern where the ideal state time series is 1906 and the bit configuration is 2005. However, referring to the state table 1401 of quantum dot pairs that take the same voltage value, there is no voltage value in which both quantum dot 1 and quantum dot 2 can be operated simultaneously. Therefore, the pattern where the ideal state time series is 1906 and the bit configuration is 2005 cannot be realized. 【0142】 When implementing step 1503 of circuit 1501, the combination of the ideal state time series and bit arrangement that has the shortest microwave irradiation time and the second smallest number of shuttle cycles is pattern 2106, where the ideal state time series is 1906 and the bit arrangement is 2006. In this case, it is necessary to adjust the voltage values ​​so that two quantum dots, quantum dot 3 which stores qubit q0 and quantum dot 2 which stores qubit q1, become operable. 【0143】 By referring to state 1407 in state table 1401 and state 1807 in table 1801, which represent pairs of quantum dots with the same voltage value, setting the voltage values ​​of quantum dot 1 and quantum dot 2 to 35mV, and the voltage values ​​of quantum dot 3 and quantum dot 4 to 35mV, matches the pattern of an ideal state with a time series of 1906 and a bit arrangement of 2006. Similarly, matching voltage values ​​can be calculated for patterns 2107 and 2108. 【0144】 When calculating the matching voltage values ​​here, the same quantum dot state tables 1401 and 1801 are referenced for all three patterns: 2106, 2107, and 2108. For this to work, the distance function generated by the distance function generation unit 101 is required to be a metric that satisfies the triangle inequality, including the Frobenius norm. 【0145】For metrics that do not satisfy the triangle inequality, such as fidelity, the relative magnitudes of crosstalk estimates can be reversed depending on how the gates are partitioned. Therefore, it is necessary to generate a state table for each of the ideal state time series 1906, 1907, and 1908, corresponding to the quantum dot sets, which increases the time required to calculate voltage values ​​that match the combination of ideal state time series and bit configuration. 【0146】 On the other hand, by using a metric that satisfies the triangle inequality, including the Frobenius norm, as a distance function, it is possible to refer to the same quantum dot state table for any of the ideal state time series 1906, 1907, and 1908, thereby reducing the time required to calculate voltage values ​​that match the combination of the ideal state time series and bit arrangement. 【0147】 In step 1707, a cost function value is calculated for the voltage values ​​that match the combinations of time series and bit configurations for each ideal state obtained in step 1706, and the combination of time series and bit configurations for the ideal state with the smallest cost function value is searched for. 【0148】 Figure 22 shows an example of the cost function evaluation result generated by the optimal quantum circuit selection unit 111 in step 1707. The cost function evaluation result 2201 includes candidate number 2202 and cost function value 2203. Candidate number 2202 corresponds to candidate number 2102 of the voltage value 2101 of the quantum dot that matches the ideal state. 【0149】 An example of a cost function used in step 1707 is (number of shuttle operations) + 1 / 100 × (voltage change [mV]) + (increase in Manhattan distance between the two bits used in the next two-bit operation). Since shuttle operations introduce noise into the qubits, the cost function is configured to select a pattern with as few shuttle operations as possible by including a term for (number of shuttle operations). Also, since the state of the qubits can change unintentionally due to changes in the voltage of the quantum dot, the cost function is configured to select a pattern with the smallest possible voltage change by including a term for (voltage change). 【0150】In addition, for a quantum computer to perform a 2-bit operation, the two qubits must be adjacent vertices in the connection graph of the quantum dots. Therefore, by inputting (the increase in the Manhattan distance between the two bits used in the next 2-bit operation), the system is configured to select a pattern in which the two bits used in the next 2-bit operation are as close together as possible. 【0151】 For example, state 2204 in the cost function evaluation result example 2201 corresponds to state 2106, where the quantum dot voltage value 2101 matches the ideal state. In this state, the number of shuttle operations is 1, and the voltage change range is 35 mV for the voltages of quantum dot 1 and quantum dot 2, and 35 mV for the voltages of quantum dot 3 and quantum dot 4. Also, in circuit 1501, the next 2-bit operation after step 1503 is step 1505. 【0152】 Therefore, the increase in Manhattan distance between the two bits used in the next two-bit operation is 1, because the Manhattan distance between qubit q0 and qubit q1 after shuttle is 2, and the Manhattan distance between qubit q0 and qubit q1 before shuttle is 1. Thus, the cost function value for pattern 2204 is calculated as (number of shuttle operations) + 1 / 100 × (voltage change [mV]) + (increase in Manhattan distance between the two bits used in the next two-bit operation) = 1 + 1 / 100 × (35 + 35) + 1 = 2.7. The cost function values ​​for other state candidates are calculated in the same way. 【0153】 Then, searching for the pattern with the smallest cost function value among the states described in the cost function evaluation result example 2201 yields pattern 2204. Note that the cost function is not limited to the above functional form when implementing the present invention. 【0154】 At the end of step 1707, update the voltage values ​​and qubit arrangement of the hardware constraint information dots to correspond to the pattern with the smallest cost function value. 【0155】Figure 23 shows an example of updated hardware constraint information generated by the optimal quantum circuit selection unit 111. The updated hardware constraint information includes a dot connection graph, voltage values ​​2301, and qubit configuration 2302. 【0156】 In step 1708, the operations from steps 1704 to 1707 are repeated for one transpiler-post quantum circuit 1501 until the final step is reached. At this time, the hardware constraint information referenced in the execution of step 1704 is the dot voltage value and qubit arrangement, which have been updated to correspond to the pattern with the smallest cost function value in the previous step of the quantum circuit. 【0157】 For example, when performing calculations from steps 1704 to 1707 for step 1504 of circuit 1501, the dot connection graph, voltage value 2301, and qubit arrangement 2302 that result in the smallest cost function value in step 1503 are referenced as hardware constraint information. 【0158】 Once steps 1704 to 1707 have been performed for one transpiled quantum circuit 1501, the same process from steps 1704 to 1709 is repeated for another transpiled quantum circuit 1502. In this case, for the other transpiled quantum circuit 1502, the hardware constraints are reset to the initial states 1601 and 1602, and the process from steps 1704 to 1709 is repeated. 【0159】 Once step 1711 is completed and the time series of the ideal state, the bit configuration, and the matching voltage value schedule have been determined for all transpiled quantum circuits, step 1712 is performed to calculate the cost function value for each transpiled quantum circuit. Here, one way to calculate the cost function for a single quantum circuit is to sum the cost functions at each step of the quantum circuit. 【0160】The voltage schedule, qubit arrangement, shuttle procedure, and transpiler-based quantum circuit with the smallest cost function value are then stored in the execution quantum circuit / voltage schedule information holding unit 113. 【0161】 Figure 24 shows an example of a qubit configuration, shuttle procedure, and voltage schedule generated by the optimal quantum circuit selection unit 111 and stored in the execution quantum circuit / voltage schedule information holding unit 113. The qubit configuration, shuttle procedure, and voltage schedule 2401 includes Step number 2402, qubit configuration / voltage 2403, shuttle procedure 2404, and corresponding quantum circuit 2405. The qubit configuration, shuttle procedure, and voltage schedule are displayed on the display device 205 in Figure 1A. 【0162】 Figure 25 is a flowchart showing an example of the procedure of the crosstalk magnitude visualization data generation unit 114. The process described below is implemented by a program executed on the memory 203 by the CPU 202 of the crosstalk mitigation system 201. 【0163】 The CPU 202 executes the crosstalk magnitude visualization data generation unit 114, thereby acquiring distance function information from the distance function information holding unit 102, quantum dot resonance frequency information from the quantum dot resonance frequency information holding unit 103, voltage dependence information of the quantum dot resonance frequency from the quantum dot resonance frequency voltage dependence information holding unit 104, and executed quantum circuit voltage schedule information from the executed quantum circuit voltage schedule information holding unit 113 (step 2501). 【0164】 Next, an approximate function of the distance function is generated (step 2502). Then, based on the approximate distance function, visualization data of the qubit's resonance frequency, gate operation, and crosstalk magnitude for each reference time is output (step 2503). 【0165】 Figure 26 shows an example of the distance function held in the distance function information holding unit 102 and the approximate distance function generated in step 2502 in the crosstalk magnitude visualization data generation unit 114. 【0166】Graph 2601 is a graph of a distance function that represents the relationship between the shift in the resonance frequency of the qubit being manipulated and the Frobenius norm. 【0167】 Graph 2602 is a graph of an approximate distance function for a distance function that represents the relationship between the shift in resonance frequency and the Frobenius norm in the qubit being manipulated. Graph 2603 is a graph of a distance function that represents the relationship between the shift in resonance frequency and the Frobenius norm in the qubit being idled. Graph 2604 is a graph of an approximate distance function for a distance function that represents the relationship between the shift in resonance frequency and the Frobenius norm in the qubit being idled. 【0168】 Let F be the approximate distance function for the distance function representing the relationship between the shift in the resonance frequency of the target qubit and the Frobenius norm, and let G be the approximate distance function for the distance function representing the relationship between the shift in the resonance frequency of the idled qubit and the Frobenius norm. Then, the two approximate functions are set so that the value of F + G is constant. In addition, F is set to be a monotonically increasing function and G is set to be a monotonically decreasing function. Furthermore, in the region where the value of the distance function is small, F and G are set so that the deviation from the original distance function is as small as possible. 【0169】 Examples of such approximate distance functions F and G can be found in the examples described in (Mathematics 5). 【0170】 Here, a is a variable representing the shift in resonance frequency, and A and L are parameters that are optimized in step 2502 so that the error between the distance function and the approximate distance function is minimized. In Figure 26, the approximate distance functions F and G corresponding to A = 2.7 and L = 120 are exemplified as graphs 2602 and 2604, respectively. 【0171】 Figure 27 shows an example of the intermediate data generated in step 2503 of the crosstalk magnitude visualization data generation unit 114, which consists of the resonance frequency and gate operation information for each step. 【0172】The resonance frequency and gate operation information 2701 for each step includes the Step number 2702, the resonance frequency shift 2703, and the gate operation 2704. The resonance frequency and gate operation information 2701 for each step is used to generate visualization data of the crosstalk magnitude. The resonance frequency and gate operation information 2701 for each step can be generated using the quantum dot resonance frequency information obtained in step 2501, the voltage dependence information of the quantum dot resonance frequency, and the executed quantum circuit voltage schedule information. 【0173】 Figure 28 shows an example animation of data visualizing the magnitude of crosstalk. The visualization data includes symbols 2802 representing qubits, and two types of rectangles 2804 and 2810 representing the magnitude of crosstalk. 【0174】 An example of an embodiment of step 2503 of the crosstalk magnitude visualization data generation unit 114 is shown in Figure 27 using the resonance frequencies and gate operation information 2701 of each step illustrated. 【0175】 The first animation 2801 displays a circle 2802 representing a qubit. Next, animation 2803 is displayed, corresponding to step 2705 of the resonant frequency and gate operation information 2701 for each step. In step 2705, the gate operation is an idle operation. When the gate operation is an idle operation, a gray rectangle 2804 with a height equal to the value of the approximate distance function F is placed on top of the circle representing the qubit. In the example of step 2705, the size of the rectangle 2804 corresponds to F (100 MHz). 【0176】 Next, animations 2805, 2808, and 2811 corresponding to the resonance frequency of each step and step 2706 of the gate operation information 2701 are displayed in order. In animation 2805, a gray rectangular block 2807 is placed on top of the block 2806 placed in animation 2803, with its height being the value of the approximate distance function F calculated using the shift in resonance frequency in step 2706. In step 2706, the gate operation is an X gate. 【0177】Therefore, the information that an X gate will be applied is represented in animation 2808. In animation 2808, a white rectangular block 2810 with the letter "X" written on it, which is the gate to be applied, is placed on top of the gray block 2809 that was placed in animation 2805. The height of the white rectangular block 2810 corresponds to parameter A calculated in step 2502. 【0178】 Then, in animation 2811, in order to represent the magnitude of the crosstalk that occurred in step 2706, a white rectangular block 2812 with the letter "X" written on it, which is the acting gate, has a height equal to the difference between the height of block 2810 and the height of block 2809. This block is placed on top of block 2813, which represents the magnitude of the crosstalk that occurred in step 2705, after the effect of block 2810 and block 2809 canceling each other out. The created animation data is stored in the crosstalk magnitude visualization data information holding unit 115. 【0179】 Here, the two approximate distance functions F and G are generated in step 2502 such that the relationship F + G = A holds. Therefore, subtracting the height F of block 2809, which represents the crosstalk of the idling operation, from the height A of block 2810, which represents the gate operation, gives A - F = G, and the height of block 2812 generated in animation 2811 can represent the magnitude of the crosstalk when the gate operation is performed. 【0180】 The animation illustrated in Figure 28 visually represents three pieces of information—the shift in the resonance frequency, the applied gate operation, and the magnitude of the crosstalk—in an easy-to-understand manner. Specifically, these three pieces of information are visualized and displayed on the display device 205 in Figure 1A. 【0181】The above embodiment includes a calculation device 101 that generates a distance function for evaluating the magnitude of crosstalk from the shift in resonance frequency in a crosstalk mitigation system, a calculation device 106 that identifies the relationship between the voltage and state of quantum dots, and a calculation device 111 that adjusts three things—the transpiled quantum circuit, the shuttle schedule, and the voltage application schedule—to reduce crosstalk. 【0182】 Specifically, the above embodiment includes a quantum dot resonance frequency information holding unit that holds the resonance frequency of the quantum dot in advance, a quantum dot resonance frequency voltage dependence information holding unit that holds the voltage dependence of the resonance frequency of the quantum dot in advance, and a hardware constraint information holding unit that holds the hardware constraints in advance. 【0183】 The system includes a transpiler-based quantum circuit information storage unit that pre-stores information about the quantum circuit after it has been transpiled into a hardware-executable form, allowing the user to execute the desired quantum circuit. 【0184】 The system includes a distance function generation unit that generates a distance function for evaluating the magnitude of crosstalk from the shift in resonance frequency, and a distance function information storage unit that stores the distance function generated by the distance function generation unit. 【0185】 The system includes a quantum dot voltage / state relationship table generation unit that acquires quantum dot resonance frequency data from the quantum dot resonance frequency information holding unit, acquires the voltage dependence of the quantum dot resonance frequency from the quantum dot resonance frequency voltage dependence information holding unit, acquires hardware constraints from the hardware constraint information holding unit, acquires distance functions from the distance function information holding unit, and generates a quantum dot voltage / state relationship table. 【0186】 The system includes a quantum dot voltage-state relationship table information holding unit that stores the quantum dot voltage-state relationship table generated by the quantum dot voltage-state relationship table generation unit. 【0187】The system includes an optimal quantum circuit selection unit that adjusts the quantum circuit, voltage schedule, and shuttle schedule to minimize crosstalk by obtaining the transpiled quantum circuit from the transpiled quantum circuit information holding unit, obtaining the voltage and state relationship table of quantum dots from the quantum dot voltage and state relationship table information holding unit, obtaining hardware constraint information from the hardware constraint information holding unit, calculating the state of the quantum dots corresponding to the transpiled quantum circuit, calculating the bit arrangement and the number of shuttle operations required to realize the bit arrangement from the hardware constraints, and calculating the voltage value of the quantum dots that match the state of the quantum dots corresponding to the transpiled quantum circuit and the bit arrangement. 【0188】 The system includes an execution quantum circuit / voltage schedule information holding unit that stores the quantum circuit calculated by the optimal quantum circuit selection unit, the voltage schedule, and the shuttle schedule. 【0189】Furthermore, the quantum dot resonance frequency data is obtained from the quantum dot resonance frequency information holding unit, the voltage dependence of the quantum dot resonance frequency is obtained from the quantum dot resonance frequency voltage dependence information holding unit, distance function information is obtained from the distance function information holding unit, the quantum circuit to be executed, the voltage schedule and the shuttle schedule are obtained from the executed quantum circuit / voltage schedule information holding unit, the approximate distance function of the distance function used to evaluate the magnitude of crosstalk during idling operation from the resonance frequency shift becomes a monotonically decreasing function with respect to the magnitude of the resonance frequency shift, and the approximate distance function of the distance function used to evaluate the magnitude of crosstalk during gate operation from the resonance frequency shift becomes a monotonically decreasing function with respect to the magnitude of the resonance frequency shift. In contrast, the system includes a crosstalk magnitude visualization data generation unit that calculates approximate distance functions for evaluating the magnitude of crosstalk during idling operations from the resonance frequency shift and approximate distance functions for evaluating the magnitude of crosstalk during gate operations from the resonance frequency shift, such that the sum of these approximate distance functions becomes a monotonically increasing function and the sum of these approximate distance functions for evaluating the magnitude of crosstalk during idling operations from the resonance frequency shift and the sum of these approximate distance functions for evaluating the magnitude of crosstalk during gate operations from the resonance frequency shift is constant, and generates visualization data that shows the relationship between the resonance frequency shift of each qubit, the type of gate operation, and the magnitude of crosstalk using these approximate functions. 【0190】 The system includes a crosstalk magnitude visualization data information holding unit that stores the visualization data generated by the crosstalk magnitude visualization data generation unit. 【0191】 Furthermore, for frequently occurring quantum circuits, it includes a transpiler-modified quantum circuit adjusted to reduce pre-calculated crosstalk, as well as a frequently occurring circuit schedule pattern information holding unit that pre-stores voltage schedules and shuttle schedules. 【0192】The optimal quantum circuit selection unit determines whether the user's desired quantum circuit is stored in the frequently occurring circuit schedule pattern. If the user's desired quantum circuit is included in the frequently occurring circuit schedule pattern, the unit uses the schedule pattern pre-stored in the frequently occurring circuit schedule pattern as the quantum circuit and voltage schedule information, thereby shortening the time required to adjust the quantum circuit, voltage schedule, and shuttle schedule to minimize crosstalk. 【0193】 Furthermore, the distance function generation unit generates a metric as a distance function that satisfies the triangle inequality and allows for easy identification of the fidelity relationship. 【0194】 Furthermore, in the optimal quantum circuit selection unit, when adjusting the quantum circuit, voltage schedule, and shuttle schedule, a cost function is used that takes into account the voltage change range, the number of shuttle operations, and the distance between the two bits used in the two-bit operation. 【0195】 According to the above embodiment, crosstalk can be quickly evaluated by setting a reference time and reference gate. This reduces the computation time required to adjust the three elements that occur when executing the user-desired quantum circuit on a quantum computer—the transpiled user-desired quantum circuit, the shuttle method, and the voltage application method—to minimize crosstalk. 【0196】 According to the above embodiment, by using an evaluation function between the resonance frequency of a qubit and the magnitude of crosstalk, which allows setting the gate's reference clock, the number of calculations required for the correspondence between the quantum dot state and voltage can be reduced. 【0197】 This reduces the computation time required to adjust the transpiled quantum circuit, shuttle schedule, and voltage application schedule of the user-desired quantum circuit in order to minimize crosstalk that occurs during the execution of the user-desired quantum circuit. 【0198】According to the above embodiment, the transpiled quantum circuit, the shuttle schedule, and the voltage application schedule can be quickly adjusted to minimize crosstalk that occurs when executing the user's desired quantum circuit. 【0199】 Thus, according to the above embodiment, crosstalk can be reduced in a crosstalk mitigation system by simultaneously considering three factors: the quantum circuit, the shuttle method, and the voltage application method. 【0200】 101 Distance function generation unit 102 Distance function information storage unit 103 Quantum dot resonance frequency information storage unit 104 Voltage dependence information storage unit for quantum dot resonance frequency 105 Hardware constraint information storage unit 106 Quantum dot voltage / state relationship table generation unit 107 Quantum dot voltage / state relationship table information storage unit 108 User-desired quantum circuit information storage unit 109 Quantum circuit transpiler 110 Quantum circuit information storage unit after transpiler 111 Optimal quantum circuit selection unit 112 Frequently occurring circuit schedule pattern information storage unit 113 Execution quantum circuit / voltage schedule information storage unit 114 Crosstalk magnitude visualization data generation unit 115 Crosstalk magnitude visualization data information storage unit

Claims

1. A crosstalk mitigation system for mitigating crosstalk in a quantum computer, comprising: a distance function generation unit that generates a distance function for evaluating the magnitude of the crosstalk from a shift in the resonance frequency using a CPU; a relation table generation unit that generates a relation table showing the voltage and state of a quantum dot based on the resonance frequency of a quantum dot, the voltage dependence of the resonance frequency of the quantum dot, hardware constraints, and the distance function using a CPU; and an optimal quantum circuit selection unit that selects an optimal quantum circuit that minimizes the crosstalk based on the transpiled quantum circuit after the user-desired quantum circuit has been transpiled so that it can be executed by the hardware, the relation table, and the hardware constraints using a CPU.

2. The crosstalk mitigation system according to claim 1, characterized in that the distance function generation unit generates the distance function based on the Hamiltonian from a predetermined metric that satisfies the triangle inequality using a CPU.

3. The crosstalk mitigation system according to claim 1, characterized in that the relation table generation unit calculates the allowable voltage for the quantum dots using a CPU and generates the relation table for pairs of quantum dots that take the same voltage value based on the hardware constraints.

4. The crosstalk mitigation system according to claim 1, characterized in that the optimal quantum circuit selection unit, using a CPU, determines the state of the quantum dot corresponding to the transpiler quantum circuit based on the transpiler quantum circuit, the relation table, and the hardware constraints; determines the number of shuttles required to realize the arrangement of the quantum dot and the arrangement of the qubit based on the hardware constraints; determines the voltage value of the quantum dot that matches the state of the quantum dot and the arrangement of the qubit corresponding to the transpiler quantum circuit; and selects the optimal quantum circuit by adjusting the arrangement of the qubit, the number of shuttles, and the voltage value of the quantum dot so that the crosstalk is reduced.

5. The crosstalk mitigation system according to claim 4, characterized in that the optimal quantum circuit selection unit uses a CPU to adjust the arrangement of the qubits, the number of shuttle operations, and the voltage value of the quantum dots so that the value of the cost function is minimized, using a cost function that takes into account the voltage change range, the number of shuttle operations, and the distance between the two qubits used in the two-qubit operation.

6. The crosstalk mitigation system according to claim 4, characterized in that it has a display unit that displays the arrangement of the qubits adjusted by the optimal quantum circuit selection unit, the number of shuttles, the voltage value of the quantum dots, and the optimal quantum circuit, controlled by a CPU.

7. The crosstalk mitigation system according to claim 1, characterized in that it has a visualization data generation unit that generates visualization data indicating the magnitude of the crosstalk based on the resonance frequency of the quantum dot, the voltage dependence of the resonance frequency of the quantum dot, the distance function, the voltage value of the quantum dot, and the optimal quantum circuit, using a CPU.

8. The crosstalk mitigation system according to claim 7, characterized in that the visualization data generation unit generates an approximation function of the distance function using a CPU, and generates the resonance frequency of the qubit, the gate operation, and the magnitude of the crosstalk for each reference time as visualization data based on the approximation function.

9. The crosstalk mitigation system according to claim 8, characterized in that it has a display unit that visualizes and displays the resonance frequency of the qubit, the gate operation, and the magnitude of the crosstalk as the visualization data generated by the visualization data generation unit.

10. A crosstalk mitigation method for mitigating crosstalk in a quantum computer, comprising: a distance function generation step in which a CPU generates a distance function for evaluating the magnitude of the crosstalk from the shift in the resonance frequency; a relation table generation step in which a CPU generates a relation table showing the voltage and state of the quantum dot based on the resonance frequency of the quantum dot, the voltage dependence of the resonance frequency of the quantum dot, hardware constraints and the distance function; and an optimal quantum circuit selection step in which a CPU selects an optimal quantum circuit that reduces the crosstalk based on the transpiled quantum circuit after the user-desired quantum circuit that the user wishes to execute has been transpiled so that it can be executed by the hardware, the relation table and the hardware constraints.

Images