Quantum operation evaluation program, quantum operation evaluation method, and information processing device

Abstract

To improve the efficiency of evaluation of an error of a quantum gate.SOLUTION: An information processing device 10 acquires measurement data 14 indicating a measured value measured after repeatedly executing a quantum gate row 13 including quantum gates 13a, 13b multiple times. The information processing device 10 specifies a variable indicating a matrix 15b, when expressing the quantum gate 13a, by a product of a matrix 15a indicating an ideal value and a matrix index of a matrix 15b indicating an error. The information processing device 10 generates a function 16 which linearly approximates the effect which the error gives to the measured value, by approximating a composite quantum gate obtained by synthesizing the quantum gates 13a, 13b, by the product of the matrix 15a, a matrix 15c indicating the ideal value of the quantum gate 13b, and the matrix index of a conversion result obtained by converting the value of the variable by using the matrix 15c. The information processing device 10 estimates the error by using the function 16 and the measurement data 14.SELECTED DRAWING: Figure 1

Description

Technical Field

[0001] The present invention relates to a quantum operation evaluation program, a quantum operation evaluation method, and an information processing apparatus.

Background Art

[0002] A quantum gate type quantum computer executes various quantum operations on qubits. A quantum computer initializes qubits, applies quantum gates to the qubits, and measures the values of the qubits. A quantum computer is implemented using a physical platform such as a superconducting quantum circuit, a semiconductor quantum dot, a diamond nitrogen vacancy (NV) center, or a nuclear magnetic resonance (NMR) molecule.

[0003] The implemented quantum computer usually has an error (deviation) in which the action of the quantum operation deviates from the ideal action. A user may evaluate the error of a quantum operation, and based on the evaluation result, may perform calibration to adjust the value of the control parameter that the quantum computer has. For example, a quantum computer may have a control parameter for adjusting the time width, amplitude, waveform, etc. of a drive pulse emitted to a qubit. By adjusting the value of the control parameter, the accuracy of the quantum operation may be improved.

[0004] Here, since the measured values of qubits are generated through a plurality of types of quantum operations, it is not easy to directly evaluate the error of each individual quantum operation. Therefore, as one of the techniques for estimating the error of a quantum operation, there is quantum tomography. Quantum tomography performs an experiment of repeatedly acquiring measured values from a quantum computer while changing the combination of quantum operations. Quantum tomography analyzes the experimental data and estimates the error of each individual quantum operation.

[0005] Note that a quantum error correction method has been proposed, which measures the value of a qubit to determine the error rate and calculates the change in the error rate with respect to the change in the parameter value of a quantum gate. In addition, a quantum tomography system has been proposed, which uses a quantum circuit to execute a tomography experiment on a quantum processor and analyzes the experimental result data according to a tomography analysis algorithm. Further, a quantum computer has been proposed, which performs a phase operation using a linear combination of a plurality of unitaries.

[0006] In addition, a quantum gate evaluation method has been proposed, which derives the Lindblad equation satisfied by a qubit and calculates the error rate of a quantum gate. Also, a superconducting quantum chip has been proposed, which uses quantum state tomography to determine the distortion of a frequency control signal for a qubit and adjusts the frequency control signal. Further, a quantum circuit generation device has been proposed, which generates a preamplitude amplification circuit for a certain quantum circuit. Moreover, a quantum computing system has been proposed, which includes a normal qubit and an auxiliary qubit, a quantum gate for setting the auxiliary qubit to a known state, and a measurement circuit for measuring the value of the normal qubit using the auxiliary qubit.

Prior Art Documents

Patent Documents

[0007]

Patent Document 1

Patent Document 2

Patent Document 3

Patent Document 4

Patent Document 5

Patent Document 6

Patent Document 7

Summary of the Invention

Problems to be Solved by the Invention

[0008] When evaluating the error of a quantum gate, quantum tomography may use a quantum circuit including an error amplification circuit that repeats the same quantum gate sequence. The error amplification circuit amplifies the minute error of the quantum gate, making the error component included in the measurement value more visible and improving the reliability of the evaluation result. On the other hand, since the error amplification circuit has a non-linear amplification effect on errors, there is a risk that data analysis will become complicated. As a result, there is a risk that the load of data analysis will increase and the numerical stability of the evaluation result will decrease.

[0009] For example, when approximating the amplification effect of the error amplification circuit with a linear function, depending on the quantum gate, a singularity where abnormal values such as infinity are calculated may appear in the search space. In this case, it is difficult to evaluate the error of the quantum gate with a simple approximation method. Therefore, in one aspect, an object of the present invention is to improve the efficiency of evaluating the error of a quantum gate.

Means for Solving the Problems

[0010] In one aspect, a quantum operation evaluation program is provided that causes a computer to execute the following processing. Measurement data indicating a measurement value of a quantum bit, which is measured after a quantum computer repeatedly executes a quantum gate sequence including a first quantum gate and a second quantum gate on the quantum bit a plurality of times, is acquired. When the first quantum gate is expressed as a product of a first matrix indicating the ideal value of the first quantum gate and a matrix exponential of a second matrix indicating an error when the quantum computer executes the first quantum gate, a variable indicating the second matrix is defined. By approximating the composite quantum gate obtained by combining the first quantum gate and the second quantum gate with a product of the first matrix, a third matrix indicating the ideal value of the second quantum gate, and a matrix exponential of a conversion result obtained by converting the value of the variable using the third matrix, a function for linearly approximating the influence of the error on the measurement value is generated. The error is estimated using the function and the measurement data.

[0011] Also, in one aspect, a method for evaluating a quantum operation executed by a computer is provided. Also, in one aspect, an information processing apparatus having a storage unit and a processing unit is provided.

Advantages of the Invention

[0012] In one aspect, the evaluation of errors in quantum gates is made more efficient.

Brief Description of the Drawings

[0013]

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Modes for Carrying Out the Invention

[0014] Hereinafter, this embodiment will be described with reference to the drawings. [First Embodiment] The first embodiment will be described.

[0015] FIG. 1 is a diagram for explaining the information processing apparatus of the first embodiment. The information processing apparatus 10 of the first embodiment evaluates the accuracy of quantum operations executed by a quantum computer by means of quantum tomography. The information processing apparatus 10 may be a so-called classical computer. Also, the information processing apparatus 10 may be a client apparatus or a server apparatus. The information processing apparatus 10 may be called a computer or a quantum operation evaluation apparatus.

[0016] The information processing apparatus 10 includes a storage unit 11 and a processing unit 12. The storage unit 11 may be a volatile semiconductor memory such as a RAM (Random Access Memory). Also, the storage unit 11 may be a non-volatile storage such as an HDD (Hard Disk Drive) or a flash memory.

[0017] The processing unit 12 is, for example, a processor such as a CPU (Central Processing Unit), a GPU (Graphics Processing Unit), or a DSP (Digital Signal Processor). However, the processing unit 12 may include an electronic circuit such as an ASIC (Application Specific Integrated Circuit) or an FPGA (Field Programmable Gate Array). The processor executes a program stored in a memory such as a RAM (which may also be the storage unit 11). A collection of processors may be called a multiprocessor or simply a "processor".

[0018] The memory unit 11 stores the measurement data 14. The measurement data 14 indicates the measurement values of the qubits measured after the quantum computer repeatedly executes a quantum gate sequence 13 a plurality of times (N times) on the qubits. The quantum computer that executes the quantum gate sequence 13 is the quantum computer whose implementation accuracy is to be evaluated. The information processing device 10 may be connected to the quantum computer and may read the measurement values from the quantum computer. Also, the information processing device 10 may receive the measurement data 14 from another information processing device connected to the quantum computer. Further, the information processing device 10 may sequentially acquire the measurement values from the quantum computer while proceeding with the data analysis described below.

[0019] The quantum gate sequence 13 includes a plurality of quantum gates including the quantum gates 13a and 13b. The quantum gate 13b is immediately after the quantum gate 13a. The plurality of quantum gates included in the quantum gate sequence 13 may be connected in series. Examples of the quantum gates 13a and 13b include a 180-degree rotation gate and a 90-degree rotation gate.

[0020] The quantum gate 13a is a quantum gate to be evaluated for accuracy. The implementation of the quantum gate 13a has an error indicating a deviation from the ideal operation. The quantum gate sequence 13 may include two or more quantum gates to be evaluated. The quantum gate 13b may be a quantum gate to be evaluated or a quantum gate outside the evaluation target. The quantum gate sequence 13 may include two or more quantum gates outside the evaluation target. In the following data analysis, the actual error of the quantum gates outside the evaluation target may be known, or it may be assumed that the quantum gates outside the evaluation target have no error, or it may be assumed that the quantum gates outside the evaluation target have a certain error.

[0021] The quantum gate sequence 13 is described by, for example, a quantum circuit. A quantum circuit that repeats the same quantum gate sequence multiple times may be called an error amplification circuit. The quantum computer executes the quantum gates of the quantum gate sequence 13 in order from the first quantum gate to the last quantum gate with respect to the quantum bits. The quantum computer continues the quantum state indicated by the quantum bits and again executes the quantum gates of the quantum gate sequence 13 in order from the first quantum gate to the last quantum gate. The error of the quantum gate 13a is amplified through the error amplification circuit. The measurement value of the quantum bit finally measured by the quantum computer includes the component of the amplified error.

[0022] In a quantum computer, even if the method of initializing the quantum bits, the types of quantum gates, and the method of measurement are the same, the measurement values are obtained probabilistically. Therefore, the measurement data 14 indicates, for example, a probability distribution listing the appearance probabilities of each of a plurality of values that the quantum bits can take. The information processing apparatus 10 may cause the quantum computer to perform a plurality of trials of initializing the quantum bits, executing the quantum gate sequence 13 a certain number of times, and measuring the values of the quantum bits. The information processing apparatus 10 may calculate the appearance probability of each value by dividing the number of appearances of each value by the number of trials.

[0023] Note that the measurement data 14 may include a plurality of measurement results corresponding to different initialization methods and different measurement methods. Further, the measurement data 14 may include a plurality of measurement results corresponding to different quantum gate sequences and may include a plurality of measurement results corresponding to different number of repetitions N.

[0024] The processing unit 12 analyzes the measurement data 14 and estimates the error when the quantum computer executes the quantum gate 13a. Here, the influence of the error of the quantum gate 13a on the measurement value is strictly non-linear. In contrast, the processing unit 12 generates a function 16 that linearly approximates the influence of the error of the quantum gate 13a on the measurement value in order to facilitate data analysis. The function 16 is a linear approximation function and is expressed using, for example, a matrix.

[0025] The processing unit 12 estimates the error of the quantum gate 13a using the function 16 and the measurement data 14. For example, the processing unit 12 extracts an amplification component proportional to the number of repetitions N from the measurement data 14. The processing unit 12 optimizes the error of the quantum gate 13a input to the function 16 so that the difference between the extracted amplification component and the output of the function 16 is minimized. The processing unit 12 formulates this optimization problem as a quadratic programming problem with semidefinite constraints, for example, and calculates the error of the quantum gate 13a using a mathematical programming solver.

[0026] In generating the function 16, the processing unit 12 generates a matrix representing the action of the entire quantum gate sequence 13 on the error from the matrices representing the individual quantum gates included in the quantum gate sequence 13 in order to obtain the change in error during one execution of the quantum gate sequence 13. For example, the processing unit 12 synthesizes the plurality of quantum gates included in the quantum gate sequence 13 in order from the beginning. In the synthesis, the processing unit 12 linearly approximates the action on the error.

[0027] Also, the processing unit 12 generates a matrix representing the action by repetition from the matrix representing the action of the entire quantum gate sequence 13 in order to obtain the change in error during N repetitions of the quantum gate sequence 13. In the amplification by repetition, the processing unit 12 linearly approximates the action on the error. Matrix eigenvalues may be used in the calculation of the linear approximation for synthesis and amplification. The processing unit 12 generates the function 16, which is a linear approximation function, using the matrix of the amplification result. At this time, the processing unit 12 may extract a component proportional to the number of repetitions N.

[0028] Here, the space to which the matrix representing the quantum operation by the quantum gate sequence 13 belongs may contain a singularity. A singularity is a point that represents a matrix for which eigenvalues satisfying certain conditions are calculated. A singularity may also be called a Critical Point. For example, a singularity corresponds to a matrix having different eigenvalues such that the values of exponential functions with the Napier's constant e as the base are the same. When the eigenvalues are complex numbers, the values of the exponential functions calculated from different eigenvalues may be the same. The processing unit 12 may determine that two eigenvalues whose difference in the values of the exponential function is less than a threshold satisfy the above-mentioned certain conditions.

[0029] Depending on the type of quantum gate included in the quantum gate sequence 13, a matrix corresponding to a singularity may appear in the above process of linear approximation. Any one of the quantum gates included in the quantum gate sequence 13 may correspond to a singularity alone, or a composite quantum gate may correspond to a singularity. An example of a quantum gate corresponding to a singularity is a 180-degree rotation gate. At a singularity, abnormal values such as division by zero can be calculated. Therefore, in a simple linear approximation, the action of the quantum gate sequence 13 on an error may not be calculated.

[0030] Therefore, in the second embodiment, the processing unit 12 defines the error of the quantum gate 13a as follows so that the influence of the singularity is suppressed. The processing unit 12 represents the quantum gate 13a including an error as the product of the matrix 15a and the matrix exponential of the matrix 15b. In FIG. 1, the matrix 15a is denoted as U1, the matrix 15b as δL', and the matrix exponential of the matrix 15b as exp(δL').

[0031] The matrix 15a is a first matrix indicating the ideal value of the quantum gate 13a. The ideal value represents an ideal transformation of a quantum state and is determined by the type of the quantum gate 13a. Usually, the matrix indicating the ideal value of a quantum gate is a unitary matrix. A unitary matrix has the property that the product of the matrix and its adjoint matrix is the identity matrix. The matrix 15b is a second matrix indicating an error when the quantum computer executes the quantum gate 13a. The error is an error indicating the deviation from the ideal value. The error indicated by the matrix 15b is an error related to the generator (Lindbladian) corresponding to the matrix logarithm of the matrix 15a, and may be called a generator error. At the stage of starting the analysis of the measurement data 14, the matrix 15b is an unknown. Therefore, the processing unit 12 defines a variable indicating the matrix 15b.

[0032] Here, the processing unit 12 may also consider defining the generator error as a matrix added to the ideal value of the generator. The ideal value of the generator is the matrix logarithm of the matrix 15a. For example, if the processing unit 12 denotes the ideal value of the generator as L ideal then it is also conceivable to define the generator error δL such that the quantum gate 13a is represented as exp(L ideal +δL). However, if the generator error is defined in this way, a matrix corresponding to a singularity may be calculated in the process of linear approximation, and the approximate calculation may become impossible.

[0033] Therefore, in the second embodiment, the processing unit 12 represents the error by the matrix 15b. The error indicated by the matrix 15b is a strictly different index from the above-mentioned generator error δL. However, both are common in that they are errors related to the generator of the quantum gate 13a. Depending on the use of the estimation result of the error, the error indicated by the matrix 15b may be sufficient, or the generator error δL may be more preferable. One of the uses of the estimation result is the calibration of the quantum computer. When the user wants to obtain the generator error δL, the user may convert the error indicated by the matrix 15b into the generator error δL.

[0034] In generating the function 16, the processing unit 12 approximates the combined quantum gate obtained by combining the quantum gates 13a and 13b as follows. The processing unit 12 approximates the combined quantum gate by the product of the matrix 15a, the matrix 15c, and the matrix exponential of the conversion result obtained by converting the value of the variable. This linear approximation utilizes the fact that the matrices 15a and 15c are unitary matrices and that the error is infinitesimal. The matrix 15c is a third matrix indicating the ideal value of the quantum gate 13b. This ideal value represents the ideal conversion of the quantum state and is determined by the type of the quantum gate 13b.

[0035] The conversion result is obtained by converting the matrix 15b, which is an unknown, using the matrix 15c. For example, the conversion result is the product of the adjoint matrix of the matrix 15c, the matrix 15b, and the matrix 15c. When the quantum gate 13b has a known or unknown error, the quantum gate 13b may be represented, similar to the quantum gate 13a, as the product of the matrix 15c and the matrix exponential of a fourth matrix indicating the error of the quantum gate 13b. In that case, the conversion result may be the sum of the product of the adjoint matrix of the matrix 15c, the matrix 15b, and the matrix 15c and the fourth matrix.

[0036] When the quantum gate sequence 13 includes three or more quantum gates, the processing unit 12 may further combine other quantum gates with respect to the combined quantum gate obtained by combining the quantum gates 13a and 13b. In this way, the processing unit 12 approximates the combined quantum gate corresponding to the entire quantum gate sequence 13. The processing unit 12 generates a matrix representing the action on the variable indicating the matrix 15b by repeating the quantum gate sequence 13 N times using the approximation result of the combined quantum gate. The processing unit 12 generates the function 16 using the generated matrix.

[0037] Note that the processing unit 12 may approximate the repeated action as follows. The combined quantum gate is represented in the form of the product of a fifth matrix and the matrix exponential of a sixth matrix. The fifth matrix is generated from the product of the matrices 15a and 15c. The sixth matrix is defined from the aforementioned conversion result and depends on the variable indicating the error of the quantum gate 13a.

[0038] The processing unit 12 approximates the repetition of the quantum gate sequence 13, for example, with the matrix exponent of the conversion result obtained by converting the fifth matrix into the sixth matrix using the fifth matrix and the number of repetitions N. This conversion result may be generated by adding the sixth matrix to the product of the adjoint matrix of the fifth matrix, the sixth matrix, and the fifth matrix, and multiplying by one-half of the number of repetitions N.

[0039] Further, the processing unit 12 may calculate a plurality of eigenvalues of the matrix logarithm of the fifth matrix, and approximate the repetition of the quantum gate sequence 13 by different approximation methods according to whether an eigenvalue satisfying a certain condition is calculated. The certain condition is, for example, that different eigenvalues with the same exponential function value are calculated. The processing unit 12 may execute the above approximation method when the certain condition is satisfied, and execute another approximation method when the certain condition is not satisfied.

[0040] The above-described approximation method utilizes the fact that the fifth matrix is a unitary matrix and the error is infinitesimal. Further, the above-described approximation method utilizes the fact that the fifth matrix corresponds to a 180-degree rotation gate, which is a typical quantum gate having a singularity. When executing the above-described approximation method, the number of repetitions N is preferably an even number.

[0041] As described above, the information processing apparatus 10 according to the first embodiment acquires the measurement data 14. The measurement data 14 indicates the measurement values of the quantum bits measured after the quantum computer repeatedly executes the quantum gate sequence 13 including the quantum gates 13a and 13b on the quantum bits. The information processing apparatus 10 represents the quantum gate 13a as the product of the matrix 15a indicating the ideal value of the quantum gate 13a and the matrix exponent of the matrix 15b indicating the error when the quantum computer executes the quantum gate 13a, and defines the variable indicating the matrix 15b.

[0042] The information processing apparatus 10 approximates a composite quantum gate obtained by combining quantum gates 13a and 13b with the product of a matrix 15a, a matrix 15c indicating the ideal value of the quantum gate 13b, and the matrix exponent of the conversion result obtained by converting the value of a variable using the matrix 15c. Through this approximation, the information processing apparatus 10 generates a function 16 that linearly approximates the influence of errors on the measurement values. The information processing apparatus 10 estimates the error using the function 16 and the measurement data 14.

[0043] As a result, the error of the quantum gate 13a implemented in the quantum computer is estimated. Therefore, the user can perform calibration to adjust the value of the control parameter of the quantum computer based on the estimated error. In addition, since an error amplification circuit that repeats the quantum gate sequence 13 multiple times is used, the error is amplified and the estimation accuracy of the error is improved.

[0044] In addition, the function 16 linearly approximates the action of the quantum gate sequence 13. Therefore, the load of quantum tomography is reduced and the numerical stability of the estimated error is improved. In addition, by representing the error of the quantum gate 13a by a matrix 15b and using the fact that the matrix 15a is a unitary matrix in the linear approximation, it is possible to prevent the approximation calculation from becoming impossible due to the influence of singularities. Therefore, even when the quantum gate sequence 13 includes a quantum gate having a singularity, linear approximation is possible and the evaluation of the error of the quantum gate 13a is made more efficient.

[0045] [Second Embodiment] Next, a second embodiment will be described. The information processing system of the second embodiment includes an information processing apparatus 100 and a quantum computer 115. The information processing apparatus 100 evaluates the accuracy of the quantum operations executed by the quantum computer 115 by quantum tomography. The information processing apparatus 100 performs calibration to adjust the value of the control parameter of the quantum computer 115 so as to improve the accuracy. The information processing apparatus 100 corresponds to the information processing apparatus 10 of the first embodiment.

[0046] FIG. 2 is a diagram showing a hardware example of the information processing system according to the second embodiment. The information processing apparatus 100 includes a CPU 101, a RAM 102, an HDD 103, a GPU 104, an input interface 105, a media reader 106, a communication interface 107, and an interface 108. These units are connected to a bus. The CPU 101 corresponds to the processing unit 12 of the first embodiment. The RAM 102 or the HDD 103 corresponds to the storage unit 11 of the first embodiment.

[0047] The CPU 101 is a processor that executes program instructions. The CPU 101 loads programs and data stored in the HDD 103 into the RAM 102 and executes the programs. The information processing apparatus 100 may have a plurality of processors.

[0048] The RAM 102 is a volatile semiconductor memory that temporarily stores programs executed by the CPU 101 and data used for calculations by the CPU 101. The information processing apparatus 100 may have a type of volatile memory other than the RAM.

[0049] The HDD 103 is a non-volatile storage that stores software programs such as an operating system (OS), middleware, and application software, and data. The information processing apparatus 100 may have other types of non-volatile storage such as a flash memory or an SSD (Solid State Drive).

[0050] The GPU 104 performs image processing in cooperation with the CPU 101 and outputs an image to a display device 111 connected to the information processing apparatus 100. The display device 111 is, for example, a CRT (Cathode Ray Tube) display, a liquid crystal display, an organic EL (Electro Luminescence) display, or a projector. Another type of output device such as a printer may be connected to the information processing apparatus 100.

[0051] Further, the GPU 104 may be used as a GPGPU (General Purpose Computing on Graphics Processing Unit). The GPU 104 can execute a program according to an instruction from the CPU 101. The information processing apparatus 100 may have a volatile semiconductor memory other than the RAM 102 as a GPU memory.

[0052] The input interface 105 receives an input signal from an input device 112 connected to the information processing apparatus 100. The input device 112 is, for example, a mouse, a touch panel, or a keyboard. A plurality of input devices may be connected to the information processing apparatus 100.

[0053] The medium reader 106 is a reading device that reads a program and data recorded on a recording medium 113. The recording medium 113 is, for example, a magnetic disk, an optical disk, or a semiconductor memory. Magnetic disks include flexible disks (FD) and HDDs. Optical disks include CDs (Compact Discs) and DVDs (Digital Versatile Discs). The medium reader 106 copies the program and data read from the recording medium 113 to other recording media such as the RAM 102 and the HDD 103. The read program may be executed by the CPU 101.

[0054] The recording medium 113 may be a portable recording medium. The recording medium 113 may be used for distributing programs and data. Also, the recording medium 113 and the HDD 103 may be referred to as computer-readable recording media.

[0055] The communication interface 107 communicates with other information processing apparatuses via a network 114. The communication interface 107 may be a wired communication interface connected to a wired communication device such as a switch or a router, or a wireless communication interface connected to a wireless communication device such as a base station or an access point.

[0056] Interface 108 is connected to quantum computer 115. Interface 108 sends commands to quantum computer 115 in response to instructions from CPU 101. Also, interface 108 receives data from quantum computer 115 and writes the received data to RAM 102 or HDD 103.

[0057] Quantum computer 115 has a quantum bit section 116, a control section 117, and a measurement section 118. Quantum bit section 116 includes a plurality of quantum bits representing quantum states. Quantum bit section 116 executes a quantum operation corresponding to a quantum gate in response to an instruction from information processing apparatus 100. The quantum operation changes the quantum state represented by the quantum bits. The behavior of the quantum operation is adjusted by the value of the control parameter input from control section 117.

[0058] Control section 117 receives a command for calibration of the quantum operation from information processing apparatus 100. The command includes the name of the control parameter and the value of the control parameter. Control section 117 inputs the value of the control parameter to quantum bit section 116. Examples of the control parameter include the time width, amplitude, waveform, etc. of the drive pulse applied to the quantum bit. By changing the value of the control parameter, the accuracy of the quantum operation changes.

[0059] Measurement section 118 measures the value of the quantum bit in response to an instruction from information processing apparatus 100 and stores the measurement value in the memory of quantum computer 115. Measurement section 118 sends the measurement value to information processing apparatus 100 in response to a request from information processing apparatus 100.

[0060] Generally, quantum information processing includes quantum computing, quantum simulation, quantum communication, quantum cryptography, quantum sensing, etc. Examples of physical platforms for quantum information processing include superconducting quantum circuits, semiconductor quantum dots, diamond NV centers, NMR molecules, neutral atoms, trapped ions, light, etc. A typical quantum information processing protocol based on quantum circuits uses three types of quantum operations: initialization, quantum gates, and measurement.

[0061] The quantum operations implemented in the quantum computer 115 have errors that show a deviation from ideal quantum operations. The information processing apparatus 100 performs evaluation and calibration on the quantum computer 115 in order to improve the accuracy of the quantum operations. The evaluation estimates the errors of the quantum operations. The calibration changes the value of the control parameter so that the error becomes smaller based on the error information. The information processing apparatus 100 may repeat the evaluation and calibration.

[0062] The information processing apparatus 100 evaluates the quantum operations by quantum tomography. The information processing apparatus 100 collects the measurement values of the qubits from the quantum computer 115 while changing the combination of initialization, quantum gates, and measurement. The information processing apparatus 100 analyzes the experimental data associating the tried combinations with the measurement values to estimate the errors of the quantum operations. Quantum tomography can estimate the errors of multiple quantum gates at once.

[0063] The information processing apparatus 100 generates a quantum circuit including an error amplification circuit that repeats the same quantum gate sequence multiple times, and causes the quantum computer 115 to execute this quantum circuit. The number of repetitions is, for example, 10 times, 100 times, 1000 times, etc. The errors of the quantum gates included in the quantum gate sequence are amplified through the error amplification circuit. As a result, the error components included in the measurement values become larger, and the evaluation accuracy is improved. Examples of quantum tomography techniques using an error amplification circuit include GST (Gate-Set Tomography), IT (Idle Tomography), and HEAT (Hamiltonian Error Amplifying Tomography).

[0064] Regarding GST, for example, it is described in the following non-patent literature. Erik Nielsen, John King Gamble, Kenneth Rudinger, Travis Scholten, Kevin Young and Robin Blume-Kohout, "Gate Set Tomography", the open journal for quantum science, volume 5, page 557, October 2021.

[0065] Regarding HEAT, for example, it is described in the following non-patent literature. Neereja Sundaresan, Isaac Lauer, Emily Pritchett, Easwar Magesan, Petar Jurcevic and Jay M. Gambetta, "Reducing Unitary and Spectator Errors in Cross Resonance with Optimized Rotary Echoes", PRX Quantum of the American Physical Society, Volume 1, page 020318, December 2020.

[0066] In addition, the error amplification circuit is also described in the following non-patent document. Gabriel O. Samach, Ami Greene, Johannes Borregaard, Matthias Christandl, Joseph Barreto, David K. Kim, Christopher M. McNally, Alexander Melville, Bethany M. Niedzielski, Youngkyu Sung, Danna Rosenberg, Mollie E. Schwartz, Jonilyn L. Yoder, Terry P. Orlando, Joel I-Jan Wang, Simon Gustavsson, Morten Kjaergaard and William D. Oliver, "Lindblad Tomography of a Superconducting Quantum Processor", Physical Review Applied of the American Physical Society, Volulme 18, page 064056, December 2022。

[0067] Yanwu Gu, Rajesh Mishra, Berthold-Georg Englert and Hui Khoon Ng, "Randomized Linear Gate-Set Tomography", PRX Quantum of the American Physical Society, Volume 2, page 030328, August 2021。

[0068] FIG. 3 is a diagram showing an example of an evaluation quantum circuit including an error amplification circuit. This quantum circuit includes an initialization circuit 141, a quantum gate sequence 142, and a measurement circuit 143. The initialization circuit 141 initializes one or more qubits to generate a desired quantum state. The quantum gate sequence 142 includes one or more quantum gates. The error amplification circuit repeats the quantum gate sequence 142 N times in series. The measurement circuit 143 measures the values of the qubits.

[0069] Between the initialization circuit 141 and the quantum gate sequence 142, non-repeating quantum gates may be included. Also, between the quantum gate sequence 142 and the measurement circuit 143, non-repeating quantum gates may be included. In FIG. 3, the X gate is a rotation gate that rotates around the x-axis, the Y gate is a rotation gate that rotates around the y-axis, and the Z gate is a rotation gate that rotates around the z-axis. The CR gate is an intersection resonance gate. The R gate is a rotation gate that rotates by a certain amount.

[0070] Quantum tomography collects experimental data while changing the combination of the quantum gate sequence 142, the number of repetitions N, the initialization circuit 141, and the measurement circuit 143. The quantum gate sequence 142 includes one or more quantum gates to be evaluated for errors. The quantum gate sequence 142 may include one or more quantum gates outside the evaluation target that are not evaluated for errors.

[0071] The ideal actions of the quantum gates to be evaluated and the quantum gates outside the evaluation target are known. The errors of the quantum gates to be evaluated in the quantum computer 115 are unknown. The errors of the quantum gates outside the evaluation target in the quantum computer 115 may be known or unknown. In the latter case, quantum tomography may regard the errors of the quantum gates outside the evaluation target as zero or assume a constant value.

[0072] Here, if we try to strictly define the action of the error amplification circuit with respect to the errors of the quantum gates, it will be necessary to solve a highly non-linear numerical optimization problem. As a result, the load of experimental data analysis increases, and the stability of solution search may decrease. Therefore, the information processing apparatus 100 linearly approximates the action of the error amplification circuit and defines the search for the errors of the quantum gates as a quadratic programming problem with semi-definite constraints. The quadratic programming problem with semi-definite constraints is a numerical optimization problem that optimizes a quadratic function under linear constraints, and the eigenvalues of the matrix are non-negative. The method of the second embodiment may be called RLT (Robust Lindbladian Tomography).

[0073] The following describes the calculation of quantum tomography in the second embodiment. The action of a quantum gate acting on a d-dimensional quantum system is described by a linear mapping shown in Equation (1). This linear mapping is a mapping from a d×d-dimensional complex number space to a d×d-dimensional complex number space, and is a trace-preserving and completely positive mapping. Here, let the representation matrix of the linear mapping in Equation (1) under the orthonormal basis shown in Equation (2) be G. This orthonormal basis is a set of d elements B 2 with a norm of 1 and orthogonal to each other. α The component G of the α-th row and β-th column of the matrix G is calculated using the trace, as shown in Equation (3), for the element B of the orthonormal basis corresponding to the α-th row αβ and the element B of the orthonormal basis corresponding to the β-th column. α β

[0074]

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[0077] There exists a linear mapping that satisfies the relationship in Equation (4) with the quantum gate defined in Equation (1) through the exponential mapping exp. This linear mapping is sometimes called the generator (Lindblad operator). Let the representation matrix of the linear mapping in Equation (4) be L. Then, there is a relationship in Equation (5) between the representation matrix G of the quantum gate and the representation matrix L of the generator, using the matrix exponential function e. Let the representation matrix of the ideal value of the generator be L ideal and the representation matrix of the error of the generator be δL. Then, G = e L is expanded as shown in Equation (5).

[0078]

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[0079]

Number

[0080] When an error is amplified through an error amplification circuit, it is easier to analyze the error of the generator corresponding to the matrix logarithm than the error of the quantum gate itself. This is because when errors accumulate, rotations occur in the qubits, and the angular deviation may not be exactly proportional to the number of repetitions N. Therefore, in the second embodiment, the information processing apparatus 100 estimates the generator error from the experimental data. Since the ideal value of the generator is known, if the generator error can be known, the actual G in the quantum computer 115 can be known. For simplicity of explanation, hereinafter, the linear mapping and its representation matrix may not be distinguished. For example, the quantum gate may be denoted as G, the generator as L, and the generator error as δL.

[0081] When preparing an error amplification circuit, the set I of quantum gates shown in Equation (6) g is given by the user. The quantum gates included in the set I g are identified by unique numbers. Among the n g different quantum gates, the first n g,1 quantum gates are the quantum gates to be evaluated, and the remaining quantum gates are the quantum gates not to be evaluated.

[0082]

Number

[0083] The quantum gate sequence forming the error amplification circuit is a quantum circuit in which one or more (typically two or more) of the quantum gates included in the set I g are arranged in series. The quantum gate sequence a is defined as in Equation (7). In Equation (7), the length of the quantum gate sequence is m. The elements on the right side of Equation (7) are the set I gIt is a number that identifies any of the quantum gates included. In the quantum gate sequence a, the same quantum gate may appear two or more times.

[0084]

Number

[0085] If the combined quantum gate corresponding to the overall action of the quantum gate sequence a is represented as G(a), G(a) is expanded as shown in Equation (8). Here, the product of three or more matrices is calculated from right to left. If the number of repetitions of the error amplification circuit is represented as N, the combined quantum gate corresponding to the overall action of the error amplification circuit is G(a) N and is represented as.

[0086]

Number

[0087] The n g,1 generated error δL shown in Equation (9) is the object of estimation. To collect the measured values measured under various conditions, a set of quantum gate sequences a and a set of the number of repetitions N shown in Equation (10) are given by the user. For the quantum gate sequence, n a different quantum gate sequences are given. For the number of repetitions, for each individual quantum gate sequence, n N different numbers of repetitions are given.

[0088]

Number

[0089]

Number

[0090] For different numbers of repetitions N and N’ given for the same quantum gate sequence, the conditions of Equation (11) are satisfied. The operation when an ideal quantum gate sequence without errors is repeated N times and the operation when the quantum gate sequence is repeated N’ times are identical. This makes it easy to extract the amplified error components from measurements with different numbers of repetitions.

[0091]

Number

[0092] Also, for each individual quantum gate sequence, a set of pairs of an initialization ρ and a measurement Π shown in Equation (12) is given by the user. This set contains n t,i pairs of the initialization ρ and the measurement Π. Thus, the quantum computer 115 generates an initial quantum state with the initialization ρ, executes the quantum gate sequence a by repeating it N times, and obtains a measurement value with the measurement Π. The quantum computer 115 performs this experiment for all combinations of a, N, and (ρ, Π).

[0093]

Number

[0094] When the vectorization of the matrix X with respect to the basis B is denoted as |X>>, the probability of obtaining a measurement value x in each experiment is calculated as in Equation (13). The matrix X is an element of a d×d-dimensional complex number space, and the vector |X>> is an element of a d 2 -dimensional complex number space. Hereinafter, i may be used as an identifier for the quantum gate sequence a, j as an identifier for the number of repetitions N, and k as an identifier for the pair of initialization and measurement (ρ, Π). Due to the probabilistic nature of quantum computing, the measurement values are obtained probabilistically, so the quantum computer 115 obtains n i,j,k samples of measurement values for each of (i, j, k).

[0095]

Number

[0096] When the frequency at which the measurement value x is obtained is represented by f i,j,k,x for each of (i, j, k), the frequency distribution of Equation (14) is calculated. The frequency f i,j,k,x is calculated by dividing the number of samples n i,j,k in which the measurement value x is obtained.

[0097]

Number

[0098] Following the experimental phase in which the information processing apparatus 100 collects the frequency distribution as described above, the information processing apparatus 100 executes a data processing phase for analyzing the experimental data indicating the frequency distribution. The data processing phase includes Step #1 of extracting an amplification component from the experimental data, Step #2 of linearly approximating the operation of the error amplification circuit, and Step #3 of solving a numerical optimization problem defined using the results of Steps #1 and #2. However, Steps #1 and #2 may be in reverse order. Further, the information processing apparatus 100 may omit Step #2 by diverting the operation of the error amplification circuit calculated in past quantum tomography.

[0099] In Step #1, the information processing apparatus 100 extracts a primary component proportional to the number of repetitions N from the experimental data. The experimental data includes a constant component independent of the number of repetitions N, a primary component proportional to the number of repetitions N, and a higher-order component of second order or higher with respect to the number of repetitions N. The ideal value of the generator corresponds to the constant component. The generator error amplified by the error amplification circuit corresponds to the primary component. Hereinafter, a method of extracting the primary component by extrapolation will be described.

[0100] The information processing apparatus 100 selects and fixes a combination of the quantum gate sequence a, the pair (ρ, Π) of initialization and measurement, and the measurement value x. The information processing apparatus 100 expands the probability p x (i, j, k) as a series with respect to the number of repetitions N. The probability p x (i, j, k) is the probability that the measurement value x is obtained under the experiment of (i, j, k). The ν-th expansion coefficient is hν That is, due to the decomposition accuracy, the infinite series expansion shown in Equation (15) is approximated by the finite series sum up to the (n - 1)th order. N

[0101]

Number

[0102] Equation (16) represents a vector obtained by summarizing the probabilities p(i, j, k) for n x iterations. T represents the transpose. Using the Vandermonde matrix V for the number of iterations N in Equation (17), the finite series sum is expressed as in Equation (18). The Vandermonde matrix V is a row vector arranging the powers of the number of iterations N from the 0th power to the (n - 1)th power, and is a matrix including n N row vectors corresponding to n N iterations. The coefficient vector h in Equation (18) is a vector arranging the expansion coefficients h from the 0th order to the (n - 1)th order. N N v N

[0103]

Number

[0104]

Number

[0105]

Number

[0106] When the n N numbers of iterations are different from each other, the Vandermonde matrix V is an invertible matrix. The coefficient vector h is calculated as in Equation (19) using the inverse matrix of the Vandermonde matrix V. In the experiment using the quantum computer 115, the probability p x ​​​​​The frequency f corresponding to the estimated value of (i, j, k) i,j,k,x is measured. Therefore, the information processing apparatus 100 uses the probability p x instead of (i, j, k), and uses the frequency f i,j,k,x . Equation (20) shows a vector obtained by summarizing the frequency f i,j,k,x for n N number of iterations. The estimated value h est of the coefficient vector is calculated as shown in Equation (21). In this way, the information processing apparatus 100 calculates the expansion coefficients from the 0th to the (n i,j,k,x -1)th order from the measured frequency f N .

[0107] [Number]

[0108] [[ID=2,8]] [Number]

[0109] [Number]

[0110] The second element of the coefficient vector h is a linear component proportional to the number of iterations N. The information processing apparatus 100 extracts the linear component while changing the measured value x. The information processing apparatus 100 calculates the coefficient vector h est 1(i, k) by grouping the linear components where (i, k) are the same and the measured value x is different. The information processing apparatus 100 calculates this coefficient vector h est 1(i, k) for all (i, k).

[0111] In step #2, the information processing apparatus 100 parameterizes the errors of the n g generators to be evaluated among the errors of the n g,1 generators together into the parameter v. The parameter v is a vector. n g,1The conversion from individual generator errors to parameter v may be a predefined affine transformation and may be defined using a matrix. As will be described later, from the optimal value of parameter v, n g,1 individual generator errors are estimated, and this parameterization is defined so that an inverse transformation is possible.

[0112] For each (i, k), the information processing apparatus 100 linearly approximates the operation of the error amplification circuit and generates a matrix C i,k indicating a component proportional to the number of iterations N. The product of the matrix C i,k and the parameter v indicates the influence of the generator error of the evaluation target on the primary component of the experimental data.

[0113] Also, the information processing apparatus 100 vectorizes the errors of the generators other than the evaluation target among the errors of the n g generators in the same way as the parameter v. The same transformation as the error of the evaluation target generator is used for this vectorization. The information processing apparatus 100 applies the matrix C i,k to this vector to generate a vector b i,k . The vector b i,k indicates the influence of the errors of the generators other than the evaluation target on the primary component of the experimental data. Since the errors of the generators other than the evaluation target are given by the user, the elements of the vector b i,k are calculated as specific numerical values. The linear approximation of the operation of the error amplification circuit will be described later.

[0114] In step #3, the information processing apparatus 100 uses the coefficient vector h est 1(i, k) generated in step #1, the matrix C i,k and the vector b i,k generated in step #2 to generate an objective function F(v) shown in Equation (22). W i,k is a weight matrix set by the user for (i, k). The information processing apparatus 100 calculates a parameter v est that minimizes the value of the objective function F(v) as shown in Equation (23). The information processing apparatus 100 uses the parameter v estReturn to the error of the generator to be evaluated.

[0115]

Number

[0116]

Number

[0117] The numerical optimization problem of solving the mathematical formula (23) is a least-squares fitting with physical constraints. The parameter v est is searched so as to satisfy the physical constraints possessed by the generator error. Since the parameter v is an affine parameterization of the generator error, the physical constraints possessed by the parameter v are expressed by linear semi-definite constraint conditions. Also, the objective function F(v) is a quadratic function of the parameter v. Therefore, this numerical optimization problem is defined as a quadratic programming problem with semi-definite constraints and is solved using a semi-definite programming solver.

[0118] Next, the linear approximation in step #2 will be described. Consider n×n complex square matrices A, B, and P as shown in the mathematical formula (24). The matrix A is diagonalizable and corresponds to the ideal value of the generator. The matrix A is decomposed as shown in the mathematical formula (25) by eigenvalue decomposition or spectral decomposition. In the mathematical formula (25), V is a matrix containing eigenvectors as column vectors, and Λ is a diagonal matrix with eigenvalues arranged on the diagonal. a j is a complex number that is an eigenvalue, and P j is the projection matrix corresponding to the eigenvalue a j . The matrix A is decomposed into the sum of products of the eigenvalue a j and the projection matrix P j .

[0119]

Number

[0120]

Number

[0121] The projection matrix P satisfies Equation (26). δ jk is the Kronecker delta. When j = k, δ jk = 1, and when j and k are different, δ jk = 0. Therefore, the product of different projection matrices corresponding to different eigenvalues becomes the zero matrix. On the other hand, the square of the same projection matrix becomes the projection matrix itself.

[0122]

Number

[0123] The eigenvalue a j of matrix A j and the projection matrix P A are used to define six linear mappings in Equations (27) to (32) as linear mappings for matrix B. dcl A indicates the decomposition to the left with respect to matrix A. dcr A indicates the decomposition to the right with respect to matrix A. cml

[0124] cmr A indicates the composition to the right with respect to matrix A. ssp A indicates the sum of spectral projections with respect to matrix A. sspc A indicates the sum of spectral projection complements with respect to matrix A.

[0125]

Number

[0126]

Number

[0127]

Number

[0128]

Number

[0129]

Number

[0130]

Number

[0131] The coefficients used in equations (27) to (30) are defined as in equation (33). Projection matrix P j , P k is the same, l jk = 1. When the projection matrices P j , P k are different, l jk is calculated from the eigenvalues a j , a k corresponding to the projection matrices P j , a k . These six linear mappings can be represented by matrices using an orthonormal basis in an n×n dimensional complex number space. The representation matrices of these six linear mappings are matrices of n 2 ×n 2 and are denoted as in equation (34).

[0132]

Number

[0133]

Mathematics

[0134] Using dcl in Equation (27), the matrix exponent of the sum of matrices A and B is calculated as in Equation (35). The second term on the right side is a higher-order component of degree two or higher with respect to matrix B. Therefore, the matrix exponent of the sum of matrices A and B is linearly approximated as the first term on the right side. Also, using dcr in Equation (28), the matrix exponent of the sum of matrices A and B is calculated as in Equation (36). Therefore, the matrix exponent of the sum of matrices A and B is also linearly approximated as the first term on the right side.

[0135]

Mathematics

[0136]

Mathematics

[0137] Also, using cml in Equation (29), the product of the matrix exponent of matrix A and the matrix exponent of matrix B is calculated as in Equation (37). Therefore, the product of the matrix exponent of matrix A and the matrix exponent of matrix B is linearly approximated as the first term on the right side. Also, using cmr in Equation (30), the product of the matrix exponent of matrix B and the matrix exponent of matrix A is calculated as in Equation (38). Therefore, the product of the matrix exponent of matrix B and the matrix exponent of matrix A is linearly approximated as the first term on the right side.

[0138]

Mathematics

[0139]

Mathematics

[0140] Using the linear mappings of equations (27) to (30), the action of the composite quantum gate obtained by composing quantum gates G1 and G2 is approximated as in equation (39). L ideal is the composite generator corresponding to the matrix logarithm of the ideal value of the composite quantum gate, and is defined as in equation (40).

[0141]

Number

[0142]

Number

[0143] Therefore, the generator error δL1 for quantum gate G1 changes as in equation (41) through the composite quantum gate. In equation (41), the change in δL1 is linearly approximated using the linear mappings dcr L , cmr L Also, the generator error δL2 for quantum gate G2 changes as in equation (42) through the composite quantum gate. In equation (42), the change in δL2 is linearly approximated using the linear mappings dcl L , cml L Equation (43) is the representation matrix of the change in δL1 shown in equation (41). Equation (44) is the representation matrix of the change in δL2 shown in equation (42).

[0144]

Number

[0145]

Number

[0146]

Number

[0147]

Number

[0148] When the quantum gate sequence includes three or more quantum gates, the information processing apparatus 100 synthesizes the quantum gates one by one from the head to the tail. The information processing apparatus 100 first synthesizes the first quantum gate and the second quantum gate. Next, the information processing apparatus 100 synthesizes the synthesized quantum gate and the third quantum gate. By repeating the synthesis, the information processing apparatus 100 generates a synthesized quantum gate corresponding to the entire quantum gate sequence. Thereby, the change of the generator error through the quantum gate sequence is linearly approximated.

[0149] Next, the information processing apparatus 100 calculates the repeated action of the quantum gate sequence. Repeating the quantum gate G N times is defined as in Equation (45). The synthesized quantum gate obtained by synthesizing the quantum gate sequence can be expressed in the form of e A+B . Assuming that there exists a c such that mod(nA)=cA, the N - fold repetition of this synthesized quantum gate is defined as in Equation (46) using ssp and sspc of Equations (31) - (32). c is a constant independent of the number of repetitions N. The first term on the right - hand side is the linear component with respect to the matrix B. The second term on the right - hand side is the higher - order component of second order or higher with respect to the matrix B.

[0150]

Number

[0151]

Number

[0152] Therefore, the generator error δL for the quantum gate G changes as shown in Equation (47) through N repetitions. In Equation (47), the change in δL is linearly approximated using the linear mappings ssp and sspc. The first term on the right side represents the component that is not amplified by N repetitions. The second term on the right side represents the linear component proportional to the number of repetitions N. Equation (48) shows the representation matrix of the operation that does not amplify δL during N repetitions. Equation (49) shows the representation matrix of the operation that amplifies δL during N repetitions.

[0153]

Number

[0154]

Number

[0155]

Number

[0156] Finally, for the error amplification circuit that repeats the quantum gate sequence N times, the information processing apparatus 100 calculates the operation on the generator error by integrating the operation of synthesizing the quantum gates and the operation of repeating the quantum gate sequence. Here, the information processing apparatus 100 generates the representation matrix of the synthesis operation and the representation matrix of the repetition operation as described above, and multiplies the representation matrix of the repetition operation from the left by the representation matrix of the synthesis operation. As the representation matrix of the repetition operation, for example, the matrix of Equation (49) proportional to the number of repetitions N is used.

[0157] In this way, the information processing apparatus 100 linearly approximates the amplification operation by which the error amplification circuit amplifies the generator error. The amplification operation calculated here is the operation in the space of the generators. In the numerical optimization using the objective function F(v), the information processing apparatus 100 converts the operation in the space of the generators into the operation in the space of the probability distribution of the measurement values.

[0158] Here, the information processing apparatus 100 generates a transformation matrix by rearranging the elements of the representation matrices of the initialization ρ and the measurement Π used in the experiment, and multiplies the transformation matrix from the left to the representation matrix of the error amplification circuit. The representation matrices of the initialization ρ and the measurement Π used here include known errors or assumed errors regarding ρ and Π, and are sometimes called model values. Thereby, the matrix C i,k included in the objective function F(v) is calculated. Also, by applying the matrix C i,k to the errors of the generators that are not the evaluation targets, the vector b i,k is calculated.

[0159] Next, the improvement of the linear approximation in step #2 will be described. For the linear approximation of the action of the quantum gate sequence, the linear mapping cml shown in Equation (29) and the linear mapping cmr shown in Equation (30) are used. The linear mappings cml and cmr include the reciprocal of the coefficient l jk shown in Equation (33).

[0160] Here, there exists a quantum gate having different eigenvalues a j , a k for the ideal values of the generators, and the a j -th power of e and the a k -th power of e become the same value. When the eigenvalues a j , a k are complex numbers, as shown in Equation (50), the a j -th power of e and the a k -th power of e may become the same value. As an example of such a quantum gate, a 180-degree rotation gate (π pulse gate) can be cited.

[0161] In this case, l jk=0, and its reciprocal is infinite, and the values of the linear mappings cml and cmr are not calculated. This represents that at the point indicating the above-mentioned generator included in the space of the generator, the differential mapping of the exponential mapping has a zero eigenvalue. Such a point on the space of the generator is sometimes called a singular point or a critical point. It can also be said that at the singular point, the linear approximation of the action of the quantum gate sequence breaks down. When the quantum gate sequence includes a quantum gate corresponding to the singular point, or when a synthesized quantum gate corresponding to the singular point is generated during synthesis, the action of the error amplification circuit cannot be calculated by the above-mentioned linear approximation method.

[0162]

Number

[0163] Therefore, the information processing apparatus 100 according to the second embodiment changes the definition of the generator error and suppresses the linear approximation using the linear mappings cml and cmr. The information processing apparatus 100 uses Equation (51) instead of Equation (5) as the definition of the quantum gate G. The second matrix exponential on the right side is the matrix exponential of the ideal value of the generator and is a unitary matrix. A unitary matrix is a matrix U having the property of Equation (52). The product of a unitary matrix and its adjoint matrix is the identity matrix. The first matrix exponential on the right side is the matrix exponential of the generator error δL'.

[0164]

Number

[0165]

Number

[0166] The information processing apparatus 100 estimates the generator error δL’ defined by Equation (51) for the quantum gate to be evaluated. The generator error δL’ is different from the generator error δL defined by Equation (5). According to the definition of Equation (51), an estimated value different from the case of Equation (5) is calculated. However, the generator errors δL and δL’ are common in that they are indicators of the errors of the quantum gate G. The user may perform calibration of the quantum computer using the calculated generator error δL’ as it is. Alternatively, the user may convert the generator error δL’ into the generator error δL and use it for calibration of the quantum computer.

[0167] For the composition of the quantum gates G1 and G2 included in the quantum gate sequence, the information processing apparatus 100 changes Equation (39) to Equation (53). In the changed composition, the linear mappings dcl, dcr, cml, and cmr are not used. The matrix U1 is a unitary matrix indicating the ideal value of the quantum gate G1 and corresponds to the matrix exponential of the ideal value of the generator L1. The matrix U2 is a unitary matrix indicating the ideal value of the quantum gate G2 and corresponds to the matrix exponential of the ideal value of the generator L2. In the transformation of Equation (53), the fact that the matrices U1 and U2 are unitary matrices is utilized.

[0168]

Number

[0169] The composite quantum gate shown in Equation (53) is approximated as in Equation (54). In the approximation of Equation (54), it is utilized that the generator errors δL1’ and δL2’ are negligible compared to the matrices U1 and U2. The ideal value of the composite quantum gate is the product of the matrices U1 and U2. The error of the composite quantum gate is expressed using the generator errors δL1’ and δL2’ and the matrix U2. The error of the composite quantum gate is the matrix exponential of the result of converting the generator error δL1’ using the matrix U2 and its adjoint matrix and adding the generator error δL2’.

[0170]

Number

[0171] The synthesis of the quantum gates included in the quantum gate sequence is executed regardless of whether a matrix corresponding to a singularity appears in the calculation process. Since the linear mappings cml and cmr are not used, the synthesis of the quantum gates can be executed even if a matrix corresponding to a singularity appears. The information processing apparatus 100 obtains the overall composite quantum gate of the quantum gate sequence by continuously applying the linear approximations of formulas (53) to (54) from the head to the tail of the quantum gate sequence.

[0172] FIG. 4 is a diagram showing an example of the synthesis of the quantum gates included in the quantum gate sequence. The quantum gate sequence 144 includes quantum gates 145, 146, 147, and 148 in order from the head. First, the information processing apparatus 100 performs a synthesis of multiplying the quantum gate 146 by the quantum gate 145. At this time, the information processing apparatus 100 multiplies the representation matrix of the quantum gate 146 on the left side of the representation matrix of the quantum gate 145.

[0173] Next, the information processing apparatus 100 performs a synthesis of multiplying the quantum gate 147 by the composite quantum gate of the quantum gates 145 and 146. At this time, the information processing apparatus 100 multiplies the representation matrix of the quantum gate 147 on the left side of the representation matrix of the composite quantum gate. Next, the information processing apparatus 100 performs a synthesis of multiplying the quantum gate 148 by the composite quantum gate of the quantum gates 145, 146, and 147. At this time, the information processing apparatus 100 multiplies the representation matrix of the quantum gate 148 on the left side of the representation matrix of the composite quantum gate. In this way, the information processing apparatus 100 obtains the composite quantum gate indicating the entire quantum gate sequence 144.

[0174] Next, the information processing apparatus 100 obtains a matrix indicating the action when the composite quantum gate is repeated N times from the composite quantum gate indicating the entire quantum gate sequence. The synthesis result of the quantum gate sequence is in the form of e δL’ U. This U is a unitary matrix indicating the ideal value of the composite quantum gate. This δL’ is the generator error of the composite quantum gate.

[0175] The information processing apparatus 100 calculates the eigenvalues of the generator L of the matrix U by eigenvalue decomposition or spectral decomposition, and determines whether the generator L corresponds to a singular point. When an eigenvalue that satisfies Equation (50) is calculated, the generator L corresponds to a singular point. When an eigenvalue that satisfies Equation (50) is not calculated, the generator L does not correspond to a singular point. The information processing apparatus 100 approximates the iterative operation by different approximation methods according to whether the generator L corresponds to a singular point.

[0176] When the generator L does not correspond to a singular point, the information processing apparatus 100 linearly approximates the iterative operation as in Equation (55). In Equation (55), an approximation using the first term on the right side of Equation (37) is performed. Here, since the generator L does not correspond to a singular point, the linear mapping cml can be calculated. Therefore, the iterative operation for the generator error δL’ of the composite quantum gate is defined using the linear mapping cml and the number of iterations N. The aforementioned matrix C i,k As a matrix for generating, for example, a matrix that acts on the generator error δL’, a portion proportional to the number of iterations N is extracted.

[0177]

Number

[0178] On the other hand, when the generator L corresponds to a singular point, the information processing apparatus 100 adopts an approximation method that does not use the linear mapping cml. To facilitate the approximate calculation, the information processing apparatus 100 assumes that the number of iterations N is an even number. Further, the information processing apparatus 100 assumes that the matrix U and its adjoint matrix are equal as shown in Equation (56). The quantum gate that satisfies Equation (56) is a 180-degree rotation gate. Therefore, the information processing apparatus 100 assumes a 180-degree rotation gate as a typical one among the composite quantum gates in which the generator L corresponds to a singular point.

[0179] However, it is also possible to extend the following approximation method when the number of iterations N is odd. Also, even when the matrix U does not exactly satisfy Equation (56) and the composite quantum gate is not exactly a 180-degree rotation gate, the information processing apparatus 100 may adopt the following approximation method as an approximate calculation.

[0180]

Number

[0181] When the generator L corresponds to a singular point, the information processing apparatus 100 linearly approximates the iterative operation as in Equation (57). In the transformation of Equation (57), the fact that the matrix U satisfies Equation (56) is utilized. Also, in the transformation of Equation (57), the fact that the matrix U is a unitary matrix is utilized. Further, in the approximation of Equation (57), the fact that the generator error δL’ is infinitesimal compared to the matrix U is utilized.

[0182]

Number

[0183] Finally, the N - fold repetition of the composite quantum gate shown in Equation (57) is approximated as in Equation (58). Thus, the iterative operation with respect to the generator error δL’ of the composite quantum gate is defined using the matrix U, its adjoint matrix, and the number of iterations N. Since the linear mappings cml and cmr are not used, even when the composite quantum gate has a singular point, the linear approximation of the iterative operation can be performed. The aforementioned matrix C i,k As a matrix for generating, for example, a matrix that acts on the generator error δL’ and extracts a portion proportional to the number of iterations N.

[0184]

Number

[0185] Next, a numerical example of the matrix used in the above calculation will be described. Here, a single-qubit system with d = 2 is considered. First, as in Equation (59), 2×2 matrices σ0, σ1, σ2, σ3 called Pauli matrices are defined. Using these matrices σ0, σ1, σ2, σ3, a Pauli matrix basis shown in Equation (60) is selected as the basis for the matrix representation of quantum gates and generators.

[0186]

Number

[0187]

Number

[0188] Also, as the basis for the vector representation of quantum gates and generators, a basis S defined by the set S1 to S shown in Equations (61) to (74) is selected. In Equations (61) to (74), the overline on B indicates the complex conjugate, and the product operator indicates the tensor product. 16

[0189]

Number

[0190]

Number

[0191]

Number

[0192]

Number

[0193]

Number

[0194]

Number

[0195]

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[0196]

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[0197]

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[0198]

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[0199]

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[0200]

Number

[0201]

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[0202]

Number

[0203] Here, consider two quantum gates. Quantum gate G1 is a rotation gate that rotates 180 degrees around the x-axis and can be denoted as the x180 gate. Quantum gate G2 is a rotation gate that rotates 90 degrees around the z-axis and can be denoted as the z90 gate. Quantum gate G1 is the quantum gate to be evaluated, and its generator error is unknown. Quantum gate G2 is a quantum gate outside the evaluation target, and its generator error is assumed to be 0.

[0204] The information processing apparatus 100 sets, as the quantum gate sequences to be tried, a quantum gate sequence including only quantum gate G1 and a quantum gate sequence including quantum gates G1 and G2 in order. The ideal action of quantum gate G1 on the quantum state ρ is given as in Equation (75). The ideal action of quantum gate G2 on the quantum state ρ is given as in Equation (76). The representation matrices of quantum gates G1 and G2 under the above Pauli matrix basis B are given as in Equation (77). Quantum gate G1 has a singularity. Quantum gate G2 does not have a singularity. The composite quantum gate G2G1 has a singularity.

[0205] [Number]

[0206] [Number]

[0207] [Number]

[0208] Figure 5 is a diagram showing an example of the action on the generator error by the first quantum gate sequence. Matrix 151 shows the action on the generator error through the composition of quantum gates and the repetition of the quantum gate sequence for the quantum gate sequence including only quantum gate G1, and shows the component proportional to the number of repetitions N. Matrix 151 is the representation matrix based on the above basis S.

[0209] FIG. 6 is a diagram showing an example of the action on the generator error by the second quantum gate sequence. Matrix 152 shows the action on the generator error through the synthesis of quantum gates and the repetition of the quantum gate sequence for the quantum gate sequence including quantum gates G1 and G2, and shows a component proportional to the number of repetitions N. Matrix 152 is a representation matrix based on the above-mentioned basis S.

[0210] Further, the information processing apparatus 100 selects five values of the number of repetitions N to be tried, which are 2, 4, 8, 16, and 32 times. The information processing apparatus 100 commonly applies these five values of the number of repetitions N to the above two quantum gate sequences.

[0211] Further, the information processing apparatus 100 prepares four initializations of x0, y0, z0, and z1 as the initialization ρ. x0 is a quantum state corresponding to the eigenvector of the eigenvalue +1 of σ1. y0 is a quantum state corresponding to the eigenvector of the eigenvalue +1 of σ2. z0 is a quantum state corresponding to the eigenvector of the eigenvalue +1 of σ3. z1 is a quantum state corresponding to the eigenvector of the eigenvalue -1 of σ3. The information processing apparatus 100 commonly applies these four initializations ρ to the above two quantum gate sequences.

[0212] Further, the information processing apparatus 100 prepares three measurements of x, y, and z as the measurement Π. x is a projective measurement corresponding to σ1. y is a projective measurement corresponding to σ2. z is a projective measurement corresponding to σ3. The information processing apparatus 100 commonly applies these three measurements Π to the above two quantum gate sequences. Therefore, in this example, the combination of the quantum gate sequence a, the number of repetitions N, the initialization ρ, and the measurement Π is 2×5×4×3 = 120 combinations.

[0213] Since the measurement results of a quantum computer are obtained stochastically, the information processing apparatus 100 acquires a plurality of samples for one combination and generates the aforementioned experimental data. However, in this numerical simulation, instead of using a quantum computer, the information processing apparatus 100 generates the generator error of the quantum gate G1 using pseudo-random numbers. The information processing apparatus 100 generates experimental data indicating the true probability distribution from this generator error.

[0214] FIG. 7 is a diagram showing an example of the correct answer and estimated value of the generator error. Matrix 153 indicates the correct answer of the generator error of the quantum gate G1. Matrix 153 is a representation matrix based on the above Pauli matrix basis B. The information processing apparatus 100 generates matrix 153 using pseudo-random numbers. Matrix 154 indicates the generator error of the quantum gate G1 estimated from matrices 151, 152 and the experimental data. Matrix 154 is a representation matrix based on the above Pauli matrix basis B. Comparing matrix 153 and matrix 154, many matrix components are estimated with high accuracy. Note that since only a part of the components of the generator error is not amplified by the above two quantum gate sequences, some matrix components are affected by that.

[0215] FIG. 8 is a diagram showing an example of the correct answer and estimated value of the vector representation of the generator error. Vector 155 is a representation vector obtained by converting matrix 153 indicating the correct answer of the generator error using the above basis S. Vector 156 is a representation vector obtained by converting matrix 154 indicating the estimated value of the generator error using the above basis S. Comparing vector 155 and vector 156, the third component, the tenth component, and the sixteenth component are affected by the lack of the quantum gate sequence. On the other hand, the other vector components are estimated with high accuracy.

[0216] Next, the functions and processing procedures of the information processing apparatus 100 will be described. FIG. 9 is a block diagram showing a functional example of the information processing apparatus. The information processing apparatus 100 includes a setting data storage unit 121, an experimental data storage unit 122, an evaluation data storage unit 123, an experimental unit 124, and an analysis unit 125. The setting data storage unit 121, the experimental data storage unit 122, and the evaluation data storage unit 123 are implemented using, for example, the RAM 102 or the HDD 103. The experimental unit 124 and the analysis unit 125 are implemented using, for example, the CPU 101 or the GPU 104 and a program.

[0217] The setting data storage unit 121 stores setting data. The setting data indicates the content of an experiment using the quantum computer 115. The setting data indicates an individual quantum gate G and its generator L. The setting data also indicates the generator error δL of a quantum gate outside the evaluation target. The setting data also indicates the quantum gate sequence a to be tried and the number of repetitions N. The setting data also indicates the initialization ρ and measurement Π to be tried.

[0218] The experimental data storage unit 122 stores experimental data. The experimental data is the aggregated measurement values read from the quantum computer 115. The experimental data indicates the frequency distribution f for each combination of the quantum gate sequence a, the number of repetitions N, the initialization ρ, and the measurement Π. The evaluation data storage unit 123 stores evaluation data. The evaluation data indicates the generator error δL’ of the quantum gate to be evaluated, estimated from the setting data and the experimental data. However, the evaluation data may indicate another index converted from the generator error δL’.

[0219] The experimental unit 124 instructs the quantum computer 115 to perform quantum calculation based on the setting data stored in the setting data storage unit 121. The experimental unit 124 reads measurement values from the quantum computer 115. The experimental unit 124 aggregates the read measurement values to generate experimental data and stores the experimental data in the experimental data storage unit 122.

[0220] The analysis unit 125 analyzes the setting data stored in the setting data storage unit 121 and the experimental data stored in the experimental data storage unit 122, and estimates the generator error of the quantum gate to be evaluated. At this time, the analysis unit 125 generates an objective function, and searches for the generator error that minimizes the value of the objective function using a mathematical programming solver. The analysis unit 125 generates evaluation data and stores it in the evaluation data storage unit 123. However, the analysis unit 125 may display the evaluation data on the display device 111 or transmit it to another information processing device.

[0221] FIG. 10 is a diagram showing an example of setting data. The setting data storage unit 121 stores a quantum gate table 131, a quantum gate sequence table 132, an iteration number table 133, and an initialization measurement table 134.

[0222] The quantum gate table 131 associates the identifier of the quantum gate, the representation matrix of the quantum gate, and the representation matrix of the generator. In the quantum gate table 131, different n g quantum gates are registered. Among the n g quantum gates, n g,1 quantum gates are the objects to be evaluated, and the remaining quantum gates are not the objects to be evaluated. For the quantum gates that are not the objects to be evaluated, the representation matrix of the generator error is further registered.

[0223] The quantum gate sequence table 132 associates the identifier i with the quantum gate sequence. The quantum gate sequence of length m is described by arranging m identifiers included in the quantum gate table 131. The iteration number table 133 associates the identifier (i, j) with the iteration number. For each quantum gate sequence included in the quantum gate sequence table 132, one or more iteration numbers (typically, two or more iteration numbers) are registered. The iteration number is preferably an even number. The initialization measurement table 134 associates the identifier (i, k), the representation matrix indicating the initialization of the quantum state, and the representation matrix indicating the measurement of the quantum state. For each quantum gate sequence included in the quantum gate sequence table 132, one or more sets of initialization and measurement are registered.

[0224] FIG. 11 is a diagram showing examples of experimental data and evaluation data. The experimental data storage unit 122 stores an experimental result table 135. The experimental result table 135 associates an identifier (i, j, k) with a frequency distribution. For each combination of the quantum gate sequence a i and the number of repetitions N i,j and the pair of initialization and measurement (ρ i,k , Π i,k ), one frequency distribution is registered. The frequency distribution is an arrangement of the frequencies of a plurality of measurement values.

[0225] The analysis unit 125 generates an objective function table 136. The objective function table 136 associates an identifier (i, k) with a matrix C and a vector b. For each combination of the quantum gate sequence a i and the pair of initialization and measurement (ρ i,k , Π i,k ), one matrix C and one vector b are calculated. Using matrices C and vectors b for all combinations of a i , (ρ i,k , Π i,k ), an objective function indicating the quality of the generator error estimation is defined.

[0226] The evaluation data storage unit 123 stores an evaluation result table 137. The evaluation result table 137 associates an identifier of a quantum gate with an estimated value of the generator error. The identifier is common to the quantum gate table 131. The evaluation result table 137 includes the generator errors of n g quantum gates that are the evaluation targets among the n g,1 quantum gates.

[0227] FIG. 12 is a flowchart showing an example of a procedure for quantum operation evaluation. (S10) The experiment unit 124 reads the setting data. Based on the setting data, the experiment unit 124 specifies a combination of the quantum gate sequence a, the number of repetitions N, the initialization ρ, and the measurement Π.

[0228] (S11) The experimental unit 124 repeats, a plurality of times, instructing the quantum computer 115 to perform quantum calculation and reading out measurement values for each combination specified in step S10. (S12) The experimental unit 124 aggregates the plurality of measurement values read out in step S11 for each combination specified in step S10, and calculates the frequency distribution f.

[0229] (S13) The analysis unit 125 generates a Vandermonde matrix V regarding the number of repetitions N. For each combination of the quantum gate sequence a, the initialization ρ, the measurement Π, and the measurement value x, the analysis unit 125 estimates the coefficient vector h of the series expansion from the Vandermonde matrix V and the frequency of the measurement value x included in the frequency distribution f calculated in step S12.

[0230] (S14) The analysis unit 125 extracts the primary component from the coefficient vector h of step S13, and estimates the coefficient vector h1 for each combination of the quantum gate sequence a, the initialization ρ, and the measurement Π. (S15) The analysis unit 125 defines the generator error δL’ of each quantum gate. The generator error δL’ of the quantum gate to be evaluated corresponds to a variable indicating an unknown number. This generator error δL’ is defined such that the quantum gate is represented in the form of formula (51).

[0231] (S16) The analysis unit 125 synthesizes the quantum gates included in the quantum gate sequence a in order from the head. At this time, the analysis unit 125 performs approximate calculations shown in formulas (53) to (54), utilizing the fact that the ideal value of the quantum gate is a unitary matrix and the generator error δL’ is small.

[0232] (S17) The analysis unit 125 performs spectral decomposition on the ideal value of the generator of the composite quantum gate corresponding to the entire quantum gate sequence, and calculates the eigenvalue a j . (S18) The analysis unit 125 compares the values of the exponential function exp(a j ) among the different eigenvalues a j calculated in step S17. The analysis unit 125 compares exp(a j) determines whether there is a pair of eigenvalues that are equal. However, if the difference between exp(a j ) is less than the threshold value, exp(a j ) may be regarded as equal. If there is a corresponding pair of eigenvalues, the process proceeds to step S20; otherwise, the process proceeds to step S19.

[0233] (S19) The analysis unit 125 calculates a linear mapping cml regarding the ideal value of the generator of the composite quantum gate. Using the calculated linear mapping cml, the analysis unit 125 calculates a matrix showing the iterative action on the generator error δL’ as shown in Equation (55). Then, the process proceeds to step S21.

[0234] [[ID=~]]

[0235] Figure 13 is a flowchart (continued) showing an example of the procedure for quantum operation evaluation. (S21) The analysis unit 125 converts the matrix calculated in step S19 or S20 into a matrix C showing the action in the space of the probability distribution of the measurement values using the initialization ρ and the measurement Π.

[0236] (S22) The analysis unit 125 calculates a vector b using the known generator error δL’ for the quantum gate not to be evaluated. Note that the analysis unit 125 may perform the processes in steps S15 to S22 in parallel with the processes in steps S11 to S14, or may perform them before the processes in steps S11 to S14. Also, the analysis unit 125 may reuse the matrix C and the vector b calculated in past quantum tomography.

[0237] ​(S23) The analysis unit 125 generates the objective function F using the matrix C in step S21, the vector b in step S22, and the coefficient vector h1 in step S14. (S24) The analysis unit 125 calculates the value of the parameter v that minimizes the value of the objective function F generated in step S23 using a mathematical programming solver.

[0238] (S25) The analysis unit 125 estimates the generator error δL' of the quantum gate to be evaluated from the value of the parameter v calculated in step S24. (S26) The analysis unit 125 generates evaluation data indicating the generator error δL' estimated in step S25 and outputs the evaluation data.

[0239] Note that the quantum gate G including an error can also be defined using the generator error δL'' instead of the generator error δL' as shown in Equation (78). When using the generator error δL', the matrix exponential of the generator error δL' is multiplied from the left side of the unitary matrix U indicating the ideal value of the quantum gate. This can be said that the generator error is decomposed on the left side. On the other hand, when using the generator error δL'', the matrix exponential of the generator error δL'' is multiplied from the right side of the unitary matrix U. This can be said that the generator error is decomposed on the right side.

[0240] The generator error δL'' may not match the generator error δL or the generator error δL'. However, the information processing apparatus 100 can evaluate the generator error δL'' in the same manner as the generator error δL'. The information processing apparatus 100 may output the generator error δL'' instead of or together with the generator error δL'. Further, the information processing apparatus 100 may convert the generator error δL'' into the generator error δL. Further, the information processing apparatus 100 may perform calibration of the quantum computer 115 using the estimated generator error δL''.

[0241]

Number

[0242] Between the generator error δL'' and the generator error δL, the relationship shown in Equation (79) holds using the unitary matrix U. Also, between the generator error δL' and the generator error δL, in the range of first-order approximation, the relationship shown in Equation (80) holds using the linear mapping dcl. Further, between the generator error δL'' and the generator error δL, in the range of first-order approximation, the relationship shown in Equation (81) holds using the linear mapping dcr.

[0243]

Number

[0244]

Number

[0245]

Number

[0246] Therefore, by substituting the aforementioned δL' with dcl(δL), a linear approximation with respect to δL is established, and the evaluation method for evaluating δL' can be used as the evaluation method for evaluating δL. Similarly, by substituting δL'' with dcr(δL), a linear approximation with respect to δL is established, and the evaluation method for evaluating δL'' can be used as the evaluation method for evaluating δL.

[0247] As described above, the information processing apparatus 100 of the second embodiment estimates the errors of the quantum gates of the quantum computer 115 using quantum tomography. For this reason, the information processing apparatus 100 can efficiently estimate the errors of a plurality of quantum gates collectively. Further, the information processing apparatus 100 causes the quantum computer 115 to execute an error amplification circuit that repeats the same quantum gate sequence. As a result, the minute errors of the quantum gates are amplified, and the accuracy of estimating errors from experimental data is improved.

[0248] Further, based on the estimated error, the user can adjust the values of the control parameters of the quantum computer 115, and the accuracy of the quantum operation of the quantum computer 115 is improved. Further, the information processing apparatus 100 converts a quantum gate into a generator, and linearly approximates the action of the error amplification circuit for the generator error. As a result, the load of data analysis is reduced and the numerical stability of the estimated error is improved.

[0249] Further, the information processing apparatus 100 defines the generator error such that the quantum gate is represented by the product of the unitary matrix indicating the ideal value of the quantum gate and the matrix exponential of the generator error. Then, the information processing apparatus 100 synthesizes a quantum gate without using the linear mappings cml and cmr by utilizing the properties of the unitary matrix and the smallness of the generator error. As a result, the information processing apparatus 100 can complete the synthesis even if a matrix corresponding to a singularity appears during the synthesis, and the types of quantum gates that can be synthesized increase.

[0250] Further, the information processing apparatus 100 calculates the repeated action of the synthesized quantum gate by different approximation methods according to whether the ideal value of the synthesized quantum gate corresponds to a singularity. When the ideal value of the synthesized quantum gate does not correspond to a singularity, the information processing apparatus 100 calculates the repeated action by the original approximation method using the linear mapping cml. As a result, the approximation accuracy is improved.

[0251] On the other hand, when the ideal value of the synthesized quantum gate corresponds to a singularity, the information processing apparatus 100 calculates the repeated action without using the linear mapping cml by utilizing the properties of the unitary matrix, the smallness of the generator error, and the fact that the unitary matrix represents a 180-degree rotation gate. As a result, the information processing apparatus 100 can complete the approximate calculation while avoiding the influence of the singularity, and the types of quantum gates to which the linear approximation can be applied increase.

Explanation of Signs

[0252] 10 Information processing apparatus 11 Storage unit 12 Processing unit 13 Quantum gate sequence 13a, 13b Quantum gates 14 Measurement data 15a, 15b, 15c Matrices 16 Function

Claims

1. A process of obtaining measurement data indicating a measurement value of the quantum bit, which is measured after a quantum computer repeatedly executes a quantum gate sequence including a first quantum gate and a second quantum gate on the quantum bit a plurality of times; A process of defining a variable indicating the second matrix when the first quantum gate is expressed as a product of a first matrix indicating an ideal value of the first quantum gate and a matrix exponent of a second matrix indicating an error when the quantum computer executes the first quantum gate; A process of generating a function for linearly approximating the influence of the error on the measurement value by approximating a composite quantum gate obtained by combining the first quantum gate and the second quantum gate with a product of the first matrix, a third matrix indicating an ideal value of the second quantum gate, and a matrix exponent of a conversion result obtained by converting the value of the variable using the third matrix; A process of estimating the error using the function and the measurement data; A quantum operation evaluation program for causing a computer to execute.

2. The conversion result is generated using the adjoint matrix of the third matrix, the value of the variable, and the product of the third matrix. The quantum operation evaluation program according to Claim 1.

3. The second quantum gate is expressed as a product of the third matrix and a matrix exponent of a fourth matrix indicating another error when the quantum computer executes the second quantum gate. The conversion result is generated by adding the fourth matrix to the product of the adjoint matrix of the third matrix, the value of the variable, and the third matrix. The quantum operation evaluation program according to Claim 1.

4. The quantum gate sequence is expressed as a product of a fifth matrix generated from the product of the first matrix and the third matrix using the approximation result of the composite quantum gate and a matrix exponent of a sixth matrix defined from the conversion result. The process of generating the function includes a process of approximating the repetition of the quantum gate sequence with a matrix exponent of another conversion result obtained by converting the sixth matrix using the fifth matrix and the number of repetitions of the quantum gate sequence. The quantum operation evaluation program according to Claim 1.

5. The other conversion result is generated by adding the sixth matrix to the product of the adjoint matrix of the fifth matrix, the sixth matrix, and the fifth matrix, and multiplying by one half of the number of repetitions. The quantum operation evaluation program according to Claim 4.

6. The quantum gate sequence is represented by the product of a fifth matrix generated from the product of the first matrix and the third matrix using the approximation result of the composite quantum gate, and the matrix exponential of a sixth matrix defined from the conversion result. The process of generating the function includes calculating a plurality of eigenvalues of the matrix logarithm of the fifth matrix, and approximating the repetition of the quantum gate sequence by different approximation methods according to whether different eigenvalues with the same exponential function value are included in the plurality of eigenvalues. The quantum operation evaluation program according to claim 1.

7. A process of acquiring measurement data indicating a measurement value of the quantum bit, which is measured after the quantum computer repeatedly executes a quantum gate sequence including a first quantum gate and a second quantum gate on the quantum bit a plurality of times. When expressing the first quantum gate as the product of a first matrix indicating the ideal value of the first quantum gate and the matrix exponential of a second matrix indicating an error when the quantum computer executes the first quantum gate, a process of defining a variable indicating the second matrix. A process of generating a function that linearly approximates the influence of the error on the measurement value by approximating a composite quantum gate obtained by combining the first quantum gate and the second quantum gate as the product of the first matrix, a third matrix indicating the ideal value of the second quantum gate, and the matrix exponential of a conversion result obtained by converting the value of the variable using the third matrix. A process of estimating the error using the function and the measurement data. A quantum operation evaluation method executed by a computer.

8. A storage unit that stores measurement data indicating a measurement value of the quantum bit, which is measured after the quantum computer repeatedly executes a quantum gate sequence including a first quantum gate and a second quantum gate on the quantum bit a plurality of times. When expressing the first quantum gate as a product of a first matrix indicating the ideal value of the first quantum gate and a matrix exponential of a second matrix indicating an error when the quantum computer executes the first quantum gate, define a variable indicating the second matrix. Approximate the composite quantum gate obtained by combining the first quantum gate and the second quantum gate by a product of the first matrix, a third matrix indicating the ideal value of the second quantum gate, and a matrix exponential of a conversion result obtained by converting the value of the variable using the third matrix, thereby generating a function for linearly approximating the influence of the error on the measurement value. A processing unit that estimates the error using the function and the measurement data; An information processing apparatus having the above.

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