Quantum gate calibration program, quantum gate calibration method, and information processing device.

Abstract

To improve the efficiency of quantum gate calibration. [Solution] The information processing device 10 selects a first value for each of several control parameters used by the quantum computer to control multiple pulse signals when executing a multi-input quantum gate, estimates a first error from the first value using an error function 13 that estimates the error between the ideal value and the actual value of the multi-input quantum gate from the values ​​of the multiple control parameters, searches for a second value for each of the multiple control parameters using the error function 13 such that the second error estimated from the second value is smaller than the first error, obtains the result of executing the multi-input quantum gate using the second value from the quantum computer, and uses the result to determine a third value to be set for each of the multiple control parameters.

Description

Technical Field

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

Background Art

[0002] A quantum computer may irradiate a quantum bit with a pulse signal as a physical implementation of a quantum operation corresponding to a quantum gate. Due to physical constraints and usage environments, the irradiated pulse signal may not be an ideal signal. Therefore, a quantum gate may have an error indicating a deviation from an ideal operation on a quantum bit.

[0003] Therefore, a quantum computer may have control parameters for adjusting the waveform of a pulse signal, such as pulse length and amplitude. A user may measure an error of a quantum gate of the quantum computer and perform calibration to change a control parameter value so that the error becomes smaller. For example, ORBIT (Optimized Randomized Benchmarking for Immediate Turn-up) measures the fidelity of a quantum gate and searches for a control parameter value that maximizes the fidelity using a search algorithm such as the Nelder-Mead method.

[0004] [[ID=I9]] In addition, among quantum gates, there are multi-input quantum gates that act on a plurality of quantum bits, such as a CNOT (Controlled NOT) gate that acts on two quantum bits. For example, the cross resonance (CR) method irradiates a control bit with a pulse signal having a resonance frequency that resonates with a target bit. Thereby, the quantum state of the target bit changes depending on the quantum state of the control bit.

[0005] It is not easy for quantum computers to implement multi-input quantum gates with high precision using only one type of pulse signal. Therefore, quantum computers sometimes implement multi-input quantum gates by combining multiple pulse signals. For example, in addition to the main CR pulse, a quantum computer may irradiate the qubit with additional pulse signals such as a cancellation tone or a rotary tone.

[0006] Furthermore, in analog processors with quantum devices arranged in a lattice, there are techniques to adjust runtime control parameters by setting the values ​​of inter-device coupling and local bias. There are also techniques to ensure that each superconducting cavity receives a variable amount of photons during quantum hardware initialization, causing photons from two coupled superconducting cavities to interact. Additionally, there are techniques to mitigate the effects of degeneracy in hybrid computing systems that include both quantum and digital processors. Finally, there are techniques to model quantum devices using Hamiltonian matrices and estimate the optimal values ​​of the quantum device's physical parameters. [Prior art documents] [Patent Documents]

[0007] [Patent Document 1] U.S. Patent Application Publication No. 2011 / 0298489 [Patent Document 2] International Publication No. 2015 / 160401 [Patent Document 3] International Publication No. 2017 / 075246 [Patent Document 4] International Publication No. 2019 / 005206 [Non-patent literature]

[0008] [Non-Patent Document 1] J. Kelly, R. Barends, B. Campbell, Y. Chen, Z. Chen, B. Chiaro, A. Dunsworth, A.G. Fowler, I. Hoi, E. Jeffrey, A. Megrant, J. Mutus, C. Neill, P.J.J. O'Malley, C. Quintana, P. Roushan, D. Sank, A. Vainsencher, J. Wenner, T.C. White, A.N. Cleland, and John M. Martinis, "Optimal Quantum Control Using Randomized Benchmarking", Physical Review Letters, Volume 112, Issue 24, June 2014 [Non-Patent Document 2] Petar Jurcevic, Ali Javadi-Abhari, Lev S. Bishop, Isaac Lauer, Daniela F. Bogorin, Markus Brink, Lauren Capelluto, Oktay Gunluk, Toshinari Itoko, Naoki Kanazawa, Abhinav Kandala, George A. Keefe, Kevin Krsulich, William Landers, Eric P. Lewandowski, Douglas T. McClure, Giacomo Nannicini, Adinath Narasgond, Hasan M. Nayfeh1, Emily Pritchett, Mary Beth Rothwell, Srikanth Srinivasan, Neereja Sundaresan, Cindy Wang, Ken X. Wei, Christopher J. Wood, Jeng-Bang Yau, Eric J. Zhang, Oliver E. Dial, Jerry M. Chow, and Jay M. Gambetta1, "Demonstration of Quantum Volume 64 on a Superconducting Quantum Computing System", Quantum Science and Technology, Volume 6, Number 2, March 2021

Summary of the Invention

Problems to be Solved by the Invention

[0009] When a multi-input quantum gate is implemented by combining multiple pulse signals, the quantum computer may have multiple control parameters to adjust the waveforms of these pulse signals. However, if there are many control parameters, parameter tuning methods that repeatedly measure the error of the quantum gate may take a long time to reach control parameter values ​​that reduce the error sufficiently, and may not reach the optimal value within a realistic timeframe. Therefore, in one aspect, the present invention aims to improve the efficiency of quantum gate calibration. [Means for solving the problem]

[0010] In one aspect, a quantum gate calibration program is provided that causes a computer to perform the following steps: select a first value for each of several control parameters used by a quantum computer to control multiple pulse signals when executing a multi-input quantum gate; estimate a first error from the first value using an error function that estimates the error between the ideal and actual values ​​of the multi-input quantum gate from the values ​​of the multiple control parameters; search for a second value for each of the multiple control parameters using the error function such that the second error estimated from the second value is smaller than the first error; obtain the result of executing the multi-input quantum gate using the second value from the quantum computer; and use the result to determine a third value to set for each of the multiple control parameters. [Effects of the Invention]

[0011] In one respect, the calibration of quantum gates becomes more efficient. [Brief explanation of the drawing]

[0012] [Figure 1] This is a diagram illustrating the information processing device of the first embodiment. [Figure 2] This figure shows an example of the hardware of the information processing system according to the second embodiment. [Figure 3] This figure shows an example of manipulating quantum states using quantum gates. [Figure 4]This figure shows an example of a microwave pulse signal. [Figure 5] This figure shows an example of manipulating quantum states using a two-input quantum gate. [Figure 6] This figure shows an example of a combination of multiple microwave pulse signals. [Figure 7] This figure shows an example of control parameters. [Figure 8] This figure shows an example of Hamiltonian coefficients. [Figure 9] This graph shows an example of the relationship between rotary tone amplitude and error. [Figure 10] This graph shows an example of the relationship between cancellation tone amplitude and error. [Figure 11] This graph shows an example of the relationship between the number of quantum gate iterations and fidelity. [Figure 12] This is a block diagram showing examples of functions of an information processing device. [Figure 13] This flowchart shows an example of the procedure for calibrating a quantum gate. [Figure 14] This flowchart shows an example of the procedure for model-based optimization. [Modes for carrying out the invention]

[0013] This embodiment will be described below with reference to the drawings. (a) First embodiment Figure 1 is a diagram illustrating an information processing device of a first embodiment. The information processing device 10 of the first embodiment calibrates quantum gates implemented in a quantum computer. The information processing device 10 is, for example, a von Neumann type classical computer. The information processing device 10 may be a client device or a server device. The information processing device 10 may also be called a computer or a quantum gate calibration device.

[0014] The information processing device 10 includes a storage unit 11 and a processing unit 12. The storage unit 11 may be a volatile memory such as RAM (Random Access Memory). Alternatively, the storage unit 11 may be a non-volatile storage such as an HDD (Hard Disk Drive) or SSD (Solid State Drive).

[0015] The processing unit 12 is 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 also include electronic circuits such as an ASIC (Application Specific Integrated Circuit) or an FPGA (Field Programmable Gate Array). The processor executes a program stored in memory, such as RAM. The processor is sometimes called a processor circuit. A collection of processors is sometimes called a multiprocessor or simply a "processor." Different processes among the multiple processes described later may be executed by different processors.

[0016] The memory unit 11 stores the error function 13 (error function E). The error function 13 is a model that estimates the error between the ideal value and the actual value of a multi-input quantum gate from the values ​​of several control parameters. A multi-input quantum gate is a quantum gate that acts on multiple qubits, and is typically a two-input quantum gate that acts on two qubits. Examples of multi-input quantum gates include the CNOT gate and the ZX gate used in the implementation of the CNOT gate. π / 2 These include gates, etc.

[0017] The quantum computer being calibrated in the first embodiment uses multiple pulse signals when executing a multi-input quantum gate. The quantum computer irradiates multiple pulse signals onto a qubit in parallel over the same period. To make the control bit and the target bit interact, the quantum computer uses, for example, the CR method. The quantum computer has multiple control parameters for controlling these multiple pulse signals. By changing the values ​​of the control parameters, the waveform of the pulse signals changes. The control parameters are, for example, the amplitude and phase of one pulse signal, the amplitude and phase of another pulse signal, and the pulse length common to multiple pulse signals.

[0018] Error function 13 approximates the relationship between multiple control parameters and the error. Error function 13 is predetermined, for example, in terms of the relationship between the error component contained in the Hamiltonian of a multi-input quantum gate, the unitary transformation that expresses the Hamiltonian in the form of an action on a qubit, and the multiple control parameters. The ideal value of a multi-input quantum gate is, for example, the unitary matrix representing an ideal multi-input quantum gate that does not contain errors. The actual value of a multi-input quantum gate is, for example, the unitary matrix representing an actual multi-input quantum gate that contains errors.

[0019] The error function 13 may estimate the magnitude of the matrix difference between the ideal value and the actual value as the error, or it may estimate the quadratic norm of the matrix difference, such as the Frobenius norm. The error function 13 may also estimate the sum of the squares of the components included in the matrix difference. Furthermore, the error function 13 may have multiple search parameters that are interconvertible with the above multiple control parameters. These multiple search parameters may include the coefficients of the Hamiltonian of the multi-input quantum gate. Due to the interconversion, searching for the optimal solution of the search parameters on the error function 13 is equivalent to searching for the optimal solution of the control parameters.

[0020] The processing unit 12 determines the values ​​of several control parameters so that the operation of a multi-input quantum gate in a given quantum computer approaches the ideal operation. In the first embodiment, the processing unit 12 performs a three-stage optimization as described below.

[0021] In the first stage, the processing unit 12 selects a first value as an initial value for each of the multiple control parameters. For example, the processing unit 12 selects value 14a for control parameter 14 (control parameter t), value 15a for control parameter 15 (control parameter ε1), and value 16a for control parameter 16 (control parameter ε2). Control parameter 14 is, for example, the pulse length. Control parameter 15 is, for example, the amplitude of the first pulse signal. Control parameter 16 is, for example, the amplitude of the second pulse signal. In the second stage, the processing unit 12 uses the values ​​from the first stage and the error function 13 to estimate a value that will result in higher accuracy for the multi-input quantum gate than the values ​​from the first stage.

[0022] For example, the processing unit 12 updates value 14a to value 14b, value 15a to value 15b, and value 16a to value 16b. In the third stage, the processing unit 12 uses the values ​​from the second stage and the actual calculation results of the quantum computer to determine a value that further increases the accuracy of the multi-input quantum gate compared to the values ​​from the second stage. The values ​​from the third stage may be the final calibration results that will be set in the quantum computer. For example, the processing unit 12 updates value 14b to value 14c, value 15b to value 15c, and value 16b to value 16c.

[0023] In the first stage, the processing unit 12 selects a first value for each of the multiple control parameters. In the first stage, the processing unit 12 does not need to consider the mutual influence of the multiple control parameters and may select the values ​​of each control parameter independently. The first value may be a default value set in the quantum computer before calibration. Alternatively, the first value may be selected according to the range of the control parameter, such as the center value of the control parameter. Furthermore, the first value may be selected based on knowledge such as past calibration results of similar quantum computers.

[0024] Furthermore, the first value may be selected by a simplified optimal value search using the output of a quantum computer. For example, the processing unit 12 selects one control parameter from among several control parameters and lists several candidate values ​​for the selected control parameter. The processing unit 12 also fixes the values ​​of the other control parameters to default values.

[0025] The processing unit 12 has the quantum computer execute a multi-input quantum gate while changing the value of the selected control parameter and measures the error. The processing unit 12 selects the value that minimizes the error from among several candidate values ​​as the first value for the selected control parameter. The processing unit 12 performs the above process as the first step for each of the multiple control parameters.

[0026] In the second stage, the processing unit 12 uses the error function 13 to estimate a first error from the first values ​​of multiple control parameters. Then, the processing unit 12 uses the error function 13 to search for a second value for each of the multiple control parameters. The second value is such that the second error estimated by the error function 13 is smaller than the first error. The first value from the first stage is used as the initial value for the second stage. In the second stage, the processing unit 12 performs an optimal value search on the model, eliminating the need to have the quantum computer execute a multi-input quantum gate.

[0027] For example, the processing unit 12 inputs the first values ​​of multiple control parameters into the error function 13 to calculate a first error as the output of the error function 13. If the error function 13 has multiple search parameters, the processing unit 12 converts the first values ​​of the multiple control parameters into the values ​​of the multiple search parameters. The values ​​of at least some of the multiple search parameters may be estimates of the Hamiltonian coefficients of a multi-input quantum gate.

[0028] For example, the processing unit 12 updates the values ​​of multiple control parameters or multiple search parameters using a gradient method. The processing unit 12 may repeatedly update the values ​​of the multiple control parameters or multiple search parameters until a certain convergence condition is met. The processing unit 12 may determine the amount of one update from the gradient of the error function 13 with respect to the control parameters or search parameters and a regularization term with a weight that varies according to the error. The second stage of optimal value search may be called nonlinear continuous optimization. If the error function 13 has multiple search parameters, the processing unit 12 returns the values ​​of the multiple search parameters after convergence to the values ​​of the multiple control parameters.

[0029] In the third stage, the processing unit 12 sets the second value described above for multiple control parameters and causes the quantum computer to execute a multi-input quantum gate. The processing unit 12 obtains the execution result of the multi-input quantum gate from the quantum computer and uses this result to determine the third value to be set for each of the multiple control parameters. The second value from the second stage is used as the initial value for the third stage. Typically, the third value is such that the error included in the output of the quantum computer is smaller than the second value.

[0030] In the third stage, the mutual influence of multiple control parameters is also considered. The processing unit 12 may repeat updating the values ​​of multiple control parameters and conducting experiments using a quantum computer until certain convergence conditions are met. The optimal value search in the third stage may be ORBIT. The processing unit 12 may determine the update amount for each of the multiple control parameters using a search algorithm such as the Nelder-Mead method. The optimal value search in the third stage may be a black-box optimization that does not depend on the type of multi-input quantum gate or the implementation method of the multi-input quantum gate.

[0031] The processing unit 12 outputs values ​​for multiple control parameters. The processing unit 12 may store the values ​​of the multiple control parameters in non-volatile storage, display them on a display device, or transmit them to another information processing device. The processing unit 12 may also set the values ​​determined in the first embodiment to the multiple control parameters of the quantum computer.

[0032] As described above, the information processing device 10 of the first embodiment selects a first value for each of the multiple control parameters used by the quantum computer to control the multiple pulse signals used when executing a multi-input quantum gate. The information processing device 10 estimates a first error from the first value using an error function 13 that estimates the error between the ideal value and the actual value of the multi-input quantum gate from the values ​​of the multiple control parameters. The information processing device 10 uses the error function 13 to search for a second value for each of the multiple control parameters such that the second error estimated from the second value is smaller than the first error. The information processing device 10 obtains the result of executing the multi-input quantum gate using the second value from the quantum computer and uses the result to determine a third value to be set for each of the multiple control parameters.

[0033] As a result, the information processing device 10 can efficiently optimize the multiple control parameters of the quantum computer, thereby streamlining the calibration of the multi-input quantum gate. In particular, the calibration method of the first embodiment is suitable for multi-input quantum gates implemented by the microwave pulse method and the CR method, and is suitable when there are many control parameters.

[0034] Furthermore, the information processing device 10 performs a relatively low-computation model-based optimization before the computationally intensive black-box optimization. This provides an initial value close to the optimal value at the start of the black-box optimization. As a result, the computational load of the black-box optimization is reduced, and the optimization accuracy is improved. In addition, the information processing device 10 can overcome the limitations on optimization accuracy caused by model errors between real-world multi-input quantum gates and the model through black-box optimization.

[0035] Furthermore, in model-based optimization, the information processing device 10 searches for the optimal values ​​of multiple control parameters simultaneously. Therefore, compared to a method that fixes the values ​​of other control parameters and searches for the optimal values ​​of each individual control parameter independently, the mutual influence of multiple control parameters is taken into consideration, improving the optimization accuracy. In addition, the information processing device 10 can sequentially execute the first stage of selecting initial values ​​for each control parameter, the second stage of model-based optimization, and the third stage of black-box optimization. This allows the information processing device 10 to achieve both improved optimization accuracy and reduced computational load.

[0036] (b) Second embodiment Figure 2 shows an example of the hardware of the information processing system according to the second embodiment. The information processing system according to the second embodiment includes an information processing device 100 and a quantum computer 20. The information processing device 100 is a von Neumann type classical computer. The information processing device 100 calibrates the quantum gates implemented in the quantum computer 20. The information processing device 100 corresponds to the information processing device 10 of the first embodiment.

[0037] The information processing device 100 includes a CPU 101, RAM 102, HDD 103, GPU 104, input interface 105, media reader 106, communication interface 107, and interface 108. The CPU 101 corresponds to the processing unit 12 of the first embodiment. The RAM 102 or HDD 103 corresponds to the storage unit 11 of the first embodiment.

[0038] The CPU 101 is a processor that executes program instructions. The CPU 101 loads the program and data from the HDD 103 into the RAM 102 and executes the program. The information processing device 100 may have multiple processors.

[0039] RAM 102 is a volatile semiconductor memory that temporarily stores programs executed by CPU 101 and data used for calculations by CPU 101. The information processing device 100 may have a type of volatile memory other than RAM.

[0040] The HDD 103 is a non-volatile storage device that stores software programs such as the operating system, middleware, and application software, as well as other data. The information processing device 100 may have other types of non-volatile storage, such as an SSD or flash memory.

[0041] The GPU 104 works in conjunction with the CPU 101 to perform image processing and outputs the image to the display device 111 connected to the information processing device 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. The GPU 104 may also be used as a GPGPU (General Purpose Computing on Graphics Processing Unit). The GPU 104 can execute programs in response to instructions from the CPU 101. The information processing device 100 may have volatile semiconductor memory other than RAM 102 as GPU memory.

[0042] The input interface 105 receives input signals from an input device 112 connected to the information processing device 100. The input device 112 is, for example, a mouse, a touch panel, or a keyboard. Multiple input devices may be connected to the information processing device 100.

[0043] The media reader 106 is a reading device that reads programs and data recorded on the recording medium 113. The recording medium 113 is, for example, a magnetic disk, an optical disk, or semiconductor memory. Magnetic disks include flexible disks (FD) and HDDs. Optical disks include CDs (Compact Discs) and DVDs (Digital Versatile Discs). The media reader 106 copies the programs and data read from the recording medium 113 to other recording media such as RAM 102 or HDD 103. The read programs may be executed by the CPU 101.

[0044] The recording medium 113 may be a portable recording medium. The recording medium 113 may be used for distributing programs and data. The recording medium 113 and the HDD 103 may also be referred to as computer-readable recording media.

[0045] The communication interface 107 communicates with other information processing devices via the network 114. The communication interface 107 may be a wired communication interface connected to a wired communication device such as a switch or router, or a wireless communication interface connected to a wireless communication device such as a base station or access point.

[0046] Interface 108 is connected to the quantum computer 20. Interface 108 sends commands to the quantum computer 20 in response to instructions from the CPU 101. Interface 108 receives the execution results of the commands from the quantum computer 20 and stores the received execution results in RAM 102.

[0047] The quantum computer 20 has a qubit section 21 and a pulse control section 22. The qubit section 21 includes a plurality of qubits. The qubits are, for example, superconducting qubits. The plurality of qubits are arranged, for example, in a lattice. When a microwave pulse signal is irradiated onto a qubit, the quantum state of the qubit changes. Pairs of qubits capable of acting on a two-input quantum gate are connected by capacitors.

[0048] The pulse control unit 22 performs quantum operations by irradiating the qubit unit 21 with microwave pulse signals. The pulse control unit 22 includes a state control unit 23 and a state readout unit 24. The state control unit 23 irradiates the qubit unit 21 with microwave pulse signals in response to commands from the information processing device 100. This executes quantum operations equivalent to quantum gates. The state control unit 23 may combine and irradiate multiple microwave pulse signals to realize a single quantum gate.

[0049] The state control unit 23 has several control parameters for adjusting the waveform of the microwave pulse signal. For example, the state control unit 23 has control parameters such as pulse length, amplitude, and phase of the microwave pulse signal. Each of these control parameters has a default value. The state control unit 23 changes the control parameter values ​​from their default values ​​in response to a command from the information processing device 100. The two-input quantum gate is implemented by the CR method. The CR method irradiates the control bit with a microwave pulse signal at a resonant frequency that resonates with the target bit.

[0050] The state readout unit 24 performs measurement operations on the qubits included in the qubit unit 21 in response to commands from the information processing device 100. A single measurement operation on a qubit probabilistically yields a measurement value of 0 or 1, depending on the quantum state of that qubit. The state readout unit 24 transmits the measurement value to the information processing device 100. Next, qubits and quantum gates will be described.

[0051] Figure 3 shows an example of manipulating a quantum state using a quantum gate. In the quantum computer 20, the quantum state of a single qubit is represented as a superposition of |0> and |1>, as shown in equation (1). In equation (1), a is a complex number representing the weight of |0>, and b is a complex number representing the weight of |1>. The square of the absolute value of a represents the probability of existence of |0>, and the square of the absolute value of b represents the probability of existence of |1>. The sum of the squares of the absolute values ​​of a and b is 1. Considering the range of possible values ​​for a and b, the quantum state can also be represented using angles θ and φ, as shown in equation (1). θ is a real number between 0 and π (inclusive), and φ is a real number between 0 and 2π (inclusive).

[0052]

number

[0053] Bloch sphere 131 is a three-dimensional representation of the space to which the quantum state of a single qubit belongs. A single Bloch vector, pointing from the origin of Bloch sphere 131 to a point on its surface, represents a single quantum state. Bloch vector 132 represents |0>, corresponding to θ=0, φ=0. Bloch vector 133 represents the quantum state in equation (2), corresponding to θ=π / 2, φ=0. Bloch vector 134 represents |1>, corresponding to θ=π, φ=0.

[0054]

number

[0055] The transformation between Bloch vector 132 and Bloch vector 133 uses a 90° rotation quantum gate as shown in equation (3). Similarly, the transformation between Bloch vector 133 and Bloch vector 134 uses a 90° rotation quantum gate. The quantum gate in equation (3) rotates the Bloch vector by π / 2 around the Y axis. The transformation between Bloch vector 132 and Bloch vector 134 uses a 180° rotation quantum gate. This 180° rotation quantum gate is, for example, the X gate among the X, Y, and Z gates in equation (4), which are represented by Pauli matrices.

[0056]

number

[0057]

number

[0058] Figure 4 shows an example of a microwave pulse signal. Microwave pulses are one physical implementation of quantum gates. The quantum computer 20 irradiates a qubit, whose quantum state is being changed, with a microwave pulse signal. The total area of ​​the microwave pulse signal waveform corresponds to the total energy supplied to the qubit and corresponds to the amount of rotation of the quantum state. By adjusting the waveform of the microwave pulse signal, a desired quantum gate can be realized.

[0059] The Hamiltonian of a microwave pulse signal is defined as shown in equation (5). The Hamiltonian is the energy that modifies the quantum state. In equation (5), H is the Hamiltonian, h is the Dirac constant, and Ω is the Rabi frequency. X is the unitary matrix corresponding to the desired quantum gate, which in this case is the Pauli X matrix. The action of the quantum gate on a qubit is expressed by the unitary transformation shown in equation (6). In equation (6), U is the unitary matrix. The second transformation holds when Ωt = π.

[0060]

number

[0061]

number

[0062] Ideally, the quantum computer 20 prefers to irradiate the qubits with a microwave pulse signal 141 whose envelope is rectangular. This would cause the quantum gate's operation to conform to its ideal value, as shown in equation (6). However, due to physical constraints, it is difficult for the quantum computer 20 to generate the microwave pulse signal 141. In reality, the quantum computer 20 generates a microwave pulse signal 142 with smooth rise and fall times. As a result, the quantum gate has an error that indicates the degree to which its operation deviates from the ideal value.

[0063] Errors in quantum gates are affected by manufacturing variations in the quantum computer 20 and also by the operating environment of the quantum computer 20. Therefore, the quantum computer 20 has control parameters to adjust the waveform of the microwave pulse signal so that errors in quantum gates can be reduced. For example, the quantum computer 20 has control parameters such as pulse length, amplitude, frequency, and phase of the microwave pulse signal. The pulse length is the time width of the envelope of the microwave pulse signal. The phase is the angle of the microwave at the start of irradiation.

[0064] Figure 5 shows an example of manipulating a quantum state using a two-input quantum gate. Quantum gates executed by quantum computers include two-input quantum gates that act on two qubits. A typical example of a two-input quantum gate is the CNOT gate.

[0065] Bloch sphere 135 represents the quantum state space of the control bit. Bloch sphere 136 represents the quantum state space of the target bit. The CNOT gate maintains the quantum state of the target bit when the control bit is 0, and inverts the 0s and 1s of the target bit when the control bit is 1. Bloch vector 137 shows the case when the control bit is 0. In this case, Bloch vector 139 does not change for the target bit. On the other hand, Bloch vector 138 shows the case when the control bit is 1. In this case, Bloch vector 139 rotates 180° and changes to Bloch vector 140 for the target bit.

[0066] The quantum computer 20 uses the CR method (cross-resonance method) as a physical implementation of a two-input quantum gate. The CR method controls the target bit according to the quantum state of the control bit via capacitive coupling between the control bit and the target bit. The CR method inputs a microwave pulse signal with a resonant frequency that resonates with the target bit to the signal line of the control bit.

[0067] By using the CR method, a two-input quantum gate called the ZX gate is realized. The ZX gate applies a Z gate to the control bit and an X gate to the target bit. Equation (7) represents the ZX equivalent of the π / 2 pulse of the ZX gate. π / 2 The gate is shown. A two-input quantum gate is represented by a 4x4 unitary matrix. ZX π / 2 The CNOT gate is realized by combining this gate with several other quantum gates.

[0068]

number

[0069] In the second embodiment, a microwave pulse signal and the CR method are used to input a ZX 2-input quantum gate. π / 2 Let's consider implementing a gate. The information processing device 100 may use the calibration method of the second embodiment for other types of two-input quantum gates, or for multi-input quantum gates that act on three or more qubits.

[0070] Figure 6 shows an example of a combination of multiple microwave pulse signals. A two-input quantum gate can generate components in various rotational directions, as its operation can be represented by a 4x4 matrix, and may have complex error components. Therefore, it can be difficult for the quantum computer 20 to realize a desired two-input quantum gate with high precision by simply adjusting the waveform of a single microwave pulse signal. Thus, the quantum computer 20 realizes a two-input quantum gate by combining multiple microwave pulse signals.

[0071] As an example, quantum computer 20 combines microwave pulse signals 143, 144, and 145 to ZX π / 2 The gate is implemented. The microwave pulse signal 143 is a CR pulse, which serves as the main microwave pulse signal. The CR pulse generates the cross-resonance described above between the control bit and the target bit.

[0072] Microwave pulse signal 144 is a cancellation tone. The purpose of the cancellation tone is to cancel out error components of the CR pulse in a specific rotational direction. Microwave pulse signal 145 is a rotary tone. The rotary tone is a microwave pulse signal that rotates in a constant rotational direction (e.g., the X-axis direction) and is intended to shake out error components in directions different from that rotational direction.

[0073] In this way, combining multiple microwave pulse signals improves the implementation accuracy of quantum gates. However, the quantum computer 20 has many control parameters to adjust the waveforms of the multiple microwave pulse signals. For example, the quantum computer 20 has control parameters such as the overall pulse length, the amplitude and phase of the CR pulse, the amplitude and phase of the cancellation tone, and the amplitude of the rotary tone.

[0074] Because there are many control parameters, the search space to which combinations of control parameter values ​​belong becomes large. Therefore, when attempting to find the optimal solution that minimizes the error of the quantum gate, the load on the information processing device 100 increases, and the search time may become longer. In addition, depending on the search method, the calibration accuracy may decrease. Therefore, the information processing device 100 of the second embodiment efficiently performs quantum gate calibration through the three-stage optimization process described below.

[0075] In the first stage, the information processing device 100 independently selects initial values ​​for each control parameter through Hamiltonian tomography. Hamiltonian tomography is a type of quantum process tomography that estimates the actual behavior of quantum gates.

[0076] The information processing device 100 repeatedly has the quantum computer 20 execute a quantum gate under certain control parameter values ​​to obtain measured values ​​of qubits. The information processing device 100 estimates the Hamiltonian coefficient of the quantum gate by statistically analyzing the measured values ​​and calculates the error component, which is the difference between the actual value and the ideal value of the Hamiltonian coefficient. The information processing device 100 samples several control parameter values ​​and performs Hamiltonian tomography on these control parameter values ​​to find the control parameter value with the smallest error component.

[0077] In this case, since the search space formed by multiple control parameters is large, the information processing device 100 changes only the value of one control parameter at a time, rather than changing the values ​​of multiple control parameters simultaneously. The information processing device 100 fixes the values ​​of the other control parameters to their default values ​​while repeatedly estimating the error component of the Hamiltonian by changing the value of one control parameter. The information processing device 100 selects the control parameter value with the smallest estimated error component from among the tried control parameter values ​​as the initial value of that control parameter. For example, the information processing device 100 selects 20 candidate values ​​for each of the six control parameters and estimates the error component by executing a quantum gate 1000 times for each candidate value.

[0078] The first stage does not consider the dependencies between multiple control parameters, so the initial values ​​selected in the first stage may be far from the optimal values. Also, there may be error components that are difficult to make zero overall, and the initial values ​​selected by individually adjusting the values ​​of multiple control parameters are not necessarily the optimal values. Therefore, the first stage is a simple search method for finding the initial values ​​for the optimization process in the second stage.

[0079] In the second stage, the information processing device 100 performs model-based optimization. Instead of actually having the quantum computer 20 execute quantum gates, model-based optimization uses a model that defines the relationship between multiple control parameters and errors. The error calculated by the model is the magnitude of the difference between the actual value and the ideal value of the unitary matrix that represents the action of the quantum gate. However, to facilitate parameter search on the model, the model in the second embodiment uses multiple search parameters that are mutually convertible with multiple control parameters. The model expressed using these multiple search parameters has generality that is independent of the type of quantum gate and generality that is independent of the detailed configuration of the microwave pulse signal.

[0080] The information processing device 100 repeatedly updates the values ​​of multiple search parameters using the gradient method until convergence occurs. The information processing device 100 calculates the error using a model from the current values ​​of the search parameters and calculates the gradient of the error with respect to the search parameters. The information processing device 100 updates the search parameter values ​​in the direction that reduces the error using the calculated gradient. The information processing device 100 converts the initial values ​​of multiple control parameters selected in the first stage into initial values ​​for multiple search parameters and starts the search using the gradient method from those initial values. The information processing device 100 converts the values ​​of multiple search parameters at the convergence point into values ​​for multiple control parameters.

[0081] The second-stage model considers the dependencies between multiple control parameters. However, the model does not necessarily accurately represent all errors inherent in the quantum gate implementation, and the errors it calculates are estimates. Therefore, while the second-stage control parameter values ​​are closer to the optimal values ​​than those in the first stage, they may still deviate from the optimal values. Consequently, the second-stage control parameter values ​​are used as the starting point for the third-stage optimization process.

[0082] In the third stage, the information processing device 100 performs ORBIT, a type of black-box optimization. The information processing device 100 causes the quantum computer 20 to execute a quantum gate m times (where m is an integer greater than or equal to 1) in succession, and then executes a quantum gate that cancels out the ideal effect of those m quantum gates. The information processing device 100 measures the qubit and determines whether the residual is zero. By repeating the above, the information processing device 100 calculates the success probability of the residual being zero, and calculates the fidelity corresponding to the number of iterations m from the success probability. Fidelity is an index representing the precision of quantum operations and is a real number between 0 and 1.

[0083] The information processing device 100 repeatedly measures the fidelity while varying the number of iterations m, and fits a nonlinear curve showing the relationship between the number of iterations m and the fidelity. From the nonlinear curve, the information processing device 100 estimates the fidelity per quantum gate operation. This allows for highly accurate evaluation of the error level, even when the error of the quantum gate is small. The information processing device 100 updates the values ​​of multiple control parameters using a search algorithm such as the Nelder-Mead method to increase the fidelity per quantum gate operation.

[0084] ORBIT is a black-box optimization that makes no assumptions about the implementation method of quantum gates. Also, ORBIT searches for the optimal value from the entire search space formed by multiple control parameters and considers the dependencies between the multiple control parameters. Therefore, the information processing apparatus 100 adopts the control parameter values calculated by ORBIT as the final calibration result. On the other hand, since the cost of measuring the fidelity once is high and the number of steps until the fidelity converges may also be large, the load on ORBIT is high.

[0085] Therefore, the information processing apparatus 100 starts ORBIT from control parameter values close to the optimal value to shorten the number of steps until the fidelity converges. As a result, the computational load on ORBIT is reduced, and the required time for ORBIT is shortened. Next, the second-stage model-based optimization will be further explained.

[0086] When defining the model, the information processing apparatus 100 defines the Hamiltonian of the quantum gate as the sum of multiple rotation components as shown in Equation (8). In Equation (8), IX is the tensor product of the X gate and the identity gate (I gate), IY is the tensor product of the Y gate and the I gate, and IZ is the tensor product of the Z gate and the I gate. ZI is the tensor product of the I gate and the Z gate, ZX is the tensor product of the X gate and the Z gate, ZY is the tensor product of the Y gate and the Z gate, and ZZ is the tensor product of the Z gate and the Z gate.

[0087]

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[0088] ν IX is the coefficient of the part excluding the influence of the rotary tone among the IX components. f is the amplitude of the rotary tone. ν IY is the coefficient of the IY component, ν IZ is the coefficient of the IZ component, ν ZI is the coefficient of the ZI component, ν ZX is the coefficient of the ZX component, ν ZY is the coefficient of the ZY component, ν ZZis the coefficient of the ZZ component. The Hamiltonian is represented by a 4x4 matrix and includes components other than the seven components mentioned above. However, since the seven components mentioned above are dominant, the models of the second embodiment ignore the components other than the seven components mentioned above. Note that the first stage Hamiltonian anthomography estimates some or all of the Hamiltonian coefficients.

[0089] From the Hamiltonian of a quantum gate that includes errors, the unitary transformation exhibiting error-inclusive behavior is defined by the transformation equation shown in equation (9). In equation (9), U is the unitary matrix representing the unitary transformation, and t is the pulse length of the microwave pulse signal. Due to the effects of errors, the unitary matrix U does not coincide with the ideal value of the quantum gate.

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[0091] Therefore, the information processing device 100 defines the error function shown in equation (10) as a model. The error function is the Hamiltonian coefficient ν IX ,ν IY ,ν ZX ,ν ZY The search parameters include the rotary tone amplitude f and pulse length t. The error function calculates the error from the values ​​of these six search parameters. The error is the sum of the squares of the matrix components contained in the matrix difference between the unitary matrix representing the actual value of the quantum gate and the unitary matrix representing the ideal value.

[0092]

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[0093] In equation (10), ZX is used as the quantum gate. π / 2 A gate is used. The error calculated by the error function corresponds to the square of the Frobenius norm. Note that the information processing device 100 may use a distance index other than the Frobenius norm as an index of error.

[0094] The relationship between the Hamiltonian coefficients in equation (8) and the control parameters is as follows: Equation (11) is the Hamiltonian coefficient ν IX and control parameter ε CR ,φ CR ,ε C ,φ C This shows the relationship with ε. CR φ is the amplitude of the CR pulse. CR ε is the phase of the CR pulse. C φ is the amplitude of the cancellation tone. C is the phase of the cancellation tone. The information processing device 100 can determine the constants A1, A2, a1 by estimating the actual Hamiltonian coefficients by first-stage Hamiltonian antometry.

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[0096] Equation (12) is the Hamiltonian coefficient ν IY and control parameter ε CR ,φ CR ,ε C ,φ C This shows the relationship. Equation (13) is the Hamiltonian coefficient ν IZ This shows that is a constant. The information processing device 100 can determine the constant A3 by estimating the actual Hamiltonian coefficients by first-stage Hamiltonian antometry. Equation (14) is the Hamiltonian coefficient ν ZI and control parameter ε CR This shows the relationship. The information processing device 100 can determine the constant A4 by estimating the actual Hamiltonian coefficients using first-stage Hamiltonian antometry.

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[0100] Equation (15) is the Hamiltonian coefficient ν ZX and control parameter ε CR ,φ CR This shows the relationship. The information processing device 100 can determine the constant A5 by estimating the actual Hamiltonian coefficients by first-stage Hamiltonian antometry. Equation (16) is the Hamiltonian coefficient ν ZY and control parameter ε CR ,φ CR This shows the relationship. Equation (17) is the Hamiltonian coefficient ν ZZ This indicates that is a constant. The information processing device 100 can determine the constant A6 by estimating the actual Hamiltonian coefficients using first-stage Hamiltonian antometry.

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[0104] The error function in equation (10) is a vector e as in equation (18). s It is expressed using . Defining the error function in the form of the sum of squares of an expression containing variables makes numerical calculations using gradient search algorithms easier. Vector e s This is expanded as shown in equation (19). In equation (19), vector n w ,n x ,ny ,n z n is a 4-dimensional unit vector. w n is a vector where only the w dimension is 1 and the other dimensions are 0. x n is a vector where only the x-dimension is 1 and the other dimensions are 0. y n is a vector where only the y-dimension is 1 and the other dimensions are 0. z This is a vector where only the z dimension is 1 and the other dimensions are 0.

[0105]

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[0107] The Hamiltonian coefficient ν included in equation (19) ZI This is estimated, for example, by the first stage of Hamiltonianthomography. In equation (19), θ is the absolute value of the vector θ(s) defined in equations (20) and (21). θ + is the vector θ + The absolute value of (s,0), ​​θ - is the vector θ - This is the absolute value of (s,0). x θ is the x-component of the vector θ(s). y θ is the y-component of the vector θ(s). z is the z component of the vector θ(s). The Hamiltonian coefficient ν is included in equation (21). IZ ,ν ZZ This is estimated, for example, by first-stage Hamiltonianthomography.

[0108]

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[0110] Expanding equation (18) using equation (19), the error function is defined as shown in equation (22). The information processing device 100 calculates the error corresponding to the current value by inputting the current value of the search parameter into the error function. The information processing device 100 calculates the amount of update to the search parameter from the gradient of the error using the parameter update formula shown in equation (23). This parameter update formula represents the Levenberg-Marquardt method. The Levenberg-Marquardt method is a type of iterative method for solving nonlinear least squares problems.

[0111]

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[0113] In equation (23), p i ,p j Δp represents one of the six search parameters, as shown in equation (24). j The search parameter p j This is the update amount. The information processing device 100 calculates an update amount that satisfies formula (23) for each of the six search parameters and adds the update amount to the current value of that search parameter. The information processing device 100 repeats the calculation of the error and the updating of the search parameter values ​​until the convergence condition is met.

[0114]

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[0115] λδ in equation (23) ijδ is a regularization term. The information processing device 100 suppresses the amount of a single update of the search parameters from becoming too large by inserting a regularization term into the parameter update formula. λ is the weight of the regularization term, and as will be described later, it is dynamically adjusted according to the degree of error reduction calculated by the error function. ij is the Kronecker delta. Search parameter p i ,p j If they are the same, then δ ij = 1, and if they are not the same, then δ ij = 0

[0116] Figure 7 shows an example of control parameters. Table 151 shows the control parameters of the quantum computer 20 and their corresponding values. As an example, the pulse length t is 200 ns and the CR pulse amplitude ε CR -3dBm, CR pulse phase φ CR The angle is 5°, and the cancellation tone amplitude ε C -20dBm, Cancellation tone phase φ C The angle is -170°, and the rotary tone amplitude f is -15dBm.

[0117] Figure 8 shows an example of Hamiltonian coefficients. Table 152 associates the Hamiltonian coefficients of quantum gates with their values. As an example, ν IX 0.001MHz, ν IY 0.001MHz, ν IZ 0.01MHz, ν ZI 300MHz, ν ZX 2MHz, ν ZY 0.001MHz, ν ZZ The frequency is 0.01 MHz. Next, we will provide further explanation regarding the first and third stages of optimization.

[0118] Figure 9 is a graph showing an example of the relationship between rotary tone amplitude and error. In the graph of Figure 9, the horizontal axis is rotary tone amplitude, and the vertical axis is Hamiltonian coefficient error. Hamiltonian coefficient error is the difference between the ideal value and the actual value of the Hamiltonian coefficient. Curve 161 shows the Hamiltonian coefficient ν ZZindicates an error. Curve 162 represents the error of the Hamiltonian coefficient ν IZ indicates an error. Curve 163 represents the error of the Hamiltonian coefficient ν ZY indicates an error. Curve 164 represents the error of the Hamiltonian coefficient ν IY indicates an error.

[0119] In the first stage, the information processing apparatus 100 fixes the pulse length, CR pulse amplitude, CR pulse phase, cancellation tone amplitude, and cancellation tone phase to default values, and measures the Hamiltonian coefficient error while changing the rotary tone amplitude. As a result, curves 161, 162, 163, and 164 are calculated.

[0120] The information processing apparatus 100 selects, as an initial value, the rotary tone amplitude at which the errors of a plurality of Hamiltonian coefficients are minimized as a whole. For example, the information processing apparatus 100 selects the rotary tone amplitude at which the sum of the squares of the Hamiltonian coefficient errors is minimized.

[0121] FIG. 10 is a graph showing an example of the relationship between the cancellation tone amplitude and the error. The horizontal axis of the graph in FIG. 10 is the cancellation tone amplitude, and the vertical axis is the Hamiltonian coefficient error. Curve 165 represents the error of the Hamiltonian coefficient ν IY indicates an error. Curve 166 represents the error of the Hamiltonian coefficient ν IX indicates an error. Curve 167 represents the error of the Hamiltonian coefficient ν ZZ indicates an error. Curve 168 represents the error of the Hamiltonian coefficient ν IZ indicates an error. Curve 169 represents the error of the Hamiltonian coefficient ν ZY indicates an error.

[0122] The information processing device 100, as in the case of Figure 9, fixes the pulse length, CR pulse amplitude, CR pulse phase, cancellation tone phase, and rotary tone amplitude to default values ​​and measures the Hamiltonian coefficient error while changing the cancellation tone amplitude. This calculates curves 165, 166, 167, 168, and 169. The information processing device 100 selects the cancellation tone amplitude that minimizes the overall error of the multiple Hamiltonian coefficients as the initial value.

[0123] Figure 11 is a graph showing an example of the relationship between the number of quantum gate iterations and fidelity. The horizontal axis of the graph in Figure 11 represents the number of quantum gate iterations m in ORBIT. The vertical axis represents the fidelity measured by ORBIT. Curve 171 shows the relationship between the number of iterations and fidelity when the quantum gate is executed using a certain control parameter value. Curve 172 shows the relationship between the number of iterations and fidelity when the quantum gate is executed using a different control parameter value.

[0124] By repeatedly applying the same quantum gate to a qubit, the errors inherent in the quantum gate are amplified, causing the fidelity to gradually decrease. Therefore, the fidelity curve slopes downwards and is convex downwards with respect to the number of iterations. The information processing device 100 can estimate the fidelity for a single iteration by fitting this curve to the fidelity measurement results. Next, the functions and processing procedures of the information processing device 100 will be described.

[0125] Figure 12 is a block diagram showing an example of the functions of an information processing device. The information processing device 100 includes a model storage unit 121, a parameter storage unit 122, a pulse setting unit 123, a tomography execution unit 124, an initial value calculation unit 125, a model-based optimization unit 126, and an ORBIT execution unit 127. The model storage unit 121 and the parameter storage unit 122 are implemented using, for example, RAM 102 or HDD 103. The pulse setting unit 123, the tomography execution unit 124, the initial value calculation unit 125, the model-based optimization unit, and the ORBIT execution unit 127 are implemented using, for example, a CPU 101 and a program.

[0126] The model memory unit 121 stores the model used for model-based optimization. The model includes the error function, gradient function, and parameter update formula. The model also includes information showing the relationship between the control parameters of the quantum computer 20 and the search parameters used in the error function. Furthermore, the model memory unit 121 stores information about the Hamiltonian and unitary matrices of the quantum gates. In addition, the model memory unit 121 stores hyperparameter values ​​such as the weights of the regularization term and convergence conditions.

[0127] The parameter storage unit 122 stores the control parameter values ​​determined through the calibration method of the second embodiment. When using the quantum computer 20, the information processing device 100 may transmit the control parameter values ​​stored in the parameter storage unit 122 to the quantum computer 20. The pulse setting unit 123 controls the waveform of the microwave pulse signal by transmitting a command specifying the control parameter values ​​to the pulse control unit 22 in response to a request from the tomography execution unit 124 or the ORBIT execution unit 127.

[0128] The tomography execution unit 124 causes the quantum computer 20 to execute a quantum gate under control parameter values ​​specified by the initial value calculation unit 125, and reads out the measured values ​​of the qubits from the quantum computer 20. The tomography execution unit 124 statistically analyzes the measured values ​​and performs Hamiltonian tomography to estimate the Hamiltonian coefficients of the quantum gate.

[0129] The initial value calculation unit 125 selects an initial value for each of the multiple control parameters. The initial value calculation unit 125 changes the value of one control parameter while fixing the values ​​of the other control parameters to their default values, and has the tomography execution unit 124 perform Hamiltonian tomography. The initial value calculation unit 125 selects a control parameter value that minimizes the error component based on the relationship between the value of the one control parameter and the error component of the Hamiltonian. The initial value calculation unit 125 outputs the selected initial value to the model-based optimization unit 126.

[0130] The model-based optimization unit 126 performs model-based optimization using the model stored in the model storage unit 121. The model-based optimization unit 126 calculates the error from the current control parameter values ​​using the error function, and repeatedly moves the control parameter values ​​by an update amount corresponding to the current gradient using the gradient function and parameter update formula. The model-based optimization unit 126 starts this search process from the initial values ​​selected by the initial value calculation unit 125, and outputs the control parameter values ​​at convergence to the ORBIT execution unit 127.

[0131] The ORBIT execution unit 127 executes ORBIT. The ORBIT execution unit 127 causes the quantum computer 20 to execute a quantum gate under certain control parameter values ​​and measures the fidelity of the quantum gate. The ORBIT execution unit 127 repeatedly updates the control parameter values ​​to increase fidelity. The ORBIT execution unit 127 starts this search process from the control parameter values ​​output by the model-based optimization unit 126 and stores the control parameter values ​​at convergence in the parameter storage unit 122. The ORBIT execution unit 127 may display the control parameter values ​​on the display device 111 or transmit them to another information processing device.

[0132] Figure 13 is a flowchart illustrating an example of the quantum gate calibration procedure. In step S10, the initial value calculation unit 125 initializes all control parameters related to the microwave pulse signal of the quantum gate to be calibrated to default values ​​held by the quantum computer 20. In step S11, the initial value calculation unit 125 selects one control parameter. The initial value calculation unit 125 enumerates candidate values ​​for the selected control parameter. For example, the initial value calculation unit 125 extracts 20 control parameter values ​​at equal intervals from the range of the control parameter.

[0133] In step S12, the tomography execution unit 124 performs Hamiltonian tomography for each of the candidate values ​​enumerated in step S11. The pulse setting unit 123 changes the value of the selected control parameter to the candidate value, and the tomography execution unit 124 causes the quantum computer 20 to execute the quantum gate. The tomography execution unit 124 analyzes the execution result of the quantum gate and estimates the Hamiltonian coefficient of the quantum gate.

[0134] In step S13, the initial value calculation unit 125 determines whether the experiments in steps S11 and S12 have been completed for all control parameters. If the experiments for all control parameters have been completed, the process proceeds to step S14; otherwise, the process returns to step S11.

[0135] In step S14, the initial value calculation unit 125 selects, for each control parameter, the candidate value with the smallest error in the Hamiltonian coefficient from among multiple candidate values ​​as the initial value. Alternatively, the initial value calculation unit 125 may select an untested control parameter value as the initial value from a regression curve showing the relationship between the control parameter value and the error component. In step S15, the model-based optimization unit 126 performs model-based optimization starting from the initial values ​​selected in step S14. Details of model-based optimization will be described later.

[0136] In step S16, the ORBIT execution unit 127 executes ORBIT starting from the control parameter values ​​calculated by the model-based optimization in step S15. The pulse setting unit 123 sets current values ​​for multiple control parameters, and the ORBIT execution unit 127 causes the quantum computer 20 to execute the quantum gate. The ORBIT execution unit 127 analyzes the execution results of the quantum gate and measures the fidelity of the quantum gate. The ORBIT execution unit 127 updates the values ​​of multiple control parameters to increase fidelity. In step S17, the ORBIT execution unit 127 outputs the optimal values ​​for the control parameters.

[0137] Figure 14 is a flowchart showing an example of the model-based optimization procedure. In step S20, the model-based optimization unit 126 defines the error function, gradient function, and parameter update formula for the quantum gate to be calibrated. In step S21, the model-based optimization unit 126 converts the initial values ​​of the multiple control parameters selected in step S14 into initial values ​​of the multiple search parameters used by the error function.

[0138] In step S22, the model-based optimization unit 126 calculates the value of the error function using the current search parameter values. In step S23, the model-based optimization unit 126 determines whether the value of the error function is greater than the previous value (i.e., whether the error has worsened). If the value of the error function is greater than the previous value, the process proceeds to step S26; otherwise, the process proceeds to step S24. If there was no previous error, the process proceeds to step S24.

[0139] In step S24, the model-based optimization unit 126 determines whether the convergence conditions are met. The convergence conditions are, for example, that the rate of change of the error function value is less than 0.1%, and the rate of change of all search parameter values ​​is less than 0.1%. If the convergence conditions are met, the process proceeds to step S31; otherwise, the process proceeds to step S25.

[0140] In step S25, the model-based optimization unit 126 halves the weight λ of the regularization term included in the parameter update formula. This makes it easier for the amount of update to the search parameters to increase. Then the process proceeds to step S28. In step S26, the model-based optimization unit 126 returns the search parameters to their previous values. In step S27, the model-based optimization unit 126 doubles the weight λ of the regularization term included in the parameter update formula. This restricts the amount of update to the search parameters to be small.

[0141] In step S28, the model-based optimization unit 126 calculates the gradient from the gradient function using the current values ​​of the search parameters. In step S29, the model-based optimization unit 126 calculates the update amount for the search parameters from the error function and gradient according to the parameter update formula. In step S30, the model-based optimization unit 126 updates the current values ​​of the search parameters by adding the update amount to the current values. Then, the process returns to step S22. In step S31, the model-based optimization unit 126 converts the values ​​of multiple search parameters at convergence to the values ​​of multiple control parameters.

[0142] As described above, the information processing device 100 of the second embodiment calibrates the two-input quantum gate by adjusting the waveforms of multiple microwave pulse signals. This improves the implementation accuracy of the two-input quantum gate using the CR method.

[0143] Furthermore, the information processing device 100 performs Hamiltonian antometry for each control parameter to select initial values. This improves the accuracy of model-based optimization and shortens the execution time of model-based optimization compared to performing it from default values ​​provided by the quantum computer 20.

[0144] Furthermore, the information processing device 100 performs model-based optimization using an error function before ORBIT. This allows ORBIT to start from control parameter values ​​close to the optimal values, thereby shortening the execution time of ORBIT. Also, since model-based optimization considers the dependencies of multiple control parameters, it can calculate control parameter values ​​close to the optimal values. Finally, ORBIT searches for control parameter values ​​that minimize the error of the quantum gate. From the above, the information processing device 100 can efficiently calibrate a two-input quantum gate. [Explanation of Symbols]

[0145] 10 Information Processing Devices 11 Storage section 12 Processing Units 13. Error Function 14, 15, 16 Control parameters 14a,14b,14c,15a,15b,15c,16a,16b,16c values

Claims

1. For each of the multiple control parameters used by a quantum computer to control multiple pulse signals when executing a multi-input quantum gate, a first value is selected. The error between the ideal value and the actual value of the aforementioned multi-input quantum gate is estimated from the first value using an error function that estimates the error from the values ​​of the aforementioned multi-control parameters, thereby estimating the first error from the first value. Using the error function, the second value of each of the multiple control parameters is searched such that the second error estimated from the second value is smaller than the first error. The results of executing the multi-input quantum gate using the second value are obtained from the quantum computer, and the third value to be set for each of the multiple control parameters is determined using the results. A quantum gate calibration program that causes a computer to perform a process.

2. The selection process includes, using the quantum computer, changing the value of one of the plurality of control parameters while fixing the values ​​of the other control parameters, measuring the error component included in the Hamiltonian of the plurality of input quantum gate, and selecting the value of the one control parameter that minimizes the measured error component as the first value for the one control parameter. The quantum gate calibration program according to claim 1.

3. The error function represents the sum of squares of the components included in the matrix difference between the first unitary matrix representing the ideal value and the second unitary matrix representing the actual value. The quantum gate calibration program according to claim 1.

4. The error function has a plurality of search parameters, including the coefficients of the Hamiltonian of the plurality input quantum gate, which are mutually convertible with the plurality of control parameters. The search process includes searching for a fourth value for each of the multiple search parameters using the error function, and converting the fourth value to the second value. The quantum gate calibration program according to claim 1.

5. The search process includes a process of repeatedly updating the values ​​of the multiple search parameters using the gradient of the error function with respect to the multiple search parameters and a regularization term having a weight that varies according to the error estimated by the error function. The quantum gate calibration program according to claim 4.

6. The plurality of control parameters include the amplitude and phase of a first pulse signal among the plurality of pulse signals, the amplitude and phase of a second pulse signal among the plurality of pulse signals, and the pulse lengths of the first pulse signal and the second pulse signal. The quantum gate calibration program according to claim 1.

7. For each of the multiple control parameters used by a quantum computer to control multiple pulse signals when executing a multi-input quantum gate, a first value is selected. The error between the ideal value and the actual value of the aforementioned multi-input quantum gate is estimated from the first value using an error function that estimates the error from the values ​​of the aforementioned multi-control parameters, thereby estimating the first error from the first value. Using the error function, the second value of each of the multiple control parameters is searched such that the second error estimated from the second value is smaller than the first error. The results of executing the multi-input quantum gate using the second value are obtained from the quantum computer, and the third value to be set for each of the multiple control parameters is determined using the results. A quantum gate calibration method in which a computer performs the processing.

8. A storage unit that stores an error function which estimates the error between the ideal value and the actual value of a multi-input quantum gate from the values ​​of multiple control parameters used to control multiple pulse signals used by a quantum computer when executing the multi-input quantum gate, A processing unit that selects a first value for each of the plurality of control parameters, estimates a first error from the first value using the error function, searches for a second value for each of the plurality of control parameters using the error function such that the second error estimated from the second value is smaller than the first error, obtains the result of executing the plurality of input quantum gate using the second value from the quantum computer, and determines a third value to be set for each of the plurality of control parameters using the result, An information processing device having

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