Control device, control method, and program

Abstract

A control device comprising: an anticipated-value calculation unit which, using a quantum circuit, alternately or simultaneously performs multiple quantum calculations of a numerator and a denominator of a formula in a virtual distillation method and calculates anticipated values for a plurality of states of the numerator and the denominator; an error suppression calculation unit which inputs the obtained plurality of states to an error suppression circuit to obtain output values; and a target-value estimation unit which repeatedly performs the calculation of the anticipated values and the acquisition of the output values, calculates measured values, and estimates quantum-calculation target values on the basis of the calculated measured values.

Description

[Technical Field]

[0001] The present invention relates to a control device, a control method, and a program. [Background technology]

[0002] Quantum computers are a technology that performs calculations by utilizing the principle of superposition in quantum mechanics, and are expected to be able to quickly solve problems such as prime factorization and quantum chemistry calculations, so their development is being actively pursued around the world. The qubits used by quantum computers not only suffer from errors in which 0 and 1 are swapped, as occurs in classical computers, but also from unique errors in which the ratio of the "superposition" of 0 and 1 is shifted. Therefore, methods are being researched to suppress the errors (quantum errors) that occur in quantum computers.

[0003] In recent years, there has been much theoretical and experimental research into medium-scale quantum computers that are likely to be developed within the next few years to decades and that are subject to noise. Since such medium-scale quantum computers do not have enough qubits to perform quantum error correction, error suppression methods are typically applied, which suppress systematic errors at the expense of statistical errors by performing post-processing after the execution of a quantum circuit. While many error suppression methods have been proposed, a protocol called virtual distillation, which can suppress general probabilistic errors, has recently been proposed (e.g., Non-Patent Document 1, Non-Patent Document 2). [Prior art documents] [Non-patent literature]

[0004] [Non-Patent Document 1] Balint Koczor, "Exponential Error Suppression for Near-Term Quantum Devices", Phys. Rev. X 11, 031057,15 September 2021 [Non-patent document 2] William J. Huggins, Sam McArdle, Thomas E. O'Brien, Joonho Lee, Nicholas C. Rubin, Sergio Boixo, K. Birgitta Whaley, Ryan Babbush, and Jarrod R. McClean, "Virtual Distillation for Quantum Error Mitigation", Phys. Rev. X 11, 041036,19 November 2021 Summary of the Invention [Problem to be solved by the invention]

[0005] In conventional virtual distillation methods, the error probability increases while fluctuating randomly, and depending on the order of calculations, etc., it may not be possible to efficiently suppress errors in quantum computing.

[0006] The disclosed technology aims to achieve efficient error suppression in quantum computing. [Means for solving the problem]

[0007] The disclosed technology is a control device that includes an expected value calculation unit that uses a quantum circuit to alternately or simultaneously perform quantum calculations on the numerator and denominator of an equation in a virtual distillation method multiple times to calculate expected values ​​for multiple states of the numerator and denominator, an error suppression calculation unit that inputs the obtained multiple states into an error suppression circuit and obtains an output value, and a target value estimation unit that repeatedly calculates the expected value and obtains the output value to calculate a measurement value and estimates a target value in the quantum calculation based on the calculated measurement value. [Effects of the Invention]

[0008] The disclosed technology aims to achieve efficient error suppression in quantum computing. [Brief explanation of the drawings]

[0009] [Figure 1] FIG. 1 is a first diagram for explaining conventional quantum computing. [Figure 2] FIG. 10 is a second diagram for explaining conventional quantum computing. [Figure 3] 1 is a diagram for explaining quantum computation according to an embodiment of the present invention; [Figure 4] FIG. 1 is a diagram illustrating an example of a system configuration of a quantum computing system. [Figure 5] FIG. 2 is a diagram illustrating an example of the functional configuration of each device included in the quantum computing system. [Figure 6] 1 is a flowchart showing an example of the flow of a quantum computing process. [Figure 7] FIG. 2 illustrates an example of a hardware configuration of a computer. DETAILED DESCRIPTION OF THE INVENTION

[0010] Hereinafter, an embodiment of the present invention (the present embodiment) will be described with reference to the drawings. The embodiment described below is merely an example, and the embodiment to which the present invention is applied is not limited to the following embodiment.

[0011] The reference numbers and names of reference documents related to the reference techniques of this embodiment are listed at the end. In the following description, the numbers of related reference documents are indicated as "[1]" etc.

[0012] (Previous problems) First, the problems of the prior art will be described. In conventional quantum computing, discussions have focused on how to suppress quantum errors under the assumption that the noise model is completely known. However, due to fluctuations in coherence time frequently observed in experiments, it is not always possible to obtain complete information about the noise model. The influence of such unknown fluctuation noise cannot be ignored when performing quantum computing on an actual quantum computer. In this embodiment, an error suppression method capable of removing unknown fluctuation noise will be described. Below, we will show that the protocol according to this embodiment can suppress unknown fluctuation noise and perform highly accurate quantum computing.

[0013] Quantum computation using entangled resources has been shown to speed up exponentially with respect to the number of qubits [1].

[0014] Quantum computing is susceptible to decoherence. Quantum error correction and quantum error suppression have been proposed to address this issue. However, traditionally, the accuracy of computation has been discussed primarily from the perspective of statistical error, under the assumption that the noise model is well characterized.

[0015] The first diagram to explain conventional quantum computing is shown in Figure 1. Conventionally, computational accuracy has been discussed mainly from the perspective of statistical error, assuming that the noise model is completely understood.

[0016] In experiments, it is not always possible to obtain complete information for the noise model, usually due to fluctuations in coherence time [6-8]. Therefore, characterizing the noise becomes difficult and leads to systematic errors. In the following, such noise is also referred to as "fluctuation noise." Systematic errors usually arise from discrepancies between the real situation and the theoretical model used by experimenters to estimate target parameters.

[0017] Figure 2 is a second diagram illustrating conventional quantum computation. Conventionally, the noise model is unknown, resulting from the discrepancy between the actual situation and the theoretical model used by experimenters to estimate the target parameters.

[0018] Such intractable noise characterization leads to inaccurate theoretical models and induces systematic errors in estimations that are, in fact, fatal to quantum computing.

[0019] In practice, systematic errors are fatal to quantum computing because they cannot be reduced by increasing the number of samples and severely limit the improvement of accuracy [9]. Although systematic errors are usually present in experiments, no general approach to handle them has yet been proposed, although several studies have addressed specific scenarios [10-12].

[0020] The first problem with conventional protocols is that in realistic quantum computers, the error probability increases while fluctuating randomly. The specific order of calculating the numerator and denominator in equation (4) in the virtual distillation method has not been specified, and if one tries to simply perform one of the calculations first and then the other, the error probability value will be different, and errors may not be suppressed efficiently. This is a problem that exists in existing protocols.

[0021] The second problem is that existing protocols are designed to find the expectation value of a unitary matrix, but in reality, there are cases where we want to find the expectation value of a projection operator for many non-unitary qubits, and existing protocols do not address this case.

[0022] (Outline of this embodiment) This embodiment describes a quantum computing protocol incorporating quantum error mitigation (QEM), which exponentially suppresses systematic quantum errors and improves sensitivity scaling even in the presence of unknown fluctuating noise.

[0023] While traditional QEM methods are designed to suppress systematic errors in the expectation values ​​generated by short-term quantum algorithms [8,14-23], they are not well suited to suppressing systematic errors arising from unknown fluctuation noise. For example, probabilistic error cancellation cancels the effects of noise by inverting the noise map based on noise characterization [15,16]. Therefore, unknown fluctuation noise significantly degrades the performance of QEM. To address this issue, error-suppressing quantum computing, inspired by refinement-based QEM [13,24], removes fluctuation noise that varies from experiment to experiment. In numerical simulations, it has been used to suppress bias-inducing Markov and time-inhomogeneous noise, thereby achieving high accuracy.

[0024] (Quantum computing with systematic errors) We now describe the general theory of systematic errors in quantum computing. In a typical quantum computing setup, we prepare an initial state and apply a unitary operator characterized by a parameter ω to this state, obtaining a state ρ. We then perform a measurement of this state, which can be described by a projection operator P that produces a binary result. The measurement result m j ∈{-1,1} is obtained from the measurement probability shown in equation (1).

[0025] p=Tr[Pρ]=x+yω (1)

[0026] where x and y are scalars. Here, we assume that ω is small and ignore higher-order terms in ω. samp Repeat this process and the average value will be

[0027]

number

[0028] To estimate the parameter ω, we need to fit this experimental data to a theoretical model. If we have imperfect knowledge of ρ, the theoretical model we estimate will differ from the actual model. The probability based on such an inaccurate theoretical model can be expressed as Equation (2).

[0029] p e =Tr[Pρ e ]=x e +y e ω···(2)

[0030] where p e , x e and y e denote the estimated values ​​of p, x, and y, respectively. Referring to equation (2), ω e =(S N -x e ) / y e Like, S N Estimate ω from the estimated ω. e may differ from ω, which leads to systematic errors.

[0031] Due to systematic errors, it is necessary to consider the uncertainty in the estimation of the target value. The uncertainty in the estimation of ω is

[0032]

number

[0033]

number

[0034] where Var[p] is the variance of p, usually Var[p]=p(1-p) / N samp Here, since ω is small, (yy e ) 2 ω 2 -2(xx e )(yy e)ω term is ignored. Most of the previous theoretical studies have used the e We focus on the first term in equation (3) by assuming that N samp The second term in equation (3) is due to the statistical error, which decreases with increasing probability p ≠ p e Systematic error caused by incorrect estimation of xx e It comes from N samp Even if the increase in e remains, so σ 2 Therefore, in this embodiment, the systematic error xx is calculated by using QEM. e Focus on reducing

[0035] (Quantum computing with suppressed quantum errors) Next, we will provide an overview of quantum error-suppressed quantum computing according to this embodiment. Here, we will explain a general framework for quantum error-suppressed quantum computing, inspired by refinement-based QEM [13, 24]. We assume that the noise varies from experiment to experiment. That is, ρ i We assume distinct quantum states for the i-th measurement, denoted by . A key quantity in our framework is the quantum error-suppressed expectation value for the measured observable O for quantum computation, as follows:

[0036]

number

[0037]

number

[0038] FIG. 3 is a diagram for explaining quantum computation according to an embodiment of the present invention.

[0039]

number

[0040] (1) Create 2n copies of the initial state ρ(0). (2) Perform unitary operations on these 2n copies simultaneously (or nearly simultaneously) under noise for an interaction time t to obtain the ρ with fluctuation noise. i Take 2n copies of (t). (3)ρ i Divide these 2n copies of (t) in half. (4) Input n of the 2n density matrices into the refinement circuit, obtain the single-shot measurement results, and calculate the numerator of equation (4). (5) Input the remaining n density matrices in the same way as (4), set O = I, and calculate the denominator of equation (4)

[25] . (6) Repeat (1)-(5)

[0041]

number

[0042]

number

[0043] Then, calculate equation (4). (7) Instead of using p in equation (1), estimate ω using the expected value (value of equation (4)) with quantum errors suppressed. Note that N input to the refinement circuit samp The density matrix of the ensemble of states can be written as

[0044]

number

[0045] In this way, equation (4) can be obtained by simple calculation.

[0046] Here we show that even in the presence of fluctuating noise, our protocol is able to filter the noisy states and extract the dominant pure state. i The spectral decomposition of

[0047]

number

[0048]

number

[0049]

number

[26] . Nevertheless, as will be shown later in the numerical simulations, our method clearly eliminates systematic errors and reduces δ in practical scenarios. 2 This allows for a dramatic improvement in ω.

[0050] Next, a configuration for realizing the above-mentioned quantum computation will be described.

[0051] 4 is a diagram showing an example of the system configuration of a quantum computing system 1. The quantum computing system 1 includes a control device 10 and a quantum computer 20. The control device 10 and the quantum computer 20 are connected so as to be able to communicate with each other.

[0052] The control device 10 is an example of the classical computer described above, and measures the quantum state of the quantum computer 20, performs calculations based on the measurement results, controls the quantum state of the quantum computer 20, and so on.

[0053] The quantum computer 20 is an example of the quantum computer described above, and is a device that includes quantum bits that are controlled or calculated by the control device 10.

[0054] 5 is a diagram showing an example of the functional configuration of each device included in the quantum computing system. The control device 10 includes an expected value calculation unit 11, an error suppression calculation unit 12, and a target value estimation unit 13. The quantum computer 20 includes a quantum circuit 21 and an error suppression circuit 22.

[0055] Based on the instruction information input to the control device 10, the expected value calculation unit 11 uses the quantum circuit 21 to perform quantum calculations of the numerator and denominator of the above-mentioned equation (4) in the virtual distillation method alternately (for example, numerator → denominator → numerator → denominator → ...) or simultaneously n times, and calculates the expected values ​​of the n states of the numerator and denominator.

[0056] The error suppression calculation unit 12 inputs the n states obtained by the expectation calculation unit 11 to the error suppression circuit 22 to obtain an output value. At this time, the projection measurement operator onto the y-axis in the GHZ state executed by the error suppression circuit 22 when calculating the numerator of equation (4) is the unitary operator constructed by the general equation described above.

[0057] The target value estimation unit 13 estimates a target value in which quantum errors are suppressed based on the measurement values ​​repeatedly performed a sufficient number of times by the expected value calculation unit 11 and the error suppression calculation unit 12. The control device 10 may transmit information indicating the estimated target value to another device or display it on a screen or the like.

[0058] Next, the operation of the control device 10 will be described.

[0059] 6 is a flowchart showing an example of the flow of quantum computing processing. When the control device 10 acquires quantum computing instruction information, the quantum computing processing starts.

[0060] Based on the instruction information, the expected value calculation unit 11 alternately performs n quantum calculations of the numerator and denominator of the virtual distillation method (step S101). Specifically, based on the instruction information input to the control device 10, the expected value calculation unit 11 uses the quantum circuit 21 to alternately (for example, numerator → denominator → numerator → denominator → ...) or simultaneously perform n quantum calculations of the numerator and denominator of the above-mentioned equation (4) in the virtual distillation method, and calculates the expected values ​​of the n states of the numerator and denominator.

[0061] Next, the error suppression calculation unit 12 inputs the data indicating the obtained n states to the error suppression circuit 22 to obtain an error-suppressed output value (step S102).

[0062] Next, the control device 10 repeatedly executes steps S101 and S102 to calculate a measurement value O (step S103). The measurement value O is, for example, the value of equation (4). Then, the target value estimation unit 13 estimates the target value ω based on the measurement value O (step S104). The specific estimation method may be as described above.

[0063] The control device 10 is realized, for example, by the hardware configuration of a computer 500 shown in Fig. 7. The computer 500 shown in Fig. 7 has an input device 501, a display device 502, an external I / F 503, a communication I / F 504, a processor 505, and a memory device 506. Each of these pieces of hardware is connected to each other via a bus 507 so as to be able to communicate with each other.

[0064] The input device 501 is, for example, a keyboard, a mouse, a touch panel, etc. The display device 502 is, for example, a display, etc. Note that the computer 500 does not necessarily have to have at least one of the input device 501 and the display device 502.

[0065] The external I / F 503 is an interface with an external device such as a recording medium 503a. Examples of the recording medium 503a include a CD (Compact Disc), a DVD (Digital Versatile Disk), an SD memory card (Secure Digital memory card), and a USB (Universal Serial Bus) memory card.

[0066] The communication I / F 504 is an interface for performing data communication with other devices, equipment, systems, etc. The processor 505 is, for example, various types of arithmetic devices such as a CPU, etc. The memory device 506 is, for example, various types of storage devices such as an HDD, SSD, RAM (Random Access Memory), ROM (Read Only Memory), flash memory, etc.

[0067] The control device 10 can realize various processes described below by having the hardware configuration of the computer 500 shown in Fig. 7. Note that the hardware configuration of the computer 500 shown in Fig. 7 is an example, and the computer 500 may have other hardware configurations. For example, the computer 500 may have multiple processors 505 or multiple memory devices 506.

[0068] (Possible experimental realization) Finally, we demonstrate how to realize our scheme using superconducting flux qubits (FQs). FQs are promising candidates for quantum computing due to their long coherence time

[30] . [27-29] In quantum computing, FQs are artificial atoms, allowing for high degrees of freedom in circuit design and the construction of a set of universal gates with high fidelity and scalability [32, 33]. Therefore, FQs can be used to generate entanglement or implement refinement-based QEM. Here, high-fidelity quantum operations, such as controlled SWAP gates, are required.

[0069] (Conclusion and outlook) In this paper, we describe quantum error-suppressed quantum computing to reduce systematic errors resulting from incorrect estimation of unknown noise, typically caused by coherence time fluctuations. Purification-based QEM-inspired quantum error-suppressed quantum computing removes the fluctuation noise, which varies from experiment to experiment. Using this method, we can reduce the systematic error to δ 2 We demonstrate the recovery of accuracy by suppressing bias-inducing Markovian and time-inhomogeneous noise, which impairs the accuracy of ω. In particular, in the latter case, our method achieved high accuracy. Note that the number of copies of the input density matrix in our method can be reduced by using other methods related to refinement-based QEM [34-36], and coherent errors can be further reduced by combining our method with generalized subspace expansion

[37] . Our simulation results suggest that our method is useful for quantum computations that are subject to systematic errors typically caused by fluctuation noise, thus paving the way to achieving high accuracy in quantum computing.

[0070] According to this embodiment, it is possible to realize efficient error suppression in quantum computing. Specifically, in response to the first conventional problem, in the quantum computing according to this embodiment, when the error probability changes during the calculation, quantum computations corresponding to the calculation of the numerator and denominator of Equation (4) in the virtual distillation method are performed simultaneously or alternately. As a result, the errors incurred during the calculation of the numerator and denominator become approximately equal, and error suppression can be performed efficiently even for time-dependent error probabilities.

[0071] In addition, to address the second problem of the conventional technology, the quantum computing according to this embodiment shows a general formula for constructing a unitary operator from projection operators for many quantum bits, and an error suppression circuit is configured using the unitary operator constructed based on this general formula. This makes it possible to calculate the expected value of the projection operator for many quantum bits that are not actually unitary.

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[0073] (Addendum) The following additional clauses are disclosed in relation to the above-described embodiment. (Additional note 1) Memory and at least one processor coupled to the memory, The processor: Using a quantum circuit, quantum calculations of the numerator and denominator of the formula in the virtual distillation method are performed alternately or simultaneously multiple times to calculate expectation values ​​of multiple states of the numerator and denominator; inputting the obtained plurality of states into an error suppression circuit to obtain an output value; The calculation of the expected value and the acquisition of the output value are repeatedly performed to calculate a measurement value, and a target value in quantum computing is estimated based on the calculated measurement value. Control device. (Additional note 2) The processor obtains the output value using a unitary operator constructed from a projection operator for many quantum bits for the error suppression circuit during calculation of the molecule in the virtual distillation method. Item 1. The control device according to item 1. (Additional note 3) Using quantum circuits, we calculate the expectation values ​​of multiple states of the numerator and denominator of the formula in the virtual distillation method, The obtained plurality of states are input to an error suppression circuit, and an output value is obtained using a unitary operator constructed from a projection operator for many quantum bits for the error suppression circuit during calculation of the molecule in the virtual distillation method; The calculation of the expected value and the acquisition of the output value are repeatedly performed to calculate a measurement value, and a target value in quantum computing is estimated based on the calculated measurement value. Control device. (Additional note 4) A computer-implemented control method comprising: Using a quantum circuit, quantum calculations of the numerator and denominator of the formula in the virtual distillation method are performed alternately or simultaneously multiple times to calculate expectation values ​​of multiple states of the numerator and denominator; inputting the obtained plurality of states into an error suppression circuit to obtain an output value; The calculation of the expected value and the acquisition of the output value are repeatedly performed to calculate a measurement value, and a target value in quantum computing is estimated based on the calculated measurement value. Control method. (Additional note 5) A computer-implemented control method comprising: Using quantum circuits, we calculate the expectation values ​​of multiple states of the numerator and denominator of the formula in the virtual distillation method, The obtained plurality of states are input to an error suppression circuit, and an output value is obtained using a unitary operator constructed from a projection operator for many quantum bits for the error suppression circuit during calculation of the molecule in the virtual distillation method; The calculation of the expected value and the acquisition of the output value are repeatedly performed to calculate a measurement value, and a target value in quantum computing is estimated based on the calculated measurement value. Control method. (Additional note 6) A non-transitory storage medium storing a program for causing a computer to function as each part of the control device described in appended claim 1 or 2. (Additional note 7) A non-transitory storage medium storing a program for causing a computer to function as each part of the control device described in appended claim 3.

[0074] Although the present embodiment has been described above, the present invention is not limited to such a specific embodiment, and various modifications and changes are possible within the scope of the gist of the present invention described in the claims. [Explanation of symbols]

[0075] 1. Quantum Computing System 10 Control device 11 Expected value calculation section 12 Error suppression calculation unit 13 Target value estimation section 20 Quantum computer 21 Quantum circuit 22 Error suppression circuit 500 computers 501 Input Device 502 Display device 503 External I / F 503a Recording media 504 Communication I / F 505 processor 506 Memory Device 507 Bus

Claims

1. An expectation value calculation unit that uses a quantum circuit to alternately or simultaneously perform quantum calculations on the numerator and denominator of the formula in the virtual distillation method multiple times to calculate expectation values ​​of multiple states of the numerator and denominator; an error suppression calculation unit that inputs the obtained plurality of states into an error suppression circuit and obtains an output value; a target value estimation unit that calculates a measurement value by repeatedly calculating the expected value and obtaining the output value, and estimates a target value in quantum computing based on the calculated measurement value; Control device.

2. The error suppression calculation unit obtains the output value using a unitary operator constructed from a projection operator for many quantum bits for the error suppression circuit during calculation of the molecule in the virtual distillation method. The control device according to claim 1 .

3. an expectation calculation unit that calculates expectation values ​​of a plurality of states of a numerator and a denominator of an equation in the virtual distillation method using a quantum circuit; An error suppression calculation unit that inputs the obtained plurality of states into an error suppression circuit and obtains an output value using a unitary operator constructed from a projection operator for many quantum bits for the error suppression circuit when calculating the molecule in the virtual distillation method; a target value estimation unit that calculates a measurement value by repeatedly calculating the expected value and obtaining the output value, and estimates a target value in quantum computing based on the calculated measurement value; Control device.

4. A computer-implemented control method comprising: Using a quantum circuit, quantum calculations of the numerator and denominator of the formula in the virtual distillation method are performed alternately or simultaneously multiple times to calculate expectation values ​​of multiple states of the numerator and denominator; inputting the obtained plurality of states into an error suppression circuit to obtain an output value; The method includes a step of repeatedly calculating the expected value and obtaining the output value to calculate a measurement value, and estimating a target value in quantum computing based on the calculated measurement value. Control method.

5. A computer-implemented control method comprising: Calculating expectation values ​​of a plurality of states of a numerator and a denominator of an equation in the virtual distillation method using a quantum circuit; Inputting the obtained plurality of states into an error suppression circuit, and obtaining an output value using a unitary operator constructed from a projection operator for many quantum bits for the error suppression circuit during calculation of the molecule in the virtual distillation method; The method includes a step of repeatedly calculating the expected value and obtaining the output value to calculate a measurement value, and estimating a target value in quantum computing based on the calculated measurement value. Control method.

6. A program for causing a computer to function as each unit in the control device according to claim 1 or 2.

7. A program for causing a computer to function as each unit in the control device according to claim 3.

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