JP7768421B2 - Control device, control method, and program - Google Patents

Description

Article 30, Paragraph 2 of the Patent Act applies. Published on December 3, 2021 at https://arxiv.org/abs/2112.01850v1, https://arxiv.org/pdf/2112.01850v1. Published on December 11, 2021 at https://arxiv.org/abs/2112.01850v2, https://arxiv.org/pdf/2112.01850v2. Published on March 22, 2022 at https://arxiv.org/abs/2112.01850v3, https://arxiv. Published at https://arxiv.org/abs/2112.01850v3 Published at https://arxiv.org/abs/2112.01850v4, https://arxiv.org/pdf/2112.01850v4 on July 13, 2022

The present invention relates to a control device, a control method, and a program.

Quantum computers are a technology that performs calculations by utilizing the principle of superposition in quantum mechanics. They are expected to be able to quickly solve problems such as prime factorization and quantum chemistry calculations, and their development is being actively pursued around the world. The qubits used by quantum computers are prone to errors where 0s and 1s are swapped, as in classical computers, but also to unique errors where the ratio of 0s and 1s in the "superposition" is shifted. Therefore, methods are being researched to suppress the errors (quantum errors) that occur in quantum computers.

In recent years, there has been active theoretical and experimental research into mid-scale quantum computers that are noisy and likely to be developed within the next few years to decades. Because such mid-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. Many error suppression methods have been proposed, but in recent years, a protocol called virtual distillation has been proposed that can suppress general probabilistic errors (e.g., Non-Patent Document 1, Non-Patent Document 2).

Balint Koczor, "Exponential Error Suppression for Near-Term Quantum Devices", Phys. Rev. X 11, 031057,15 September 2021 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

With 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.

The disclosed technology aims to achieve efficient error suppression in quantum computing.

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 the 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.

The disclosed technology aims to achieve efficient error suppression in quantum computing.

FIG. 1 is a first diagram for explaining conventional quantum computing. FIG. 10 is a second diagram for explaining conventional quantum computing. 1 is a diagram for explaining quantum computation according to an embodiment of the present invention; FIG. 1 is a diagram illustrating an example of a system configuration of a quantum computing system. FIG. 2 is a diagram illustrating an example of the functional configuration of each device included in the quantum computing system. 1 is a flowchart showing an example of the flow of a quantum computing process. FIG. 2 illustrates an example of a hardware configuration of a computer.

The following describes an embodiment of the present invention (the present embodiment) with reference to the drawings. The embodiment described below is merely an example, and the embodiments to which the present invention can be applied are not limited to the following embodiment.

Note that the reference numbers and names of reference documents related to the reference technologies of this embodiment are listed at the end. In the following explanation, the numbers of related reference documents are indicated as "[1]" etc.

(Conventional 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.

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

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

Figure 1 is the first diagram used to explain conventional quantum computing. Traditionally, computational accuracy has been discussed primarily from the perspective of statistical error, assuming that the noise model is perfectly understood.

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.

Figure 2 is a second diagram to explain conventional quantum computing. Traditionally, the noise model is unknown, resulting from the discrepancy between the actual situation and the theoretical model used by experimenters to estimate target parameters.

Such intractable noise characterization leads to inaccurate theoretical models and induces systematic errors in estimation. In fact, systematic errors are fatal to quantum computing.

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, some studies have addressed specific scenarios, but no general approach to dealing with them has yet been proposed [10-12].

The first problem with conventional protocols is that in realistic quantum computers, the error probability increases while fluctuating randomly. The specific order in which the numerator and denominator of equation (4) are calculated in the virtual distillation method is not specified, and if one simply performs one of the calculations before the remaining calculation, the error probability value will be different, and errors may not be efficiently suppressed. This is a problem that exists in existing protocols.

The second problem with existing protocols is that, while they calculate the expectation value of a unitary matrix, in reality there are cases where we want to calculate the expectation value of a projection operator for many non-unitary quantum bits. However, existing protocols do not address this case.

(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.

While conventional 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.

(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 to obtain 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).

p=Tr[Pρ]=x+yω...(1)

Here, x and y are scalars. Here, we assume that ω is small and ignore higher-order terms of ω. When the measurement is repeated N _samp times, the average value is

is obtained.

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

p _e =Tr[Pρ _e ]=x _e +y _e ω...(2)

where p _e , x _{e ,} and y _e are the estimated values of p, x, and y, respectively. Referring to equation (2), we estimate ω from S _N as ω _e = (S _N - x _e )/y _e . The estimated ω _e may differ from ω, which leads to a systematic error.

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

where the brackets indicate the ensemble average and is calculated as follows:

Here, Var[p] is the variance of p, and typically Var[p] = p(1-p)/N _samp . Here, the term (y-y _e ) ² ω ² -2(x-x _e )(y-y _e )ω is ignored because ω is small. Most previous theoretical studies focus on the first term in equation (3) by assuming ρ = ρ _e . This term originates from statistical error, which decreases as N _samp increases. The second term in equation (3) originates from the systematic error x-x _e caused by an incorrect estimation of the probability p ≠ p _e . Since x-x _e remains even when N _samp increases, it impairs the accuracy of σ ² ω. Therefore, in this embodiment, we focus on reducing the systematic error x-x _e using QEM.

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

where:

is the unnormalized refined density matrix and _Nsamp is the number of measurements. The filtering effect on fluctuation noise is discussed below.

Figure 3 is a diagram for explaining quantum computation according to an embodiment of the present invention.

FIG. 1 is a schematic diagram of the protocol for calculating σ. The procedure is as follows:

(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 the interaction time t to obtain 2n copies of ρ _i (t) with fluctuation noise. (3) Divide these 2n copies of ρ _i (t) in half. (4) Input n of the 2n density matrices into the refinement circuit, obtain a single-shot measurement result, 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)

and

Calculate the following.

Then, calculate equation (4). (7) Instead of using p in equation (1), estimate ω using the expectation value with suppressed quantum errors (the value of equation (4)). Note that the density matrix of the ensemble of N _samp states input to the refinement circuit can be written as follows:

In this way, equation (4) can be obtained through simple calculations.

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. We define the spectral decomposition of _{ρi as}

This can be expressed as:

Here, p _max = max _ik p ⁽ⁱ⁾ _k ,

is the corresponding eigenstate. Therefore, the contribution of states other than the eigenstate is exponentially suppressed as the copy number n increases. This means that our method can eliminate fluctuation noise. In general, the dominant eigenvector of a mixed state is distorted by noise and differs from the ideal quantum state. This is called coherent mismatch [26]. Nevertheless, as we will show later in the numerical simulations, our method clearly eliminates systematic errors and enables a dramatic improvement of δ ² ω in practical scenarios.

Next, we will explain the configuration that realizes the above-mentioned quantum computing.

Figure 4 is a diagram showing an example of the system configuration of a quantum computing system. The quantum computing system 1 comprises a control device 10 and a quantum computer 20. The control device 10 and the quantum computer 20 are connected so that they can communicate with each other.

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, etc.

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

Figure 5 is a diagram showing an example of the functional configuration of each device included in a 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.

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.

The error suppression calculation unit 12 inputs the n states obtained by the expectation calculation unit 11 into the error suppression circuit 22 and obtains an output value. In this case, 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 formula described above.

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, etc.

Next, the operation of the control device 10 will be explained.

Figure 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 begins.

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 (e.g., 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.

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

Next, the control device 10 repeatedly executes steps S101 and S102 to calculate the 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.

The control device 10 is realized, for example, by the hardware configuration of a computer 500 shown in Figure 7. The computer 500 shown in Figure 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 so that they can communicate with each other via a bus 507.

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.

The external I/F 503 is an interface with external devices such as a recording medium 503a. Examples of recording media 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.

The communication I/F 504 is an interface for data communication with other devices, equipment, systems, etc. The processor 505 is, for example, a CPU or other computing device. The memory device 506 is, for example, a HDD, SSD, RAM (Random Access Memory), ROM (Read Only Memory), flash memory, or other storage device.

The control device 10 has the hardware configuration of the computer 500 shown in Figure 7, which enables it to perform the various processes described below. Note that the hardware configuration of the computer 500 shown in Figure 7 is only 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.

(Possible experimental realization)
Finally, we demonstrate how to implement 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.

(Conclusion and outlook)
In this paper, we describe quantum error-suppressed quantum computation to reduce systematic errors resulting from incorrect estimation of unknown noise, typically caused by coherence time fluctuations. Inspired by refinement-based QEM, quantum error-suppressed quantum computation eliminates fluctuation noise, which varies from experiment to experiment. Using this method, we demonstrate the recovery of accuracy by suppressing bias-inducing Markovian and time-inhomogeneous noise, where systematic errors impair the accuracy of δ ² 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]. 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.

According to this embodiment, it is possible to achieve efficient error suppression in quantum computing. Specifically, in response to the first conventional problem, quantum computing according to this embodiment performs quantum computations corresponding to the calculation of the numerator and denominator of equation (4) in the virtual distillation method simultaneously or alternately when the error probability changes during the calculation. This makes the errors incurred by both the numerator and denominator when calculating them approximately equal, enabling efficient error suppression even for time-dependent error probabilities.

In addition, to address the second problem of the conventional technology, the quantum computing of this embodiment shows a general formula for constructing a unitary operator from projection operators for many quantum bits, and an error suppression circuit is constructed 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.

(References)
[1] PWShor, SIAM Journal on Computing, vo1.26, no.5, pp.1484-1509, 1997.
[2] W. Wasilewski, K. Jensen, H. Krauter, JJ Renema, MV Balabas, and ES Polzik, Phys. Rev. Lett. 104, 133601 (2010).
[3] M. Mehboudi, A. Sanpera, and LA Correa, J. Phys. A: Math. Theor. 52, 303001 (2019).
[4] KV Hovhannisyan, MR Jrgensen, GT Landi, AM Alhambra, JB Brask, and M. Perarnau-Llobet, PRX Quantum 2, 020322 (2021).
[5] M. Beau and A. del Campo, Phys. Rev. Lett. 119, 010403 (2017).
[6] F. Yan, S. Gustavsson, A. Kamal, J. Birenbaum, AP Sears, D. Hover, TJ Gudmundsen, D. Rosenberg, G. Samach, S. Weber, JL Yoder, TP Orlando, J. Clarke, AJ Kerman, and WD Oliver, Nat. Commun. 7, 12964 (2016).
[7] LV Abdurakhimov, I. Mahboob, H. Toida, K. Kakuyanagi, and S. Saito, Appl. Phys. Lett. 115, 262601 (2019).
[8] A. Kandala, K. Temme, AD Corcoles, A. Mezzacapo, JM Chow, and JM Gambetta, Nature 567, 491 (2019).
[9] T. Wolf, P. Neumann, K. Nakamura, H. Sumiya, T. Ohshima, J. Isoya, and J. Wrachtrup, Phys. Rev. X 5, 041001 (2015).
[10] G. Strubi and C. Bruder, Phys. Rev. Lett. 110, 083605 (2013).
[11] S. Pang, JRG Alonso, TA Brun, and AN Jordan, Phys. Rev. A 94, 012329 (2016).
[12] J. Martnez-Rincon, W.-T. Liu, GI Viza, and JC Howell, Phys. Rev. Lett. 116, 100803 (2016).
[13] B. Koczor, Phys. Rev. X 11, 031057 (2021).
[14] S. Endo, Z. Cai, SC Benjamin, and X. Yuan, J. Phys. Soc. Jpn. 90, 032001 (2021).
[15] K. Temme, S. Bravyi, and JM Gambetta, Phys. Rev. Lett. 119, 180509 (2017).
[16] S. Endo, SC Benjamin, and Y. Li, Phys. Rev. X 8, 031027 (2018).
[17] Y. Li and SC Benjamin, Phys. Rev. X 7, 021050 (2017).
[18] C. Song, J. Cui, H. Wang, J. Hao, H. Feng, and Y. Li, Sci. Adv. 5, eaaw5686 (2019).
[19] S. Zhang, Y. Lu, K. Zhang, W. Chen, Y. Li, J.-N. Zhang, and K. Kim, Nat. Commun. 11, 587 (2020).
[20] S. McArdle, X. Yuan, and S. Benjamin, Phys. Rev. Lett. 122, 180501 (2019).
[21] X. Bonet-Monroig, R. Sagastizabal, M. Singh, and TE O'Brien, Phys. Rev. A 98, 062339 (2018).
[22] J. Sun, X. Yuan, T. Tsunoda, V. Vedral, SC Benjamin, and S. Endo, Phys. Rev. Applied 15, 034026 (2021).
[23] R. LaRose, A. Mari, S. Kaiser, PJ Karalekas, AA Alves, P. Czarnik, ME Mandouh, MH Gordon, Y. Hindy, A. Robertson, P. Thakre, N. Shammah, and WJ Zeng, arXiv preprint arXiv:2009.04417 (2020).
[24] WJ Huggins, S. McArdle, TE O'Brien, J. Lee, NC Rubin, S. Boixo, KB Whaley, R. Babbush, and JR McClean, Phys. Rev. X 11, 041036 (2021).
[25] Procedures (4) and (5) can be done in any order.
[26] B. Koczor, arXiv preprint arXiv:2104.00608 (2021).
[27] I. Chiorescu, Y. Nakamura, CM Harmans, and J. Mooij, Science 299, 1869 (2003).
[28] A. Lupascu, CJM Verwijs, RN Schouten, CJPM Harmans, and JE Mooij, Phys. Rev. Lett. 93, 177006 (2004).
[29] JH Plantenberg, PC de Groot, CJPM Harmans, and JE Mooij, Nature 447, 836 (2007).
[30] J. Bylander, S. Gustavsson, F. Yan, F. Yoshihara, K. Harrabi, G. Fitch, DG Cory, Y. Nakamura, J.-S. Tsai, and WD Oliver, Nat. Phys. 7, 565 (2011).
[31] M. Bal, C. Deng, J.-L. Orgiazzi, FR Ong, and A. Lupascu, Nat. Commun. 3, 1324 (2012).
[32] J. Clarke and FK Wilhelm, Nature 453, 1031 (2008).
[33] Y. Makhlin, G. Schon, and A. Shnirman, Rev. Mod. Phys. 73, 357 (2001).
[34] P. Czarnik, A. Arrasmith, L. Cincio, and PJ Coles, arXiv preprint arXiv:2102.06056 (2021).
[35] M. Huo and Y. Li, arXiv preprint arXiv:2105.01239 (2021).
[36] Z. Cai, arXiv preprint arXiv:2107.07279 (2021).
[37] N. Yoshioka, H. Hakoshima, Y. Matsuzaki, Y. Tokunaga, Y. Suzuki, and S. Endo, arXiv preprint arXiv:2107.02611 (2021).

(Additional Note)
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.
The control device according to claim 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 unit in the control device according to claim 1 or 2.
(Supplementary Note 7)
A non-transitory storage medium storing a program for causing a computer to function as each unit in the control device described in appended claim 3.

The present embodiment has been described above, but the present invention is not limited to such a specific embodiment, and various modifications and variations are possible within the scope of the gist of the present invention as described in the claims.

1 Quantum computing system 10 Control device 11 Expected value calculation unit 12 Error suppression calculation unit 13 Target value estimation unit 20 Quantum computer 21 Quantum circuit 22 Error suppression circuit 500 Computer 501 Input device 502 Display device 503 External I/F
503a Recording medium 504 Communication I/F
505 Processor 506 Memory device 507 Bus

Claims (7)

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. 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 . 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. 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. 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. A program for causing a computer to function as each part of the control device described in claim 1 or 2. A program for causing a computer to function as each part of the control device described in claim 3.