TY - JOUR

T1 - Amplitude estimation via maximum likelihood on noisy quantum computer

AU - Tanaka, Tomoki

AU - Suzuki, Yohichi

AU - Uno, Shumpei

AU - Raymond, Rudy

AU - Onodera, Tamiya

AU - Yamamoto, Naoki

N1 - Funding Information:
This work was supported by MEXT Quantum Leap Flagship Program Grant Numbers JPMXS0118067285 and JPMXSO120319794. The authors acknowledge helpful discussions with Takahiko Satoh for designing the quantum circuit, and thank Naoki Kanazawa for useful comments about IBM Quantum Systems. The results presented in this paper were obtained in part using an IBM Quantum quantum computing system as part of the IBM Quantum Network. The views expressed are those of the authors and do not reflect the official policy or position of IBM or the IBM Quantum team.
Funding Information:
This work was supported by MEXT Quantum Leap Flagship Program Grant Numbers JPMXS0118067285 and JPMXSO120319794. The authors acknowledge helpful discussions with Takahiko Satoh for designing the quantum circuit, and thank Naoki Kanazawa for useful comments about IBM Quantum Systems. The results presented in this paper were obtained in part using an IBM Quantum quantum computing system as part of the IBM Quantum Network. The views expressed are those of the authors and do not reflect the official policy or position of IBM or the IBM Quantum team.
Publisher Copyright:
© 2021, The Author(s).

PY - 2021/9

Y1 - 2021/9

N2 - Recently we find several candidates of quantum algorithms that may be implementable in near-term devices for estimating the amplitude of a given quantum state, which is a core subroutine in various computing tasks such as the Monte Carlo methods. One of those algorithms is based on the maximum likelihood estimate with parallelized quantum circuits. In this paper, we extend this method so that it incorporates the realistic noise effect, and then give an experimental demonstration on a superconducting IBM Quantum device. The maximum likelihood estimator is constructed based on the model assuming the depolarization noise. We then formulate the problem as a two-parameters estimation problem with respect to the target amplitude parameter and the noise parameter. In particular we show that there exist anomalous target values, where the Fisher information matrix becomes degenerate and consequently the estimation error cannot be improved even by increasing the number of amplitude amplifications. The experimental demonstration shows that the proposed maximum likelihood estimator achieves quantum speedup in the number of queries, though the estimation error saturates due to the noise. This saturated value of estimation error is consistent to the theory, which implies the validity of the depolarization noise model and thereby enables us to predict the basic requirement on the hardware components (particularly the gate error) in quantum computers to realize the quantum speedup in the amplitude estimation task.

AB - Recently we find several candidates of quantum algorithms that may be implementable in near-term devices for estimating the amplitude of a given quantum state, which is a core subroutine in various computing tasks such as the Monte Carlo methods. One of those algorithms is based on the maximum likelihood estimate with parallelized quantum circuits. In this paper, we extend this method so that it incorporates the realistic noise effect, and then give an experimental demonstration on a superconducting IBM Quantum device. The maximum likelihood estimator is constructed based on the model assuming the depolarization noise. We then formulate the problem as a two-parameters estimation problem with respect to the target amplitude parameter and the noise parameter. In particular we show that there exist anomalous target values, where the Fisher information matrix becomes degenerate and consequently the estimation error cannot be improved even by increasing the number of amplitude amplifications. The experimental demonstration shows that the proposed maximum likelihood estimator achieves quantum speedup in the number of queries, though the estimation error saturates due to the noise. This saturated value of estimation error is consistent to the theory, which implies the validity of the depolarization noise model and thereby enables us to predict the basic requirement on the hardware components (particularly the gate error) in quantum computers to realize the quantum speedup in the amplitude estimation task.

KW - Amplitude estimation

KW - Depolarizing noise

KW - IBM quantum systems

KW - Maximum likelihood estimation

KW - Quantum computing

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U2 - 10.1007/s11128-021-03215-9

DO - 10.1007/s11128-021-03215-9

M3 - Article

AN - SCOPUS:85114270458

SN - 1570-0755

VL - 20

JO - Quantum Information Processing

JF - Quantum Information Processing

IS - 9

M1 - 293

ER -