TY - JOUR

T1 - Noisy quantum amplitude estimation without noise estimation

AU - Tanaka, Tomoki

AU - Uno, Shumpei

AU - Onodera, Tamiya

AU - Yamamoto, Naoki

AU - Suzuki, Yohichi

N1 - Funding Information:
We thank Jun Suzuki for helpful discussions. This work was supported by the MEXT Quantum Leap Flagship program through Grants No. JPMXS0118067285 and No. JPMXS0120319794. 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:
© 2022 American Physical Society.

PY - 2022/1

Y1 - 2022/1

N2 - Many quantum algorithms contain an important subroutine - the quantum amplitude estimation. As the name implies, this is essentially the parameter estimation problem and thus can be handled via the established statistical estimation theory. However, this problem has an intrinsic difficulty that the system, i.e., the real quantum computing device, inevitably introduces unknown noise; the probability distribution model then has to incorporate many nuisance noise parameters, resulting that the construction of an optimal estimator becomes inefficient and difficult. For this problem we apply the theory of nuisance parameters (more specifically, the parameter orthogonalization method) to precisely compute the maximum likelihood estimator for only the target amplitude parameter by removing the other nuisance noise parameters. That is, we can estimate the amplitude parameter without estimating the noise parameters. We validate the parameter orthogonalization method in a numerical simulation and study the performance of the estimator in the experiment using a real superconducting quantum device.

AB - Many quantum algorithms contain an important subroutine - the quantum amplitude estimation. As the name implies, this is essentially the parameter estimation problem and thus can be handled via the established statistical estimation theory. However, this problem has an intrinsic difficulty that the system, i.e., the real quantum computing device, inevitably introduces unknown noise; the probability distribution model then has to incorporate many nuisance noise parameters, resulting that the construction of an optimal estimator becomes inefficient and difficult. For this problem we apply the theory of nuisance parameters (more specifically, the parameter orthogonalization method) to precisely compute the maximum likelihood estimator for only the target amplitude parameter by removing the other nuisance noise parameters. That is, we can estimate the amplitude parameter without estimating the noise parameters. We validate the parameter orthogonalization method in a numerical simulation and study the performance of the estimator in the experiment using a real superconducting quantum device.

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U2 - 10.1103/PhysRevA.105.012411

DO - 10.1103/PhysRevA.105.012411

M3 - Article

AN - SCOPUS:85122559439

VL - 105

JO - Physical Review A

JF - Physical Review A

SN - 2469-9926

IS - 1

M1 - 012411

ER -