# Noisy quantum amplitude estimation without noise estimation

Tomoki Tanaka, Shumpei Uno, Tamiya Onodera, Naoki Yamamoto, Yohichi Suzuki

## 抄録

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.

本文言語 English 012411 Physical Review A 105 1 https://doi.org/10.1103/PhysRevA.105.012411 Published - 2022 1月

• 原子分子物理学および光学

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