Amplitude estimation via maximum likelihood on noisy quantum computer

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

研究成果: Article査読

13 被引用数 (Scopus)


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.

ジャーナルQuantum Information Processing
出版ステータスPublished - 2021 9月

ASJC Scopus subject areas

  • 電子材料、光学材料、および磁性材料
  • 統計物理学および非線形物理学
  • 理論的コンピュータサイエンス
  • 信号処理
  • モデリングとシミュレーション
  • 電子工学および電気工学


「Amplitude estimation via maximum likelihood on noisy quantum computer」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。