Amplitude estimation without phase estimation

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

Research output: Contribution to journalArticle

Abstract

This paper focuses on the quantum amplitude estimation algorithm, which is a core subroutine in quantum computation for various applications. The conventional approach for amplitude estimation is to use the phase estimation algorithm, which consists of many controlled amplification operations followed by a quantum Fourier transform. However, the whole procedure is hard to implement with current and near-term quantum computers. In this paper, we propose a quantum amplitude estimation algorithm without the use of expensive controlled operations; the key idea is to utilize the maximum likelihood estimation based on the combined measurement data produced from quantum circuits with different numbers of amplitude amplification operations. Numerical simulations we conducted demonstrate that our algorithm asymptotically achieves nearly the optimal quantum speedup with a reasonable circuit length.

Original languageEnglish
Article number75
JournalQuantum Information Processing
Volume19
Issue number2
DOIs
Publication statusPublished - 2020 Feb 1

Keywords

  • Classical post-processing
  • Cramér–Rao bound
  • Maximum likelihood estimation
  • Quantum amplitude estimation

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Statistical and Nonlinear Physics
  • Theoretical Computer Science
  • Signal Processing
  • Modelling and Simulation
  • Electrical and Electronic Engineering

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