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  • Letter
  • Open Access

Quadratic acceleration of multistep probabilistic algorithms for state preparation

Hirofumi Nishi1,2,*, Taichi Kosugi1,2, Yusuke Nishiya1,2, and Yu-ichiro Matsushita1,2,3

  • 1Laboratory for Materials and Structures, Institute of Innovative Research, Tokyo Institute of Technology, Yokohama 226-8503, Japan
  • 2Quemix Incorporated, Taiyo Life Nihombashi Building, 2-11-2, Nihombashi Chuo-ku, Tokyo 103-0027, Japan
  • 3Quantum Material and Applications Research Center, National Institutes for Quantum Science and Technology, 2-12-1, Ookayama, Meguro-ku, Tokyo 152-8552, Japan

  • *nishi.h.ac@m.titech.ac.jp
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Phys. Rev. Research 6, L022041 – Published 13 May, 2024

DOI: https://doi.org/10.1103/PhysRevResearch.6.L022041

Abstract

Quantum state preparation is a fundamental building block for various problems on a quantum computer. A nonunitary operator is typically designed to decay unwanted states contained in an initial state using ancilla qubits and a probabilistically action. In this Letter, we clarify that this probabilistic nature is a drag for quantum advantages: The probabilistic algorithms do not accelerate the computational process compared to classical ones. Combining quantum amplitude amplification (QAA) with multistep probabilistic algorithms is proposed to address this drawback, achieving quadratic acceleration and quantum advantages. We also find that the multistep probabilistic method with QAA exhibits advantages over quantum phase estimation in terms of infidelity. We also demonstrate it to confirm the quadratic acceleration, using a probabilistic imaginary-time evolution method as an example.

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Phys. Rev. Research 6, L022041– Published 13 May, 2024
  • Received 21 August 2023
  • Accepted 16 January 2024
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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