• Open Access

Calculation of the Green's function on near-term quantum computers

Suguru Endo, Iori Kurata, and Yuya O. Nakagawa
Phys. Rev. Research 2, 033281 – Published 20 August 2020

Abstract

The Green's function plays a crucial role when studying the nature of quantum many-body systems, especially strongly correlated systems. Although the development of quantum computers in the near future may enable us to compute energy spectra of classically intractable systems, methods to simulate the Green's function with near-term quantum algorithms have not been proposed yet. Here, we propose two methods to calculate the Green's function of a given Hamiltonian on near-term quantum computers. The first one makes use of a variational dynamics simulation of quantum systems and computes the dynamics of the Green's function in real time directly. The second one utilizes the Lehmann representation of the Green's function and a method which calculates excited states of the Hamiltonian. Both methods require shallow quantum circuits and are compatible with near-term quantum computers. We numerically simulated the Green's function of the Fermi-Hubbard model and demonstrated the validity of our proposals.

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  • Received 29 October 2019
  • Accepted 8 July 2020

DOI:https://doi.org/10.1103/PhysRevResearch.2.033281

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.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & Technology

Authors & Affiliations

Suguru Endo1,*, Iori Kurata2,†, and Yuya O. Nakagawa1,‡

  • 1QunaSys Inc., Aqua Hakusan Building 9F, 1-13-7 Hakusan, Bunkyo, Tokyo 113-0001, Japan
  • 2Department of Applied Physics, The University of Tokyo, Tokyo 113-8656, Japan

  • *endo@qunasys.com
  • iori-kurata636@g.ecc.u-tokyo.ac.jp
  • nakagawa@qunasys.com

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Vol. 2, Iss. 3 — August - October 2020

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