Parent Hamiltonian as a benchmark problem for variational quantum eigensolvers

Fumiyoshi Kobayashi, Kosuke Mitarai, and Keisuke Fujii
Phys. Rev. A 105, 052415 – Published 10 May 2022

Abstract

The variational quantum eigensolver (VQE), which has attracted attention as a promising application of noisy intermediate-scale quantum devices, finds a ground state of a given Hamiltonian by variationally optimizing the parameters of quantum circuits called Ansätze. Since the difficulty of the optimization depends on the complexity of the problem Hamiltonian and the structure of the Ansätze, it has been difficult to systematically analyze the performance of optimizers for the VQE. To resolve this problem, we propose a technique to construct a benchmark problem whose ground state is guaranteed to be achievable with a given Ansatz by using the idea of a parent Hamiltonian of a low-depth parametrized quantum circuit. We compare the convergence of several optimizers by varying the distance of the initial parameters from the solution and find that the converged energies showed a thresholdlike behavior depending on the distance. This work provides a systematic way to analyze optimizers for the VQE and contribute to the design of the Ansatz and its initial parameters.

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  • Received 12 October 2021
  • Revised 22 March 2022
  • Accepted 21 April 2022

DOI:https://doi.org/10.1103/PhysRevA.105.052415

©2022 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & Technology

Authors & Affiliations

Fumiyoshi Kobayashi1,*, Kosuke Mitarai1,2,3, and Keisuke Fujii1,2,4

  • 1Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyama, Toyonaka, Osaka 560-8531, Japan
  • 2Center for Quantum Information and Quantum Biology, Institute for Open and Transdisciplinary Research Initiatives, Osaka University, 1-2 Machikaneyama, Toyonaka, Osaka 560-0043, Japan
  • 3JST, PRESTO, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012, Japan
  • 4Center for Emergent Matter Science, RIKEN, Wako Saitama 351-0198, Japan

  • *fkobayashi@qi.mp.es.osaka-u.ac.jp

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Issue

Vol. 105, Iss. 5 — May 2022

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