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Probabilistic imaginary-time evolution in state-vector-based and shot-based simulations and on quantum devices

Satoshi Ejima1,2,*, Kazuhiro Seki3,†, Benedikt Fauseweh4,5,‡, and Seiji Yunoki2,3,6,7,§

  • 1Institute of Software Technology, German Aerospace Center (DLR), 22529 Hamburg, Germany
  • 2Computational Condensed Matter Physics Laboratory, RIKEN Pioneering Research Institute (PRI), Saitama 351-0198, Japan
  • 3Quantum Computational Science Research Team, RIKEN Center for Quantum Computing (RQC), Saitama 351-0198, Japan
  • 4Institute of Software Technology, German Aerospace Center (DLR), 51147 Cologne, Germany
  • 5Department of Physics, TU Dortmund University, Otto-Hahn-Straße 4, 44227 Dortmund, Germany
  • 6Computational Quantum Matter Research Team, RIKEN Center for Emergent Matter Science (CEMS), Wako, Saitama 351-0198, Japan
  • 7Computational Materials Science Research Team, RIKEN Center for Computational Science (R-CCS), Kobe, Hyogo 650-0047, Japan

  • *Contact author: satoshi.ejima@dlr.de
  • †Contact author: kazuhiro.seki@riken.jp
  • ‡Contact author: Benedikt.Fauseweh@dlr.de
  • §Contact author: yunoki@riken.jp
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Phys. Rev. Research 7, 043182 – Published 19 November, 2025

DOI: https://doi.org/10.1103/2s2p-kvcx

Abstract

Imaginary-time evolution, an important technique in tensor network and quantum Monte Carlo algorithms on classical computers, has recently been adapted to quantum computing. In this study, we focus on probabilistic imaginary-time evolution (PITE) algorithm and derive its formulation in the context of state-vector-based simulations, where quantum state vectors are directly used to compute observables without statistical errors. We compare the results with those of shot-based simulations, which estimate observables through repeated projective measurements. Applying the PITE algorithm to the Heisenberg chain, we investigate optimal initial conditions for convergence. We further demonstrate the method on the transverse-field Ising model using a state-of-the-art trapped-ion quantum device. Finally, we explore the potential of error mitigation in this framework, highlighting practical considerations for near-term digital quantum simulations.

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Phys. Rev. Research 7, 043182– Published 19 November, 2025
  • Received 7 April 2025
  • Accepted 8 October 2025
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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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