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  • Open Access

Quantum-Trajectory-Inspired Lindbladian Simulation

Sirui Peng1,2, Xiaoming Sun1, Qi Zhao3, and Hongyi Zhou1,*

  • *Contact author: zhouhongyi@ict.ac.cn
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PRX Quantum 6, 030358 – Published 22 September, 2025

DOI: https://doi.org/10.1103/ssrs-8x32

Abstract

Simulating the dynamics of open quantum systems is a crucial task in quantum computing, offering wide-ranging applications but remaining computationally challenging. In this paper, we propose two quantum algorithms for simulating the dynamics of open quantum systems governed by Lindbladians. We introduce a new approximation channel for short-time evolution, inspired by the quantum trajectory method, which underpins the efficiency of our algorithms. The first algorithm achieves a gate complexity independent of the number of jump operators, m, marking a significant improvement in efficiency. The second algorithm achieves near-optimal dependence on the evolution time t and precision ϵ and introduces only an additional O~(m) factor, which strictly improves upon state-of-the-art gate-based quantum algorithm that has an O~(m2) factor. The improvement stems from the integration of the new approximation channel with a novel structured linear combination of unitaries method. In both our algorithms, the reduction of dependence on m significantly enhances the efficiency of simulating practical dissipative processes characterized by a large number of jump operators.

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Popular Summary

Simulating the dynamics of open quantum systems is a critical area in quantum computing, with numerous applications in fields like quantum chemistry, physics, and optimization. These systems interact with their environment, introducing complex dissipative effects that increase the computational difficulty. Lindblad master equations are commonly used to model such systems, but existing quantum simulation algorithms are computationally expensive, especially as they depend on the number of jump operators m representing environmental interactions.

We present two innovative quantum algorithms for simulating Markovian open quantum systems governed by Lindbladians. These algorithms utilize a new approximation for short-time evolution, inspired by the quantum trajectory method. The first algorithm eliminates the dependence on m, while the second algorithm has an O(m) dependence with near-optimal dependence on evolution time t and precision, which strictly improves the previously best gate-based algorithm with O(m) dependence.

Our results address a crucial bottleneck in simulating systems with large numbers of jump operators, which is common in real-world quantum systems like those in quantum chemistry and condensed-matter physics, and provides exponential speedup in many cases. By reducing the computational overhead, our algorithms make it more feasible to model complex, dissipative quantum processes, advancing the practical use of quantum computers for real-world problems.

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Outline

Information

PRX Quantum 6, 030358– Published 22 September, 2025
  • Received 12 September 2024
  • Revised 18 February 2025
  • Accepted 15 August 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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