Quantum-Trajectory-Inspired Lindbladian Simulation

TL;DR

This paper introduces two quantum algorithms inspired by quantum trajectories for simulating open quantum systems governed by Lindbladians, significantly improving efficiency especially with many jump operators.

Contribution

The paper presents two novel quantum algorithms that reduce dependence on the number of jump operators and improve simulation efficiency for open quantum systems.

Findings

First algorithm has gate complexity independent of jump operators.

Second algorithm achieves near-optimal dependence on time and precision.

Both algorithms improve efficiency for systems with many jump operators.

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 $\epsilon$ and introduces only an additional $\tilde{O}(m)$ factor, which strictly improves upon state-of-the-art gate-based quantum algorithm that has an $\tilde O(m^2)$ 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.