Quantum-Trajectory-Inspired Lindbladian Simulation

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.