Lindbladian Simulation with Logarithmic Precision Scaling via Two Ancillas

Quantum computers promise efficient simulation of Lindbladian dynamics in open quantum systems, with broad applications in quantum chemistry, quantum error correction, and quantum state preparation. However, simulating open systems is more challenging than simulating closed systems, inherently requiring nonunitary operations. Existing approaches face unique challenges: methods with higher theoretical efficiency demand numerous ancillae and multiqubit operations that are experimentally challenging, while more experimentally feasible methods incur deep quantum circuits to control simulation errors. Here, we introduce a powerful framework, the linear combinations of superoperators, to systematically compensate for simulation errors and overcome these challenges. Utilizing simple gates and experimentally accessible Trotter decompositions, our approach achieves an exponential reduction in circuit depth with respect to the simulation precision, if only two ancillas are allowed to be used. We further extend the approach to time-dependent Lindbladians, achieving for the first time logarithmic depth in precision. Numerical simulations demonstrate significant performance advantages, establishing our method as a practical and scalable solution for simulating open quantum systems on near-term quantum hardware.