Exponentially reduced circuit depths in Lindbladian simulation

Abstract: Quantum computers can efficiently simulate Lindbladian dynamics, enabling powerful applications in open system simulation, thermal and ground-state preparation, autonomous quantum error correction, dissipative engineering, and more. Despite the abundance of well-established algorithms for closed-system dynamics, simulating open quantum systems on digital quantum computers remains challenging due to the intrinsic requirement for non-unitary operations. Existing methods face a critical trade-off: either relying on resource-intensive multi-qubit operations with experimentally challenging approaches or employing deep quantum circuits to suppress simulation errors using experimentally friendly methods. In this work, we challenge this perceived trade-off by proposing an efficient Lindbladian simulation framework that minimizes circuit depths while remaining experimentally accessible. Based on the incoherent linear combination of superoperators, our method achieves exponential reductions in circuit depth using at most two ancilla qubits and the straightforward Trotter decomposition of the process. Furthermore, our approach extends to simulate time-dependent Lindbladian dynamics, achieving logarithmic dependence on the inverse accuracy for the first time. Rigorous numerical simulations demonstrate clear advantages of our method over existing techniques. This work provides a practical and scalable solution for simulating open quantum systems on quantum devices.