Exponentially accurate open quantum simulation via randomized dissipation with minimal ancilla

Simulating open quantum systems is an essential technique for understanding complex physical phenomena and advancing quantum technologies. Some quantum algorithms simulate Lindblad dynamics exponentially accurately, i.e., they achieve logarithmically short circuit depth in terms of accuracy, but they need to coherently encode all possible jump operators with a large ancilla consumption. Minimizing the gate and ancilla counts while achieving such a logarithmic scaling in accuracy remains an important challenge. In this work, we present two randomized quantum algorithms for simulating general Lindblad dynamics with multiple jump operators aimed at an observable estimation that achieve a circuit depth with not only logarithmic scaling in accuracy but also either partial or complete independence from the parameters specifying the Lindbladian. This is based on a novel random circuit compilation method that leverages dissipative processes with only a single jump operator, leading to the proposed methods using minimal ancilla qubits - 4+lceillog₂ Mrceil in the first case and 7 in the other, where each single jump operator has at most M Pauli strings. In addition, we numerically demonstrate the practical advantage over existing approaches by providing a detailed analysis of the required gate and ancilla counts. This work represents a significant step towards making open quantum system simulations more feasible on early fault-tolerant quantum computing devices.