Error-mitigated deep-circuit quantum simulation of open systems: Steady state and relaxation rate problems

Deep-circuit quantum computation, like Shor's algorithm, is undermined by error accumulation, and near-future techniques are far from adequate for full-fledged correction. Instead of resorting to shallow-circuit algorithms, recent theoretical research suggests that digital simulation (DQS) closed systems robust against the accumulation Trotter errors, as long local observables concerned. In this paper, we investigate open systems. First, prove deviation in steady state obtained depends only on a single step, which indicates may not be disastrous. By numerical circuits DQS dissipative XYZ model, then show correct results can recovered mitigation rate below sharp threshold. We explain threshold behavior existence dissipation-driven phase transition. Finally, propose new error-mitigation technique based scaling vicinity critical point Our expand territory available algorithms stimulate further experimental efforts practical applications.