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

TL;DR

This paper demonstrates that digital quantum simulation of open quantum systems can be error-mitigated effectively, with steady states resilient to Trotter errors and a new mitigation technique based on phase transition scaling.

Contribution

It proves that steady state errors depend only on single-step Trotter errors and introduces a novel error mitigation method leveraging quantum phase transition properties.

Findings

Steady state deviation depends only on single Trotter step error.

Quantum error mitigation is effective below a certain error threshold.

A new error-mitigation technique based on phase transition scaling is proposed.

Abstract

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