Quantum error correction under numerically exact open-quantum-system dynamics

Abstract

The known quantum error-correcting codes are typically built on approximative open-quantum-system models such as Born-Markov master equations. However, it is an open question how such codes perform in actual physical systems that, to some extent, necessarily exhibit phenomena beyond the limits of these models. To this end, we employ numerically exact open-quantum-system dynamics to analyze the performance of a five-qubit error-correction code where each qubit is coupled to its own bath. We first focus on the performance of a single error-correction cycle covering timescales and coupling strengths beyond those of Born-Markov models. We observe distinct power-law behavior of the error-corrected channel infidelity t2a: a≲2 in the ultrashort times t<3/ωc and a≈1/2 in the short-time range 3/ωc