Coherence in quantum error-correcting codes

Stefanie Beale, Joel Wallman, Mauricio Gutiérrez, Kenneth R. Brown, Raymond Laflamme

Published 2018-05-22Version 1

Typical studies of quantum error correction assume probabilistic Pauli noise, largely because it is relatively easy to analyze and simulate. Consequently, the effective logical noise due to physically realistic coherent errors is relatively unknown. Here we prove that encoding a system in a stabilizer code and measuring error syndromes decoheres errors, that is, converts coherent errors to probabilistic Pauli errors, even when no recovery operations are applied. Two practical consequences are that the error rate in a logical circuit is well-quantified by the average gate fidelity at the logical level and that essentially optimal recovery operators can be determined by independently optimizing the logical fidelity of the effective noise per syndrome.