Asymmetric quantum error correction via code conversion

TL;DR

This paper develops fault-tolerant circuits for converting between asymmetric and symmetric quantum codes, optimizing error correction in systems with asymmetric decoherence, thereby improving efficiency without sacrificing universality.

Contribution

It introduces fault-tolerant code conversion circuits between asymmetric and symmetric quantum codes, enhancing error correction efficiency in asymmetric decoherence environments.

Findings

Conversion circuits reduce logical circuit failure rates in asymmetric error conditions.

Asymmetric codes improve error correction efficiency in systems with phase error dominance.

Universal quantum computation remains feasible with combined asymmetric and symmetric codes.

Abstract

In many physical systems it is expected that environmental decoherence will exhibit an asymmetry between dephasing and relaxation that may result in qubits experiencing discrete phase errors more frequently than discrete bit errors. In the presence of such an error asymmetry, an appropriately asymmetric quantum code - that is, a code that can correct more phase errors than bit errors - will be more efficient than a traditional, symmetric quantum code. Here we construct fault tolerant circuits to convert between an asymmetric subsystem code and a symmetric subsystem code. We show that, for a moderate error asymmetry, the failure rate of a logical circuit can be reduced by using a combined symmetric asymmetric system and that doing so does not preclude universality.