Gauge subsystems, separability and robustness in autonomous quantum memories

Abstract

Quantum error correction provides a fertile context for exploring the interplay of feedback control, microscopic physics and non-commutative probability. In this paper we deepen our understanding of this nexus through high-level analysis of a class of quantum memory models that we have previously proposed, which implement continuous-time versions of well-known stabilizer codes in autonomous nanophotonic circuits that require no external clocking or control. We demonstrate that the presence of the gauge subsystem in the nine-qubit Bacon–Shor code allows for a loss-tolerant layout of the corresponding nanophotonic circuit that substantially ameliorates the effects of optical propagation losses, argue that code separability allows for simplified restoration feedback protocols, and propose a modified fidelity metric for quantifying the performance of realistic quantum memories. Our treatment of these topics exploits the homogeneous modeling framework of autonomous nanophotonic circuits, but the key ideas translate to the traditional setting of discrete time, measurement-based quantum error correction.