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Quantum error correction provides a fertile context for exploring theinterplay of feedback control, microscopic physics and noncommutativeprobability. In this paper we deepen our understanding of this nexus throughhigh-level analysis of a class of quantum memory models that we have previouslyproposed, which implement continuous-time versions of well-known stabilizercodes in autonomous nanophotonic circuits that require no external clocking orcontrol. We show that the presence of the gauge subsystem in the nine-qubitBacon-Shor code allows for an optimized layout of the correspondingnanophotonic circuit that substantially ameliorates the effects of opticalpropagation losses, argue that code separability allows for simplifiedrestoration feedback protocols, and propose a modified fidelity metric forquantifying the performance of realistic quantum memories. Our treatment ofthese topics exploits the homogeneous modeling framework of autonomousnanophotonic circuits, but the key ideas translate to the traditional settingof discrete time, measurement-based quantum error correction.

Gauge subsystems, separability, and robustness in autonomous quantum memories