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.
Highlights
Quantum error correction provides a fertile context for exploring the interplay of feedback control, microscopic physics and noncommutative probability
Whereas the latter approach has emphasized the connections of quantum error correction and quantum computation to many body physics [1, 2], the quantum control community has viewed decoherence suppression as a problem that should ideally be formulated as a non-commutative generalization of classical stochastic and hybrid control theory
We have previously shown how the the Gough-James quantum network algebra [9, 10, 11] can be utilized together with a recent limit theorem for quantum stochastic differential equations (QSDEs) [12] to facilitate the derivation of an intuitive master equation for a given quantum memory model from an explicit construction of the underlying nanophotonic circuit, in a manner inspired by schematic capture methods of contemporary electrical engineering [8, 13]
Summary
Quantum error correction provides a fertile context for exploring the interplay of feedback control, microscopic physics and noncommutative probability. If the code is separable, in the sense that disjoint sets of stabilizer generators mediate X and Z error syndrome extraction, the quantum memory
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