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.Quantum feedback control provides a systems engineering perspective on the analysis and design of quantum memories, complementing alternative ideas extending from theoretical physics. Whereas the latter approach has emphasized the connections of quantum error

Symmetries and conserved quantities in Lindblad master equations

“…In Ref. [6], an L comprising two jump operators (which are closely related to stabilizer generators of qubit codes [73]) will have a unique Bell state as its steady state. We study a system with one of those jump operators whose ρ ss will be of the form of the fourth structure from Eq.…”

Dissipative Encoding of Quantum Information

“…Within the more general formulation of QEC theory afforded by the subsystem notion [5,8] (also later referred to as "operator QEC," OQEC [9]), a stabilizer code encodes the information to be protected in a subsystem of a subspace of H P [10]. Notably, the presence of auxiliary "gauge degrees" of freedom in subsystem codes can both lead to simpler error-recovery procedures, with implications for quantum fault-tolerance [11], as well as to intrinsic tolerance of the code against additional errors [12].…”

Focus on Quantum Memory

“…On the theoretical side, there are in-depth studies of existing quantum memory protocols [14][15][16], proposals for new memory protocols [17][18][19][20][21][22][23][24], and proposals for new applications of quantum memories [25][26][27][28]. As for new theoretical analysis of existing protocols, [14] uses a quantum input-output model to study gradient echo memories, which makes it possible to obtain analytical results in the regime of high-efficiency experiments.…”

“…Reference [21] proposes to realize a quantum memory for propagating microwave photons using a solid-state spin ensemble and a microwave cavity. Finally there are three proposals based on quantum error correction; [22] proposes a model for self-correcting quantum memories and quantum computers (albeit in six spatial dimensions), [23] studies a continuous-time version of stabilizer codes in nanophotonic circuits, and [24] studies holonomic quantum computing in ground states of spin chains.…”