Topology of Discrete Quantum Feedback Control

Abstract

A general framework for analyzing the topology of quantum channels of single-particle systems is developed to find a class of genuinely dynamical topological phases that can be realized by means of discrete quantum feedback control. We provide a symmetry classification of quantum channels by identifying ten symmetry classes of discrete quantum feedback control with projective measurements. We construct various types of topological feedback control by using topological Maxwell demons that achieve robust feedback-controlled chiral or helical transport against noise and decoherence. Topological feedback control thus offers a versatile tool for creating and controlling nonequilibrium topological phases in open quantum systems that are distinct from non-Hermitian and Lindbladian systems and should provide a guiding principle for topology-based design of quantum feedback control.

43 pages, 24 figures. v2: new results and discussions added. v3: published version

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Cited by in corpus (5)

• Symmetry and Topology of Monitored Quantum Dynamics
• Liouvillian topology and nonreciprocal dynamics in open Floquet chains
• Symmetry and Topology of Successive Quantum Feedback Control
• Dissipative quantum North-East-Center model: steady-state phase diagram, universality and nonergodic dynamics
• Liouvillian skin effects in two-dimensional electron systems at finite temperatures