Topology of Discrete Quantum Feedback Control

TL;DR

This paper develops a framework to classify and realize topological phases in single-particle quantum systems using discrete feedback control, enabling robust transport and control in open quantum systems.

Contribution

It introduces a symmetry classification of quantum channels and constructs topological feedback control methods using Maxwell demons for robust quantum transport.

Findings

Identifies ten symmetry classes of quantum feedback channels.

Demonstrates topological feedback control achieving robust transport.

Provides a new approach to topological phases in open quantum systems.

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.