Symmetry and Topology of Successive Quantum Feedback Control

Abstract

We establish a symmetry classification for a general class of quantum feedback control. For successive feedback control with a non-adaptive sequence of bare measurements (i.e., with positive Kraus operators), we prove that the symmetry classification collapses to the ten-fold AZ${}^{†}$ classes, specifying the allowed topology of CPTP maps associated with feedback control. We demonstrate that a chiral Maxwell's demon with Gaussian measurement errors exhibits quantized winding numbers. Moreover, for general (non-bare) measurements, we explicitly construct a protocol that falls outside the ten-fold classification. These results broaden and clarify the principles in engineering topological aspects of quantum control robust against disorder and imperfections.

arXiv comment9 pages, 4 figures

References in corpus (53)

• Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
• Edge states and topological invariants of non-Hermitian systems
• Exceptional Topology of Non-Hermitian Systems
• Non-Hermitian Physics
• A quantum gas microscope - detecting single atoms in a Hubbard regime optical lattice
• Topological phases of non-Hermitian systems
• Symmetry and Topology in Non-Hermitian Physics
• Single-Atom Resolved Fluorescence Imaging of an Atomic Mott Insulator
• Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems
• Topological Origin of Non-Hermitian Skin Effects
• Topological Band Theory for Non-Hermitian Hamiltonians
• Correspondence between winding numbers and skin modes in non-hermitian systems
• Experimental Study of Active LRC Circuits with PT-Symmetries
• Real-time quantum feedback prepares and stabilizes photon number states
• A Straightforward Introduction to Continuous Quantum Measurement
• Observation of parity-time symmetry breaking transitions in a dissipative Floquet system of ultracold atoms
• Quantum feedback control of a superconducting qubit: Persistent Rabi oscillations
• Cooling of a mirror by radiation pressure
• Progressive field-state collapse and quantum non-demolition photon counting
• Second Law of Thermodynamics with Discrete Quantum Feedback Control
• Periodic Table for Topological Bands with Non-Hermitian Bernard-LeClair Symmetries
• Real-time quantum error correction beyond break-even
• Observing single quantum trajectories of a superconducting qubit
• Non-Hermitian topological phenomena: A review
• Feedback cooling of a cantilever's fundamental mode below 5 mK
• Parity-time-symmetric quantum critical phenomena
• Continuous quantum error correction via quantum feedback control
• Observing a quantum Maxwell demon at work
• Repeated quantum error correction on a continuously encoded qubit by real-time feedback
• Quantum non-demolition measurement of a superconducting two-level system
• Deterministic Squeezed States with Joint Measurements and Feedback
• Coherent Quantum-Noise Cancellation for Optomechanical Sensors
• Experimental rectification of entropy production by a Maxwell's Demon in a quantum system
• Spin squeezing of a cold atomic ensemble with the nuclear spin of one-half
• Information-to-work conversion by Maxwell's demon in a superconducting circuit-QED system
• Information gain and loss for a quantum Maxwell's demon
• Non-Hermitian boundary and interface states in nonreciprocal higher-order topological metals and electrical circuits
• Contractivity of positive and trace preserving maps under $L_p$ norms
• Thermodynamics of Quantum Information Flows
• A dual-species Rydberg array
• Full mechanical characterization of a cold damped mirror
• Integral Quantum Fluctuation Theorems under Measurement and Feedback control
• Quantum feedback by discrete quantum non-demolition measurements: towards on-demand generation of photon-number states
• Topologically protected modes in non-equilibrium stochastic systems
• Exceptional non-Hermitian topological edge mode and its application to active matter
• Autonomous dissipative Maxwell's demon in a diamond spin qutrit
• Squashed States of Light: Theory and Applications to Quantum Spectroscopy
• Quantum Fluctuation Theorem under Continuous Measurement and Feedback
• A simple formula for pooling knowledge about a quantum system
• Role of Topology in Relaxation of One-Dimensional Stochastic Processes
• Quantum error correction benchmarks for continuous weak parity measurements
• Experimentally probing entropy reduction via iterative quantum information transfer
• Topology of Discrete Quantum Feedback Control