Continuous quantum error correction via quantum feedback control

Abstract

We describe a protocol for continuously protecting unknown quantum states from decoherence that incorporates design principles from both quantum error correction and quantum feedback control. Our protocol uses continuous measurements and Hamiltonian operations, which are weaker control tools than are typically assumed for quantum error correction. We develop a cost function appropriate for unknown quantum states and use it to optimize our state-estimate feedback. Using Monte Carlo simulations, we study our protocol for the three-qubit bit-flip code in detail and demonstrate that it can improve the fidelity of quantum states beyond what is achievable using quantum error correction when the time between quantum error correction cycles is limited.

12 pages, 6 figures, REVTeX; references fixed

References in corpus (2)

• Quantum Trajectories and Quantum Measurement Theory
• Spin Squeezing in the Ising Model

Cited by in corpus (160)

• Quantum Error Correction for Quantum Memories
• Control of quantum phenomena: Past, present, and future
• Quantum control theory and applications: A survey
• A Straightforward Introduction to Continuous Quantum Measurement
• Quantum feedback control of a superconducting qubit: Persistent Rabi oscillations
• Phase preserving amplification near the quantum limit with a Josephson Ring Modulator
• Quantum enhanced measurements without entanglement
• Observation of quantum jumps in a superconducting artificial atom
• Feedback control of quantum state reduction
• Deterministic entanglement of superconducting qubits by parity measurement and feedback
• Adaptive homodyne measurement of optical phase
• Building a fault-tolerant quantum computer using concatenated cat codes
• Quantum feedback: theory, experiments, and applications
• Engineered Dissipation for Quantum Information Science
• Coherent-feedback quantum control with a dynamic compensator
• Quantum memories based on engineered dissipation
• Deterministic Dicke state preparation with continuous measurement and control
• Designing quantum memories with embedded control: photonic circuits for autonomous quantum error correction
• Dynamics of simultaneously measured non-commuting observables
• Protecting a Bosonic Qubit with Autonomous Quantum Error Correction
• Autonomous Quantum Error Correction and Application to Quantum Sensing with Trapped Ions
• Direct Characterization of Quantum Dynamics
• The SLH framework for modeling quantum input-output networks
• Current fluctuations in open quantum systems: Bridging the gap between quantum continuous measurements and full counting statistics
• Internal Consistency of Fault-Tolerant Quantum Error Correction in Light of Rigorous Derivations of the Quantum Markovian Limit
• Symmetry breaking and error correction in open quantum systems
• Qubit models of weak continuous measurements
• Experimental demonstration of coherent feedback control on optical field squeezing
• Learning in Quantum Control: High-Dimensional Global Optimization for Noisy Quantum Dynamics
• Quantum error correction for continuously detected errors
• A practical scheme for error control using feedback
• Reversing quantum trajectories with analog feedback
• Pair-cat codes: autonomous error-correction with low-order nonlinearity
• Enhancement of Field Squeezing Using Coherent Feedback
• Coherent versus measurement feedback: Linear systems theory for quantum information
• Experimental demonstration of continuous quantum error correction
• Constraints on relaxation rates for N-level quantum systems
• Robust observer for uncertain linear quantum systems
• Quantum risk-sensitive estimation and robustness
• Unconventional Rydberg pumping and applications in quantum information processing
• Continuous quantum error correction by cooling
• Constructive control of quantum systems using factorization of unitary operators
• Optimal Quantum Filtering and Quantum Feedback Control
• Direct Characterization of Quantum Dynamics: General Theory
• Environment-Assisted Quantum State Restoration Via Weak Measurement
• Universal quantum interfaces
• Continuous quantum error correction for non-Markovian decoherence
• Feedback control in quantum optics: an overview of experimental breakthroughs and areas of application
• Dissipation-induced continuous quantum error correction for superconducting circuits
• Quantum Speed Limits under Continuous Quantum Measurements
• Physical model of continuous two-qubit parity measurement in a cavity-QED network
• Floquet-Mode Traveling-Wave Parametric Amplifiers
• Restoration of Quantum State in Dephasing Channel
• Active protection of a superconducting qubit with an interferometric Josephson isolator
• Quantum cooling and squeezing of a levitating nanosphere via time-continuous measurements
• Implementation-independent sufficient condition of the Knill-Laflamme type for the autonomous protection of logical qudits by strong engineered dissipation
• Gradient Ascent Pulse Engineering with Feedback
• High fidelity feed-back assisted parity measurement in circuit QED
• On quantum error-correction by classical feedback in discrete time
• Feedback Control of Non-linear Quantum Systems: a Rule of Thumb
• Weak measurement and control of entanglement generation
• Deterministic generation of remote entanglement with active quantum feedback
• Frequency Locking of an Optical Cavity using LQG Integral Control
• High-efficiency measurement of an artificial atom embedded in a parametric amplifier
• Efficient feedback controllers for continuous-time quantum error correction
• Quantum filter reduction for measurement-feedback control via unsupervised manifold learning
• Generation and stabilization of a three-qubit entangled W state in circuit QED via quantum feedback control
• Design of nanophotonic circuits for autonomous subsystem quantum error correction
• Equation of motion for process matrix: Hamiltonian identification and dynamical control of open quantum systems
• Quantum error correction for continuously detected errors with any number of error channels per qubit
• Quantum computation with cat qubits
• Simulation of complex dynamics of mean-field $p$-spin models using measurement-based quantum feedback control
• Weak Qubit Measurement with a Nonlinear Cavity: Beyond Perturbation Theory
• Machine Learning for Continuous Quantum Error Correction on Superconducting Qubits
• Fault-tolerant measurement-free quantum error correction with multi-qubit gates
• Replacing Quantum Feedback with Open-Loop Control and Quantum Filtering
• Construction of bilinear control Hamiltonians using the series product and quantum feedback
• Adiabatic evolution under quantum control
• Illustrating the Geometry of Coherently Controlled Quantum Channels
• Dispersive readout of a flux qubit at the single photon level
• Continuous Dynamical Decoupling with Bounded Controls
• Designing open quantum systems with known steady states: Davies generators and beyond
• Spontaneous symmetry breaking induced by quantum monitoring
• Practical Limits of Error Correction for Quantum Metrology
• Continuous quantum error correction for evolution under time-dependent Hamiltonians
• Chaos in Continuously Monitored Quantum Systems: An Optimal Path Approach
• Autonomous Quantum State Transfer by Dissipation Engineering
• Measurement-based direct quantum feedback control in an open quantum system
• Qubit purification speed-up for three complementary continuous measurements
• Error correcting Bacon-Shor code with continuous measurement of noncommuting operators
• Continuous Quantum Error Correction Through Local Operations
• Always-On Quantum Error Tracking with Continuous Parity Measurements
• Multi-time correlators in continuous measurement of qubit observables
• Exact signal correlators in continuous quantum measurements
• Quantum memory at nonzero temperature in a thermodynamically trivial system
• A Perturbative Approach to Continuous-Time Quantum Error Correction
• Continuous measurements for control of superconducting quantum circuits
• Entanglement-Preserving Limit Cycles from Sequential Quantum Measurements and Feedback
• Feedback-stabilized dynamical steady states in the Bose-Hubbard model
• Quantum Subdivision Capacities and Continuous-time Quantum Coding
• Method for quantum-jump continuous-time quantum error correction
• Implementation of the three-qubit phase-flip error correction code with superconducting qubits
• Bacon-Shor code with continuous measurement of non-commuting operators
• Quantum filtering of a thermal master equation with purified reservoir
• Volterra filters for quantum estimation and detection
• Loss and Saturation in Superconducting Travelling-Wave Parametric Amplifiers
• Unified Quantum State Tomography and Hamiltonian Learning Using Transformer Models: A Language-Translation-Like Approach for Quantum Systems
• Gauge subsystems, separability, and robustness in autonomous quantum memories
• Robust quantum sensing with strongly interacting probe systems
• Feedback-induced nonlinearity and superconducting on-chip quantum optics
• Continuous quantum error detection and suppression with pairwise local interactions
• Eventum Mechanics of Quantum Trajectories: Continual Measurements, Quantum Predictions and Feedback Control
• Optimal Zeno Dragging for Quantum Control: A Shortcut to Zeno with Action-based Scheduling Optimization
• Quantum proportional-integral (PI) control
• Enforcing dissipative entanglement by feedback
• Stabilizing two-qubit entanglement with dynamically decoupled active feedback
• Toward a Theory of Phase Transitions in Quantum Control Landscapes
• Accelerating Dissipative State Preparation with Adaptive Open Quantum Dynamics
• Optimal conditions for high-fidelity dispersive readout of a qubit with a photon-number-resolving detector
• Quantum error correction benchmarks for continuous weak parity measurements
• Correlators exceeding one in continuous measurements of superconducting qubits
• Fighting decoherence in a continuous two-qubit odd or even parity measurement with a closed-loop setup
• Unraveling-paired dynamical maps can recover the input of quantum channels
• Controlling quantum flux through measurement: an idealised example
• Fidelity-Enhanced Variational Quantum Optimal Control
• Quantum Consensus Dynamics by Entangling Maxwell Demon
• Geometric phases along quantum trajectories
• Dynamical Gaussian state transfer with quantum error correcting architecture
• Applications of Feedback Control in Quantum Systems
• Quantum error correction using weak measurements
• Measurement based estimator scheme for continuous quantum error correction
• Molecular machines for quantum error correction
• Quantum jump metrology in a two-cavity network
• On exponential stabilization of N-level quantum angular momentum systems
• Quantum Property Preservation
• Correcting noisy quantum gates with shortcuts to adiabaticity
• Global stability criterion for a quantum feedback control process on a single qubit and exponential stability in case of perfect detection efficiency
• Bounds on Autonomous Quantum Error Correction
• Feedback exponential stabilization of GHZ states of multi-qubit systems
• Spatial correlations in the qubit properties of D-Wave 2000Q measured and simulated qubit networks
• Viewing protected superconducting qubits through the lens of the cat qubit
• Error threshold in active steering protocols for few-qubit systems
• Parameter Estimation, Model Reduction and Quantum Filtering
• Optimal nonlinear filtering of quantum state
• On the Capability of Measurement-Based Quantum Feedback
• Nonlinear effect on quantum control for two-level systems
• Towards scalable active steering protocols for genuinely entangled state manifolds
• Continuous quantum correction on Markovian and Non-Markovian models
• Noise-Canceling Quantum Feedback: non-Hermitian Dynamics with Applications to State Preparation and Magic State Distillation
• Towards self-correcting quantum codes for neutral atom arrays
• Optimal quantum precision in noise estimation: Is entanglement necessary?
• Real-time Information, Uncertainty and Quantum Feedback Control
• Symmetry and Topology of Successive Quantum Feedback Control
• Passive quantum error correction of photon loss at breakeven
• Filtering and Control in Quantum Optics
• Set Stabilizability of Quantum Systems
• Amplified Quantum Dynamics and Enhanced Parameter Sensitivity via Coherent Feedback in Collective Atomic Spin Systems
• Control of Quantum Systems Despite Feedback Delay
• Stochastic optimization for learning quantum state feedback control
• On exponential stabilization of two-qubit systems