Noise-Canceling Quantum Feedback: non-Hermitian Dynamics with Applications to State Preparation and Magic State Distillation
arXiv:2507.05611 · doi:10.1103/cnxj-m1wn
Abstract
Time-continuous quantum measurement allows for the tracking of a quantum system in real time via sequences of short, and individually weak, measurement intervals. Such measurements are necessarily invasive, imparting backaction to the system, and allowing the observer to update their state estimate based on stochastic measurement outcomes. Feedback control then involves real-time interventions by an observer, conditioned on the time-continuous measurement signal that they receive. We here consider diffusive quantum trajectories, and focus on the "noise-canceling" subset of feedback protocols that aim to minimize the degree of stochasticity in the dynamics. We derive such a class of feedback operations, showing that under the idealized assumptions of pure states, unit measurement efficiency, and zero time-delay in implementing feedback operations, perfectly noise-canceling feedback always exists. We consider the resulting noise-canceled dynamics generated by an effective non-Hermitian Hamiltonian; while non-Hermitian Hamiltonians from continuous monitoring generally describe rare dynamics (accessible by costly post-selection), the use of noise-canceling feedback here leads to non-Hermitian dynamics that occur deterministically. We demonstrate this via examples of entangled state preparation and stabilization. We then illustrate the potential for the application of noise-cancellation to boost success rates in magic state distillation protocols. We show that adding feedback based on noise-cancellation into a time-continuous 5-to-1 distillation protocol leads to higher probabilities of successful distillation across a range of input errors, and extends the threshold on input errors for which the protocol is effective. Our results highlight the efficacy of noise-canceling feedback-aided protocols for quantum state preparation and stabilization tasks.
15 + 14 pages, 12 figures
References in corpus (100)
- Quantum entanglement
- Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
- Circuit Quantum Electrodynamics
- Introduction to Quantum Noise, Measurement and Amplification
- Non-Hermitian Physics
- Pseudo-Hermiticity versus PT Symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian
- Universal Quantum Computation with ideal Clifford gates and noisy ancillas
- The physics of exceptional points
- Dynamically encircling exceptional points in a waveguide: asymmetric mode switching from the breakdown of adiabaticity
- Pseudo-Hermiticity versus PT-Symmetry II: A complete characterizatio n of non-Hermitian Hamiltonians with a real spectrum
- Pseudo-Hermiticity versus PT-Symmetry III: Equivalence of pseudo-Her miticity and the presence of antilinear symmetries
- Four qubits can be entangled in nine different ways
- The Einstein-Podolsky-Rosen paradox: from concepts to applications
- Exceptional Points of Non-hermitian Operators
- Quantum exceptional points of non-Hermitian Hamiltonians and Liouvillians: The effects of quantum jumps
- Observation of parity-time symmetry breaking in a single spin system
- Measurement-based quantum control of mechanical motion
- Quantum state tomography across the exceptional point in a single dissipative qubit
- Observing single quantum trajectories of a superconducting qubit
- Bloch vectors for qudits
- Non-Hermitian Quantum Sensing: Fundamental Limits and Non-Reciprocal Approaches
- Magic state distillation with low overhead
- Dynamically encircling exceptional points: Exact evolution and polarization state conversion
- To catch and reverse a quantum jump mid-flight
- Quantum trajectory approach to circuit QED: Quantum jumps and the Zeno effect
- Observation of measurement-induced entanglement and quantum trajectories of remote superconducting qubits
- Generating Entangled Microwave Radiation Over Two Transmission Lines
- Quantum feedback: theory, experiments, and applications
- Encircling an Exceptional Point
- Continuous quantum error correction via quantum feedback control
- Quantum Trajectories and Quantum Measurement Theory
- Universal fault-tolerant quantum computation with only transversal gates and error correction
- Stabilizing feedback controls for quantum systems
- General description of quasi-adiabatic dynamical phenomena near exceptional points
- Magic State Distillation: Not as Costly as You Think
- Novel constructions for the fault-tolerant Toffoli gate
- Hybrid-Liouvillian formalism connecting exceptional points of non-Hermitian Hamiltonians and Liouvillians via postselection of quantum trajectories
- Magic state distillation in all prime dimensions using quantum Reed-Muller codes
- Dynamics of simultaneously measured non-commuting observables
- Quantum jumps in the non-Hermitian dynamics of a superconducting qubit
- Efficient magic state factories with a catalyzed |CCZ> to 2|T> transformation
- Multilevel distillation of magic states for quantum computing
- Decoherence Induced Exceptional Points in a Dissipative Superconducting Qubit
- How to project qubits faster using quantum feedback
- Matching and maximum likelihood decoding of a multi-round subsystem quantum error correction experiment
- Quantum error correction for continuously detected errors
- A unified framework for magic state distillation and multi-qubit gate-synthesis with reduced resource cost
- A practical scheme for error control using feedback
- Efficient Quantum Filtering for Quantum Feedback Control
- Experimental demonstration of continuous quantum error correction
- Topological quantum state control through exceptional-point proximity
- Dynamics of a qubit while simultaneously monitoring its relaxation and dephasing
- Reconsidering Rapid Qubit Purification by Feedback
- Resolving the topology of encircling multiple exceptional points
- Experimental Demonstration of Logical Magic State Distillation
- Continuous quantum error correction for non-Markovian decoherence
- Operational formulation of homodyne detection
- Rapid Measurement of Quantum Systems using Feedback Control
- Control of spontaneous emission dynamics in microcavities with chiral exceptional surfaces
- Stabilization of Stochastic Quantum Dynamics via Open and Closed Loop Control
- Entanglement genesis under continuous parity measurement
- Using Spontaneous Emission of a Qubit as a Resource for Feedback Control
- Non-Hermitian adiabatic transport in spaces of exceptional points
- Deterministic generation of remote entanglement with active quantum feedback
- Quantum Feedback Control: How to use Verification Theorems and Viscosity Solutions to Find Optimal Protocols
- Exponential Stability of Subspaces for Quantum Stochastic Master Equations
- Ignorance is bliss: General and robust cancellation of decoherence via no-knowledge quantum feedback
- Theory of remote entanglement via quantum-limited phase-preserving amplification
- Implementation of a canonical phase measurement with quantum feedback
- Rapid purification of quantum systems by measuring in a feedback-controlled unbiased basis
- Quantum feedback for rapid state preparation in the presence of control imperfections
- Quantum error correction for continuously detected errors with any number of error channels per qubit
- Robust mode conversion in NV centers using exceptional points
- Unifying theory of quantum state estimation using past and future information
- Measuring Fluorescence to Track a Quantum Emitter's State: A Theory Review
- Pontryagin-Optimal Control of a non-Hermitian Qubit
- Locally optimal measurement-based quantum feedback with application to multi-qubit entanglement generation
- Continuous quantum error correction for evolution under time-dependent Hamiltonians
- Discussion of the adiabatic hypothesis in control schemes using exceptional points
- Quantum Dynamics with Stochastic Non-Hermitian Hamiltonians
- 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
- Continuous measurements for control of superconducting quantum circuits
- Creating and controlling exceptional points of non-Hermitian Hamiltonians via homodyne Lindbladian invariance
- Entanglement-Preserving Limit Cycles from Sequential Quantum Measurements and Feedback
- Robust Adaptive measurement for qubit state preparation
- Maximum information gain in weak or continuous measurements of qudits: complementarity is not enough
- Optimal Zeno Dragging for Quantum Control: A Shortcut to Zeno with Action-based Scheduling Optimization
- Quantum proportional-integral (PI) control
- A Logarithmic Bayesian Approach to Quantum Error Detection
- Optimality of feedback control for qubit purification under inefficient measurement
- Entanglement of a pair of quantum emitters via continuous fluorescence measurements: a tutorial
- Quantum filtering one bit at a time
- Single-shot energetic-based estimator for entanglement in a half-parity measurement setup
- Global versus local optimality in feedback-controlled qubit purification: new insights from minimizing Rényi entropies
- Time-delayed quantum feedback and incomplete decoherence suppression with no-knowledge measurement
- Topological Operations Around Exceptional Points via Shortcuts to Adiabaticity
- Adiabatic quantum control hampered by entanglement
- Completely positive trace-preserving maps for higher-order unraveling of Lindblad master equations