Optimal approximate quantum error correction for quantum metrology

Abstract

For a generic set of Markovian noise models, the estimation precision of a parameter associated with the Hamiltonian is limited by the $1/\sqrt{t}$ scaling where $t$ is the total probing time, in which case the maximal possible quantum improvement in the asymptotic limit of large $t$ is restricted to a constant factor. However, situations arise where the constant factor improvement could be significant, yet no effective quantum strategies are known. Here we propose an optimal approximate quantum error correction (AQEC) strategy asymptotically saturating the precision lower bound in the most general adaptive parameter estimation scheme where arbitrary and frequent quantum controls are allowed. We also provide an efficient numerical algorithm finding the optimal code. Finally, we consider highly-biased noise and show that using the optimal AQEC strategy, strong noises are fully corrected, while the estimation precision depends only on the strength of weak noises in the limiting case.

arXiv comment6+7 pages, 1 figure

References in corpus (43)

• Quantum sensing
• Advances in Quantum Metrology
• Quantum metrology
• Quantum metrology with nonclassical states of atomic ensembles
• On the Improvement of Frequency Stardards with Quantum Entanglement
• General framework for estimating the ultimate precision limit in noisy quantum-enhanced metrology
• Advances in Photonic Quantum Sensing
• The elusive Heisenberg limit in quantum enhanced metrology
• Quantum Metrology in Non-Markovian Environments
• Quantum enhanced measurements without entanglement
• Using entanglement against noise in quantum metrology
• Improved quantum metrology using quantum error-correction
• Performance and structure of single-mode bosonic codes
• Reversing quantum dynamics with near-optimal quantum and classical fidelity
• Quantum Error Correction for Metrology
• Achieving the Heisenberg limit in quantum metrology using quantum error correction
• Magnet field sensing beyond the standard quantum limit under the effect of decoherence
• Noisy metrology beyond the standard quantum limit
• Increasing sensing resolution with error correction
• The ultimate precision limits for noisy frequency estimation
• Efficient tools for quantum metrology with uncorrelated noise
• Autonomous Quantum Error Correction and Application to Quantum Sensing with Trapped Ions
• Adaptive quantum metrology under general Markovian noise
• Fundamental quantum interferometry bound for the squeezed-light-enhanced gravitational-wave detector GEO600
• Quantum parameter estimation with optimal control
• Quantum metrology with full and fast quantum control
• General conditions for approximate quantum error correction and near-optimal recovery channels
• Parameter estimation of quantum channels
• Optimum Quantum Error Recovery using Semidefinite Programming
• Sequential feedback scheme outperforms the parallel scheme for Hamiltonian parameter estimation
• Ultimate Precision of Adaptive Noise Estimation
• Generalizable control for quantum parameter estimation through reinforcement learning
• Restoring Heisenberg scaling in noisy quantum metrology by monitoring the environment
• Ancilla-free quantum error correction codes for quantum metrology
• A simple approach to approximate quantum error correction based on the transpose channel
• Robust quantum metrological schemes based on protection of quantum Fisher information
• Ultimate limits for quantum magnetometry via time-continuous measurements
• Spatial noise filtering through error correction for quantum sensing
• Sensing in the Presence of Observed Environments
• Two-sided bounds on minimum-error quantum measurement, on the reversibility of quantum dynamics, and on the maximum overlap problem using directional iterates
• Perturbative quantum error correction
• Many-body effects in quantum metrology
• Fault-tolerant quantum metrology

Cited by in corpus (26)

• Mitiq: A software package for error mitigation on noisy quantum computers
• Mid-circuit cavity measurement in a neutral atom array
• Optimal Scheme for Quantum Metrology
• Review: Quantum Metrology and Sensing with Many-Body Systems
• Asymptotic theory of quantum channel estimation
• Probe incompatibility in multiparameter noisy quantum metrology
• Optimal Strategies of Quantum Metrology with a Strict Hierarchy
• Using adaptiveness and causal superpositions against noise in quantum metrology
• Optimal probes and error-correction schemes in multi-parameter quantum metrology
• Using Quantum Metrological Bounds in Quantum Error Correction: A Simple Proof of the Approximate Eastin-Knill Theorem
• Geometric distinguishability measures limit quantum channel estimation and discrimination
• New perspectives on covariant quantum error correction
• Quantum-enhanced radiometry via approximate quantum error correction
• Enhanced Quantum Metrology with Non-Phase-Covariant Noise
• New bounds on adaptive quantum metrology under Markovian noise
• Fully-Optimized Quantum Metrology: Framework, Tools, and Applications
• Achieving metrological limits using ancilla-free quantum error-correcting codes
• Spin Squeezing with Arbitrary Quadratic Collective-Spin Interaction
• Time-energy uncertainty relation for noisy quantum metrology
• RLD Fisher Information Bound for Multiparameter Estimation of Quantum Channels
• Toward a Theory of Phase Transitions in Quantum Control Landscapes
• Covariant Quantum Error-Correcting Codes with Metrological Entanglement Advantage
• Fisher information susceptibility for multiparameter quantum estimation
• Universal bounds for quantum metrology in the presence of correlated noise
• Fidelity-based distance bounds for $N$-qubit approximate quantum error correction
• Stabilizer codes for Heisenberg-limited many-body Hamiltonian estimation