Frequency Tracking and Parameter Estimation for Robust Quantum State-Estimation

Abstract

In this paper we consider the problem of tracking the state of a quantum system via a continuous measurement. If the system Hamiltonian is known precisely, this merely requires integrating the appropriate stochastic master equation. However, even a small error in the assumed Hamiltonian can render this approach useless. The natural answer to this problem is to include the parameters of the Hamiltonian as part of the estimation problem, and the full Bayesian solution to this task provides a state-estimate that is robust against uncertainties. However, this approach requires considerable computational overhead. Here we consider a single qubit in which the Hamiltonian contains a single unknown parameter. We show that classical frequency estimation techniques greatly reduce the computational overhead associated with Bayesian estimation and provide accurate estimates for the qubit frequency

6 figures, 13 pages

References in corpus (12)

• A Straightforward Introduction to Continuous Quantum Measurement
• Mixed state sensitivity of several quantum information benchmarks
• Time-Symmetric Quantum Theory of Smoothing
• Robust quantum parameter estimation: coherent magnetometry with feedback
• Qubit feedback and control with kicked quantum nondemolition measurements: A quantum Bayesian analysis
• Robust observer for uncertain linear quantum systems
• Reconsidering Rapid Qubit Purification by Feedback
• Single shot parameter estimation via continuous quantum measurement
• Optimal waveform estimation for classical and quantum systems via time-symmetric smoothing. II. Applications to atomic magnetometry and Hardy's paradox
• Rapid state purification protocols for a Cooper pair box
• Guidance and Control in a Josephson Charge Qubit
• Optimal waveform estimation for classical and quantum systems via time-symmetric smoothing

Cited by in corpus (25)

• Quantum feedback: theory, experiments, and applications
• Restoring Heisenberg scaling in noisy quantum metrology by monitoring the environment
• Quantum Speed Limits under Continuous Quantum Measurements
• Feedback Control of Rabi Oscillations in Circuit QED
• Structure identification and state initialization of spin networks with limited access
• Rapid estimation of drifting parameters in continuously measured quantum systems
• Multi-parameter estimation along quantum trajectories with Sequential Monte Carlo methods
• Robustness of System-Filter Separation for the Feedback Control of a Quantum Harmonic Oscillator Undergoing Continuous Position Measurement
• Experimental Bayesian calibration of trapped ion entangling operations
• Implementation schemes for unsharp measurements with trapped ions
• Adaptive measurement filter: efficient strategy for optimal estimation of quantum Markov chains
• Estimation of classical parameters via continuous probing of complementary quantum observables
• Process tomography via sequential measurements on a single quantum system
• Confidence and Backaction in the Quantum Filter Equation
• Quantum state tomography with time-continuous measurements: reconstruction with resource limitations
• Quantum frequency estimation with conditional states of continuously monitored independent dephasing channels
• An interleaved sampling scheme for the characterization of single qubit dynamics
• Estimation of parameters in circuit QED by continuous quantum measurement
• Online Parameter Estimation for Continuously Monitored Quantum Systems
• Equation of Motion for Estimation Fidelity of Monitored Oscillating Qubits
• Optimal nonlinear filtering of quantum state
• Current-based metrology with two-terminal mesoscopic conductors
• Estimating quantum Markov chains using coherent absorber post-processing and pattern counting estimator
• Hybrid filtering for a class of nonlinear quantum systems subject to classical stochastic disturbances
• Completely positive trace-preserving maps for higher-order unraveling of Lindblad master equations