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arXiv · 0908.1200

Parameter Estimation, Model Reduction and Quantum Filtering

Bradley A. Chase
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Abstract

This dissertation explores the topics of parameter estimation and model reduction in the context of quantum filtering. Chapters 2 and 3 provide a review of classical and quantum probability theory, stochastic calculus and filtering. Chapter 4 studies the problem of quantum parameter estimation and introduces the quantum particle filter as a practical computational method for parameter estimation via continuous measurement. Chapter 5 applies these techniques in magnetometry and studies the estimator's uncertainty scalings in a double-pass atomic magnetometer. Chapter 6 presents an efficient feedback controller for continuous-time quantum error correction. Chapter 7 presents an exact model of symmetric processes of collective qubit systems.

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Bradley A. Chase. 2009-08-08. Parameter Estimation, Model Reduction and Quantum Filtering. https://arxiv.org/abs/0908.1200

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