Optimal Quantum Filtering and Quantum Feedback Control

Abstract

Quantum mechanical systems exhibit an inherently probabilistic nature upon measurement. Using a quantum noise model to describe the stochastic evolution of the open quantum system and working in parallel with classical indeterministic control theory, we present the theory of nonlinear optimal quantum feedback control. The resulting quantum Bellman equation is then applied to the explicitly solvable quantum linear-quadratic-Gaussian (LQG) problem which emphasizes many similarities with the corresponding classical control problem.

14 pages, extended introduction and free particle example included

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Cited by in corpus (22)

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• Network Synthesis of Linear Dynamical Quantum Stochastic Systems
• Entanglement-enhanced time-continuous quantum control in optomechanics
• Synthesis of linear quantum stochastic systems via quantum feedback networks
• Violation of Bell's Inequality in Electromechanics
• Quantum filtering: a reference probability approach
• Combining Floquet and Lyapunov techniques for time-dependent problems in optomechanics and electromechanics
• A transverse Hamiltonian variational technique for open quantum stochastic systems and its application to coherent quantum control
• Information flow and error scaling for fully-quantum control
• Quantum Pontryagin Principle under Continuous Measurements and Feedback
• Risk-sensitive performance criteria and robustness of quantum systems with a relative entropy description of state uncertainty
• Weyl variations and local sufficiency of linear observers in the mean square optimal coherent quantum filtering problem
• Quantum Feedback Networks and Control: A Brief Survey
• Evolution of quasi-characteristic functions in quantum stochastic systems with Weyl quantization of energy operators
• Gaussian Stochastic Linearization for Open Quantum Systems Using Quadratic Approximation of Hamiltonians
• Covariance Dynamics and Entanglement in Translation Invariant Linear Quantum Stochastic Networks
• A Gradient Descent Approach to Optimal Coherent Quantum LQG Controller Design
• Physical Realizability and Mean Square Performance of Translation Invariant Networks of Interacting Linear Quantum Stochastic Systems
• Risk-sensitive Dissipativity of Linear Quantum Stochastic Systems under Lur'e Type Perturbations of Hamiltonians
• Stabilizing Preparation of Quantum Gaussian States via Continuous Measurement
• Implementation of Bilinear Hamiltonian Interactions between Linear Quantum Stochastic Systems via Feedback
• On the generalization of linear least mean squares estimation to quantum systems with non-commutative outputs