Quantum Feedback Control: How to use Verification Theorems and Viscosity Solutions to Find Optimal Protocols
arXiv:0808.1102 · doi:10.1080/00107510802601781
Abstract
While feedback control has many applications in quantum systems, finding optimal control protocols for this task is generally challenging. So-called "verification theorems" and "viscosity solutions" provide two useful tools for this purpose: together they give a simple method to check whether any given protocol is optimal, and provide a numerical method for finding optimal protocols. While treatments of verification theorems usually use sophisticated mathematical language, this is not necessary. In this article we give a simple introduction to feedback control in quantum systems, and then describe verification theorems and viscosity solutions in simple language. We also illustrate their use with a concrete example of current interest.
12 pages, revtex4
References in corpus (37)
- Resolving photon number states in a superconducting circuit
- Entanglement-free Heisenberg-limited phase estimation
- A Straightforward Introduction to Continuous Quantum Measurement
- Cooling a nanomechanical resonator with quantum back-action
- Feedback-control of quantum systems using continuous state-estimation
- Generating Single Microwave Photons in a Circuit
- Second Law of Thermodynamics with Discrete Quantum Feedback Control
- Quantum feedback control and classical control theory
- Feedback control of quantum state reduction
- Adaptive homodyne measurement of optical phase
- A simple model of quantum trajectories
- Statistical Inference, Distinguishability of Quantum States, And Quantum Entanglement
- Stabilizing feedback controls for quantum systems
- Feedback cooling of a single trapped ion
- Feedback cooling of a nanomechanical resonator
- Optimal Unravellings for Feedback Control in Linear Quantum Systems
- Quantum Kalman Filtering and the Heisenberg Limit in Atomic Magnetometry
- Deterministic single photons via conditional quantum evolution
- Quantum Feedback Control of Atomic Motion in an Optical Cavity
- Information Tradeoff Relations for Finite-Strength Quantum Measurements
- Information, disturbance and Hamiltonian quantum feedback control
- Stochastic Schrodinger equations
- How to project qubits faster using quantum feedback
- A practical scheme for error control using feedback
- Feedback stabilization of quantum ensembles: a global convergence analysis on complex flag manifolds
- Bellman equations for optimal feedback control of qubit states
- Hamilton-Jacobi-Bellman equations for Quantum Filtering and Control
- Reconsidering Rapid Qubit Purification by Feedback
- Parametrization of the feedback Hamiltonian realizing a pure steady state
- Rapid Measurement of Quantum Systems using Feedback Control
- Quantum feedback cooling of a single trapped ion in front of a mirror
- Locally Optimal Control of Quantum Systems with Strong Feedback
- Feedback control of spin systems
- Efficient feedback controllers for continuous-time quantum error correction
- Single-bit Feedback and Quantum Dynamical Decoupling
- Effects of Measurement back-action in the stabilization of a Bose-Einstein condensate through feedback
- Weak measurement and rapid state reduction in bipartite quantum systems
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- Control of quantum phenomena: Past, present, and future
- Quantum control theory and applications: A survey
- Modeling and Control of Quantum Systems: An Introduction
- Direct and Indirect Couplings in Coherent Feedback Control of Linear Quantum Systems
- Fluctuation theorems in presence of information gain and feedback
- Feedback Control Using Only Quantum Back-Action
- Deterministic generation of remote entanglement with active quantum feedback
- Dynamical programming of continuously observed quantum systems
- The Quantum Theory of MIMO Markovian Feedback with Diffusive Measurements
- Atomic Quantum Technologies for Quantum Matter and Fundamental Physics Applications
- Coherent vs. measurement-based feedback for controlling a single qubit
- Maximum information gain in weak or continuous measurements of qudits: complementarity is not enough
- Optimality of qubit purification protocols in the presence of imperfections
- Optimal Zeno Dragging for Quantum Control: A Shortcut to Zeno with Action-based Scheduling Optimization
- Generalized entropy production fluctuation theorems for quantum systems
- Enforcing dissipative entanglement by feedback
- A wave-function Monte Carlo method for simulating conditional master equations
- Optimality of feedback control for qubit purification under inefficient measurement
- Quantum feedback control in quantum photosynthesis
- Quantum Pontryagin Principle under Continuous Measurements and Feedback
- Global versus local optimality in feedback-controlled qubit purification: new insights from minimizing Rényi entropies
- Optimal measurement-based feedback control for a single qubit: a candidate protocol
- Noise-Canceling Quantum Feedback: non-Hermitian Dynamics with Applications to State Preparation and Magic State Distillation