Quantum Pontryagin Principle under Continuous Measurements and Feedback
This work provides a theoretical framework for optimal control of quantum systems under continuous measurements, which is important for quantum control theory and applications.
The paper develops a quantum Pontryagin principle for continuous measurements and feedback under compatible events, deriving the maximum principle in both Schrödinger and Heisenberg pictures and proposing an LQG scheme to avoid stochastic equations.
In this note we develop the theory of the quantum Pontryagin principle for continuous measurements and feedback. The analysis is carried out under the assumption of compatible events in the output channel. The plant is a quantum system, which generally is in a mixed state, coupled to a continuous measurement channel. The Pontryagin Maximum Principle is derived in both the Schrödinger picture and Heisenberg picture, in particular in statistical moment coordinates. To avoid solving stochastic equations we derive a LQG scheme which is more suitable for control purposes.