Optimal unravellings for feedback control in linear quantum systems

Area of Science:

• Quantum Control
• Information Theory
• Quantum Dynamics

Background:

• Classical feedback control theory is well-established for systems with linear dynamics.
• Quantum systems present unique control challenges due to their inherent properties.
• The role of environmental measurements in quantum control remains an active area of research.

Purpose of the Study:

• To determine the optimal measurement strategy on an environment for quantum control problems.
• To investigate the applicability of classical control theory concepts to quantum systems.
• To identify mathematical frameworks for solving quantum feedback control problems.

Main Methods:

• Formulating the quantum control problem within the stationary linear-quadratic-Gaussian (LQG) framework.
• Utilizing semidefinite programming to find optimal solutions.
• Extending the results to include Markovian feedback control.

Main Results:

• The optimal measurement on the environment for a broad class of quantum control problems can be formulated as a semidefinite program.
• This approach is effective for state-based optimal control problems.
• The derived methods are also applicable to Markovian (current-based) feedback control.

Conclusions:

• Semidefinite programming provides a powerful tool for optimizing quantum feedback control.
• The study bridges classical and quantum control theory by extending applicable frameworks.
• Efficient quantum control strategies can be designed by optimizing environmental measurements.