Variational approach to the optimal control of coherently driven, open quantum system dynamics

TL;DR

This paper introduces a variational method for optimal control of open quantum systems, leveraging Hamiltonian eigenframe reformulation to minimize costs like time and heat loss, demonstrated on two-level systems with thermal baths.

Contribution

It develops a novel variational control technique in the Hamiltonian eigenframe for open quantum systems, enabling efficient cost minimization.

Findings

Effective control strategies for two-level systems are derived.

The method reduces heat and time costs in quantum thermodynamic processes.

Applicable to systems interacting with bosonic or fermionic environments.

Abstract

Quantum coherence inherently affects the dynamics and the performances of a quantum machine. Coherent control can, at least in principle, enhance the work extraction and boost the velocity of evolution in an open quantum system. Using advanced tools from the calculus of variations and reformulating the control problem in the instantaneous Hamiltonian eigenframe, we develop a general technique for minimizing a wide class of cost functionals when the external control has access to full rotations of the system Hamiltonian. The method is then applied both to time and heat loss minimization problems and explicitly solved in the case of a two level system in contact with either bosonic or fermionic thermal environments.