Reachability, Coolability, and Stabilizability of Open Markovian Quantum Systems with Fast Unitary Control

Abstract

Open Markovian quantum systems with fast and full Hamiltonian control can be reduced to an equivalent control system on the standard simplex modelling the dynamics of the eigenvalues of the density matrix describing the quantum state. We explore this reduced control system for answering questions on reachability and stabilizability with immediate applications to the cooling of Markovian quantum systems. We show that for certain tasks of interest, the control Hamiltonian can be chosen time-independent. -- The reduction picture is an example of dissipative interconversion between equivalence classes of states, where the classes are induced by fast controls.

38 pages, one figure

References in corpus (2)

• Time-optimal synthesis of unitary transformations in coupled fast and slow qubit system
• Exploring the Limits of Controlled Markovian Quantum Dynamics with Thermal Resources

Cited by in corpus (1)

• Bringing Quantum Systems under Control: A Tutorial Invitation to Quantum Computing and Its Relation to Bilinear Control Systems