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

TL;DR

This paper studies the control of open Markovian quantum systems with fast Hamiltonian control, showing how their eigenvalue dynamics can be simplified and used for tasks like cooling, with some controls being time-independent.

Contribution

It introduces a reduction of quantum control systems to eigenvalue dynamics on the simplex, enabling analysis of reachability and stabilizability with applications to cooling.

Findings

Control Hamiltonian can be chosen time-independent for certain tasks.

Eigenvalue dynamics can be modeled on the standard simplex.

Reduction simplifies analysis of quantum state 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.