Stabilization of Stochastic Quantum Dynamics via Open and Closed Loop Control

TL;DR

This paper explores methods for stabilizing quantum states using open-loop and feedback control, demonstrating conditions where feedback is unnecessary and providing new feedback strategies when needed.

Contribution

It introduces parametrization-free solutions for quantum state stabilization and generalizes feedback control laws for quantum systems.

Findings

Dissipative effects can stabilize states without feedback.

Constructive conditions for open-loop control are derived.

New feedback control laws are proposed for complex stabilization tasks.

Abstract

In this paper we investigate parametrization-free solutions of the problem of quantum pure state preparation and subspace stabilization by means of Hamiltonian control, continuous measurement and quantum feedback, in the presence of a Markovian environment. In particular, we show that whenever suitable dissipative effects are induced either by the unmonitored environment or by non Hermitian measurements, there is no need for feedback control to accomplish the task. Constructive necessary and sufficient conditions on the form of the open-loop controller can be provided in this case. When open-loop control is not sufficient, filtering-based feedback control laws steering the evolution towards a target pure state are provided, which generalize those available in the literature.