Discrete-Time Controllability for Feedback Quantum Dynamics

TL;DR

This paper investigates the controllability of discrete-time quantum systems, demonstrating that feedback control enables asymptotic state transitions and, under certain conditions, finite-time controllability with a linear time scale.

Contribution

It introduces conditions under which finite-time controllability is achievable in discrete-time quantum systems and provides a method to design control actions.

Findings

Feedback control enables arbitrary asymptotic state-to-state transitions.

Finite-time controllability can be achieved with linear scaling in system dimension.

An iterative procedure for designing control actions is provided.

Abstract

Controllability properties for discrete-time, Markovian quantum dynamics are investigated. We find that, while in general the controlled system is not finite-time controllable, feedback control allows for arbitrary asymptotic state-to-state transitions. Under further assumption on the form of the measurement, we show that finite-time controllability can be achieved in a time that scales linearly with the dimension of the system, and we provide an iterative procedure to design the unitary control actions.