Engineering Stable Discrete-Time Quantum Dynamics via a Canonical QR Decomposition

Saverio Bolognani, Francesco Ticozzi

Published Jan 1, 2009• 29 citations

Abstract

We analyze the asymptotic behavior of discretetime, Markovian quantum systems with respect to a subspace of interest. Global asymptotic stability of subspaces is relevant to quantum information processing, in particular for initializing the system in pure states or subspace codes. We provide a linearalgebraic characterization of the dynamical properties leading to invariance and attractivity of a given quantum subspace. We then construct a design algorithm for discrete-time feedback control that allows to stabilize a target subspace, proving that if the control problem is feasible, then the algorithm returns an effective control choice. In order to prove this result, a canonical QR matrix decomposition is derived, and also used to establish the control scheme potential for the simulation of open-system dynamics.

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