Engineering Stable Discrete-Time Quantum Dynamics via a Canonical QR Decomposition
Abstract
We analyze the asymptotic behavior of discrete-time, 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 linear-algebraic 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.
Cite
@article{arxiv.0908.2078,
title = {Engineering Stable Discrete-Time Quantum Dynamics via a Canonical QR Decomposition},
author = {Saverio Bolognani and Francesco Ticozzi},
journal= {arXiv preprint arXiv:0908.2078},
year = {2014}
}
Comments
12 pages, 1 figure