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

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2 Author(s)
Bolognani, S. ; Dipt. di Ing. dell''Inf., Univ. di Padova, Padova, Italy ; Ticozzi, F.

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.

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Automatic Control, IEEE Transactions on  (Volume:55 ,  Issue: 12 )