Extending robustness and randomization from consensus to symmetrization algorithms

Luca Mazzarella 1 Francesco Ticozzi 1, 2 Alain Sarlette 3
3 QUANTIC - QUANTum Information Circuits
ENS Paris - École normale supérieure - Paris, Inria Paris-Rocquencourt, UPMC - Université Pierre et Marie Curie - Paris 6, MINES ParisTech - École nationale supérieure des mines de Paris, CNRS - Centre National de la Recherche Scientifique : UMR8551
Abstract : This work interprets and generalizes consensus-type algorithms as switching dynam-ics leading to symmetrization of some vector variables with respect to the actions of a finite group.We show how the symmetrization framework we develop covers applications as diverse as consensuson probability distributions (either classical or quantum), uniform random state generation, andopen-loop disturbance rejection by quantum dynamical decoupling. Robust convergence results areexplicitly provided in a group-theoretic formulation, both for deterministic and for randomized dy-namics. This indicates a way to directly extend the robustness and randomization properties ofconsensus-type algorithms to more fields of application.
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Submitted on : Tuesday, December 29, 2015 - 1:46:20 PM
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Luca Mazzarella, Francesco Ticozzi, Alain Sarlette. Extending robustness and randomization from consensus to symmetrization algorithms. SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2015, 53 (4), pp.2076-2099. ⟨10.1137/130945090⟩. ⟨hal-01093934⟩

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