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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-PSL - École normale supérieure - Paris, Inria Paris-Rocquencourt, UPMC - Université Pierre et Marie Curie - Paris 6, Mines Paris - PSL (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
Last modification on : Friday, November 25, 2022 - 7:07:32 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, 2015, 53 (4), pp.2076-2099. ⟨10.1137/130945090⟩. ⟨hal-01093934⟩



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