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arXiv · 1311.3364

Extending robustness & randomization from Consensus to Symmetrization Algorithms

Luca Mazzarella·Francesco Ticozzi·Alain Sarlette
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Abstract

This work interprets and generalizes consensus-type algorithms as switching dynamics 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 consensus on probability distributions (either classical or quantum), uniform random state generation, and open-loop disturbance rejection by quantum dynamical decoupling. Robust convergence results are explicitly provided in a group-theoretic formulation, both for deterministic and for randomized dynamics. This indicates a way to directly extend the robustness and randomization properties of consensus-type algorithms to more fields of application.

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Luca Mazzarella, Francesco Ticozzi, Alain Sarlette. 2013-11-14. Extending robustness & randomization from Consensus to Symmetrization Algorithms. https://arxiv.org/abs/1311.3364

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