Extending robustness & randomization from Consensus to Symmetrization Algorithms
Quantum Physics
2015-06-17 v3
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.
Cite
@article{arxiv.1311.3364,
title = {Extending robustness & randomization from Consensus to Symmetrization Algorithms},
author = {Luca Mazzarella and Francesco Ticozzi and Alain Sarlette},
journal= {arXiv preprint arXiv:1311.3364},
year = {2015}
}