Exchanging identical particles and topological quantum computing. (arXiv:1810.05208v3 [quant-ph] UPDATED)

The phase factor $(-1)^{2s}$ that features in the exchange symmetry for
identical spin-$s$ fermions or bosons is not simply and automatically equal to
the phase factor one can observe in an interference experiment that involves
physically exchanging two such particles. The observable phase contains, in
general, single-particle geometric and dynamical phases as well, induced by
both spin and spatial exchange transformations. By extending the analysis to
(non-abelian) anyons it is argued that, similarly, there are single-anyon
geometric and dynamical contributions in addition to purely topological unitary
transformations that accompany physical exchanges of anyons. Work remains to be
done in order to demonstrate---if it is still true---that those additional
contributions to the gates in anyonic topological quantum computers do not
destroy the inherent robustness of the ideal gates. This negative result is
described most clearly in terms of the Berry matrix.

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