2,753 research outputs found
Enumerating Abelian Returns to Prefixes of Sturmian Words
We follow the works of Puzynina and Zamboni, and Rigo et al. on abelian
returns in Sturmian words. We determine the cardinality of the set
of abelian returns of all prefixes of a Sturmian word in
terms of the coefficients of the continued fraction of the slope, dependingly
on the intercept. We provide a simple algorithm for finding the set
and we determine it for the characteristic Sturmian words.Comment: 19page
Resource Letter GPP-1: Geometric Phases in Physics
This Resource Letter provides a guide to the literature on the geometric
angles and phases in classical and quantum physics. Journal articles and books
are cited for the following topics: anticipations of the geometric phase,
foundational derivations and formulations, books and review articles on the
subject, and theoretical and experimental elaborations and applications.Comment: 13 pages (TeX); some new references adde
Non-Abelian statistics and topological quantum information processing in 1D wire networks
Topological quantum computation provides an elegant way around decoherence,
as one encodes quantum information in a non-local fashion that the environment
finds difficult to corrupt. Here we establish that one of the key
operations---braiding of non-Abelian anyons---can be implemented in
one-dimensional semiconductor wire networks. Previous work [Lutchyn et al.,
arXiv:1002.4033 and Oreg et al., arXiv:1003.1145] provided a recipe for driving
semiconducting wires into a topological phase supporting long-sought particles
known as Majorana fermions that can store topologically protected quantum
information. Majorana fermions in this setting can be transported, created, and
fused by applying locally tunable gates to the wire. More importantly, we show
that networks of such wires allow braiding of Majorana fermions and that they
exhibit non-Abelian statistics like vortices in a p+ip superconductor. We
propose experimental setups that enable the Majorana fusion rules to be probed,
along with networks that allow for efficient exchange of arbitrary numbers of
Majorana fermions. This work paves a new path forward in topological quantum
computation that benefits from physical transparency and experimental realism.Comment: 6 pages + 17 pages of Supp. Mat.; 10 figures. Supp. Mat. has doubled
in size to establish results more rigorously; many other improvements as wel
- …