3 research outputs found
SU(m) non-Abelian anyons in the Jain hierarchy of quantum Hall states
We show that different classes of topological order can be distinguished by
the dynamical symmetry algebra of edge excitations. Fundamental topological
order is realized when this algebra is the largest possible, the algebra of
quantum area-preserving diffeomorphisms, called . We argue that
this order is realized in the Jain hierarchy of fractional quantum Hall states
and show that it is more robust than the standard Abelian Chern-Simons order
since it has a lower entanglement entropy due to the non-Abelian character of
the quasi-particle anyon excitations. These behave as SU() quarks, where
is the number of components in the hierarchy. We propose the topological
entanglement entropy as the experimental measure to detect the existence of
these quantum Hall quarks. Non-Abelian anyons in the fractional
quantum Hall states could be the primary candidates to realize qbits for
topological quantum computation.Comment: 5 pages, no figures, a few typos corrected, a reference adde
Quantum picturalism for topological cluster-state computing
Topological quantum computing is a way of allowing precise quantum
computations to run on noisy and imperfect hardware. One implementation uses
surface codes created by forming defects in a highly-entangled cluster state.
Such a method of computing is a leading candidate for large-scale quantum
computing. However, there has been a lack of sufficiently powerful high-level
languages to describe computing in this form without resorting to single-qubit
operations, which quickly become prohibitively complex as the system size
increases. In this paper we apply the category-theoretic work of Abramsky and
Coecke to the topological cluster-state model of quantum computing to give a
high-level graphical language that enables direct translation between quantum
processes and physical patterns of measurement in a computer - a "compiler
language". We give the equivalence between the graphical and topological
information flows, and show the applicable rewrite algebra for this computing
model. We show that this gives us a native graphical language for the design
and analysis of topological quantum algorithms, and finish by discussing the
possibilities for automating this process on a large scale.Comment: 18 pages, 21 figures. Published in New J. Phys. special issue on
topological quantum computin
On the Quantum Computational Complexity of the Ising Spin Glass Partition Function and of Knot Invariants
It is shown that the canonical problem of classical statistical
thermodynamics, the computation of the partition function, is in the case of
+/-J Ising spin glasses a particular instance of certain simple sums known as
quadratically signed weight enumerators (QWGTs). On the other hand it is known
that quantum computing is polynomially equivalent to classical probabilistic
computing with an oracle for estimating QWGTs. This suggests a connection
between the partition function estimation problem for spin glasses and quantum
computation. This connection extends to knots and graph theory via the
equivalence of the Kauffman polynomial and the partition function for the Potts
model.Comment: 8 pages, incl. 2 figures. v2: Substantially rewritte