3,773 research outputs found
Quantum entanglement, unitary braid representation and Temperley-Lieb algebra
Important developments in fault-tolerant quantum computation using the
braiding of anyons have placed the theory of braid groups at the very
foundation of topological quantum computing. Furthermore, the realization by
Kauffman and Lomonaco that a specific braiding operator from the solution of
the Yang-Baxter equation, namely the Bell matrix, is universal implies that in
principle all quantum gates can be constructed from braiding operators together
with single qubit gates. In this paper we present a new class of braiding
operators from the Temperley-Lieb algebra that generalizes the Bell matrix to
multi-qubit systems, thus unifying the Hadamard and Bell matrices within the
same framework. Unlike previous braiding operators, these new operators
generate {\it directly}, from separable basis states, important entangled
states such as the generalized Greenberger-Horne-Zeilinger states, cluster-like
states, and other states with varying degrees of entanglement.Comment: 5 pages, no figur
Estimating the conditions for polariton condensation in organic thin-film microcavities
We examine the possibility of observing Bose condensation of a confined
two-dimensional polariton gas in an organic quantum well. We deduce a suitable
parameterization of a model Hamiltonian based upon the cavity geometry, the
biexciton binding energy, and similar spectroscopic and structural data. By
converting the sum-over-states to a semiclassical integration over
-dimensional phase space, we show that while an ideal 2-D Bose gas will not
undergo condensation, an interacting gas with the Bogoliubov dispersion
close to will undergo Bose condensation at a given
critical density and temperature. We show that is sensitive
to both the cavity geometry and to the biexciton binding energy. In particular,
for strongly bound biexcitons, the non-linear interaction term appearing in the
Gross-Pitaevskii equation becomes negative and the resulting ground state will
be a localized soliton state rather than a delocalized Bose condensate.Comment: 2 figure
An economic analysis of the short-term rental market: Local regulatory decisions
In recent years, short-term home rental companies such as Airbnb and Vacation Rentals by Owner (VRBO) have grown in popularity throughout the United States and the world. The lack of regulation of this rapid growth, which stemmed from the legal grey area these rentals fall under, caused some states to adopt specific regulatory policies. These regulatory policies attempt to better monitor this sector, to tax rental earnings, and to reduce perceived negative externalities to this new market. This thesis researches the benefits and costs that short-term rentals (STRs) provide to cities and the regulatory implications on the growing rental market. Using census data along with a STR regulatory index developed by the R Street Institute that measure city-level regulations, this paper presents evidence that city-level regulations of STRs were largely unpredictable. Although no widespread common factors explain regulatory decisions, local sales tax rates, residents’ political policy preferences, city population age, and owner-occupied median home values were found to have some influence in explaining variations among cities in short-term rental regulation
Quantum logic as superbraids of entangled qubit world lines
Presented is a topological representation of quantum logic that views
entangled qubit spacetime histories (or qubit world lines) as a generalized
braid, referred to as a superbraid. The crossing of world lines is purely
quantum in nature, most conveniently expressed analytically with
ladder-operator-based quantum gates. At a crossing, independent world lines can
become entangled. Complicated superbraids are systematically reduced by
recursively applying novel quantum skein relations. If the superbraid is closed
(e.g. representing quantum circuits with closed-loop feedback, quantum lattice
gas algorithms, loop or vacuum diagrams in quantum field theory), then one can
decompose the resulting superlink into an entangled superposition of classical
links. In turn, for each member link, one can compute a link invariant, e.g.
the Jones polynomial. Thus, a superlink possesses a unique link invariant
expressed as an entangled superposition of classical link invariants.Comment: 4 page
Knots in interaction
We study the geometry of interacting knotted solitons. The interaction is
local and advances either as a three-body or as a four-body process, depending
on the relative orientation and a degeneracy of the solitons involved. The
splitting and adjoining is governed by a four-point vertex in combination with
duality transformations. The total linking number is preserved during the
interaction. It receives contributions both from the twist and the writhe,
which are variable. Therefore solitons can twine and coil and links can be
formed.Comment: figures now in GIF forma
The Asymptotic Number of Attractors in the Random Map Model
The random map model is a deterministic dynamical system in a finite phase
space with n points. The map that establishes the dynamics of the system is
constructed by randomly choosing, for every point, another one as being its
image. We derive here explicit formulas for the statistical distribution of the
number of attractors in the system. As in related results, the number of
operations involved by our formulas increases exponentially with n; therefore,
they are not directly applicable to study the behavior of systems where n is
large. However, our formulas lend themselves to derive useful asymptotic
expressions, as we show.Comment: 16 pages, 1 figure. Minor changes. To be published in Journal of
Physics A: Mathematical and Genera
Topological quantum gate entangler for a multi-qubit state
We establish a relation between topological and quantum entanglement for a
multi-qubit state by considering the unitary representations of the Artin braid
group. We construct topological operators that can entangle multi-qubit state.
In particular we construct operators that create quantum entanglement for
multi-qubit states based on the Segre ideal of complex multi-projective space.
We also in detail discuss and construct these operators for two-qubit and
three-qubit states.Comment: 6 page
Canonical quantum gravity in the Vassiliev invariants arena: I. Kinematical structure
We generalize the idea of Vassiliev invariants to the spin network context,
with the aim of using these invariants as a kinematical arena for a canonical
quantization of gravity. This paper presents a detailed construction of these
invariants (both ambient and regular isotopic) requiring a significant
elaboration based on the use of Chern-Simons perturbation theory which extends
the work of Kauffman, Martin and Witten to four-valent networks. We show that
this space of knot invariants has the crucial property -from the point of view
of the quantization of gravity- of being loop differentiable in the sense of
distributions. This allows the definition of diffeomorphism and Hamiltonian
constraints. We show that the invariants are annihilated by the diffeomorphism
constraint. In a companion paper we elaborate on the definition of a
Hamiltonian constraint, discuss the constraint algebra, and show that the
construction leads to a consistent theory of canonical quantum gravity.Comment: 21 Pages, RevTex, many figures included with psfi
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
Lens Spaces and Handlebodies in 3D Quantum Gravity
We calculate partition functions for lens spaces L_{p,q} up to p=8 and for
genus 1 and 2 handlebodies H_1, H_2 in the Turaev-Viro framework. These can be
interpreted as transition amplitudes in 3D quantum gravity. In the case of lens
spaces L_{p,q} these are vacuum-to-vacuum amplitudes \O -> \O, whereas for
the 1- and 2-handlebodies H_1, H_2 they represent genuinely topological
transition amplitudes \O -> T^2 and \O -> T^2 # T^2, respectively.Comment: 14 pages, LaTeX, 5 figures, uses eps
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