26 research outputs found
Quantum Computing via The Bethe Ansatz
We recognize quantum circuit model of computation as factorisable scattering
model and propose that a quantum computer is associated with a quantum
many-body system solved by the Bethe ansatz. As an typical example to support
our perspectives on quantum computation, we study quantum computing in
one-dimensional nonrelativistic system with delta-function interaction, where
the two-body scattering matrix satisfies the factorisation equation (the
quantum Yang--Baxter equation) and acts as a parametric two-body quantum gate.
We conclude by comparing quantum computing via the factorisable scattering with
topological quantum computing.Comment: 6 pages. Comments welcom
Universal Baxterization for -graded Hopf algebras
We present a method for Baxterizing solutions of the constant Yang-Baxter
equation associated with -graded Hopf algebras. To demonstrate the
approach, we provide examples for the Taft algebras and the quantum group
.Comment: 8 page
Quantum Algebras Associated With Bell States
The antisymmetric solution of the braided Yang--Baxter equation called the
Bell matrix becomes interesting in quantum information theory because it can
generate all Bell states from product states. In this paper, we study the
quantum algebra through the FRT construction of the Bell matrix. In its four
dimensional representations via the coproduct of its two dimensional
representations, we find algebraic structures including a composition series
and a direct sum of its two dimensional representations to characterize this
quantum algebra. We also present the quantum algebra using the FRT construction
of Yang--Baxterization of the Bell matrix.Comment: v1: 15 pages, 2 figures, latex; v2: 18 pages, 2 figures, latex,
references and notes adde
Generating W states with braiding operators
Braiding operators can be used to create entangled states out of product
states, thus establishing a correspondence between topological and quantum
entanglement. This is well-known for maximally entangled Bell and GHZ states
and their equivalent states under Stochastic Local Operations and Classical
Communication, but so far a similar result for W states was missing. Here we
use generators of extraspecial 2-groups to obtain the W state in a four-qubit
space and partition algebras to generate the W state in a three-qubit space. We
also present a unitary generalized Yang-Baxter operator that embeds the W
state in a -qubit space.Comment: 13 pages, Published versio
Representations of the quantum doubles of finite group algebras and solutions of the Yang--Baxter equation
Quantum doubles of finite group algebras form a class of quasi-triangular
Hopf algebras which algebraically solve the Yang--Baxter equation. Each
representation of the quantum double then gives a matrix solution of the
Yang--Baxter equation. Such solutions do not depend on a spectral parameter,
and to date there has been little investigation into extending these solutions
such that they do depend on a spectral parameter. Here we first explicitly
construct the matrix elements of the generators for all irreducible
representations of quantum doubles of the dihedral groups . These results
may be used to determine constant solutions of the Yang--Baxter equation. We
then discuss Baxterisation ans\"atze to obtain solutions of the Yang--Baxter
equation with spectral parameter and give several examples, including a new
21-vertex model. We also describe this approach in terms of minimal-dimensional
representations of the quantum doubles of the alternating group and the
symmetric group .Comment: 19 pages, no figures, changed introduction, added reference