139 research outputs found
Braid Matrices and Quantum Gates for Ising Anyons Topological Quantum Computation
We study various aspects of the topological quantum computation scheme based
on the non-Abelian anyons corresponding to fractional quantum hall effect
states at filling fraction 5/2 using the Temperley-Lieb recoupling theory.
Unitary braiding matrices are obtained by a normalization of the degenerate
ground states of a system of anyons, which is equivalent to a modification of
the definition of the 3-vertices in the Temperley-Lieb recoupling theory as
proposed by Kauffman and Lomonaco. With the braid matrices available, we
discuss the problems of encoding of qubit states and construction of quantum
gates from the elementary braiding operation matrices for the Ising anyons
model. In the encoding scheme where 2 qubits are represented by 8 Ising anyons,
we give an alternative proof of the no-entanglement theorem given by Bravyi and
compare it to the case of Fibonacci anyons model. In the encoding scheme where
2 qubits are represented by 6 Ising anyons, we construct a set of quantum gates
which is equivalent to the construction of Georgiev.Comment: 25 pages, 13 figure
Obtaining localization properties efficiently using the Kubo-Greenwood formalism
We establish, through numerical calculations and comparisons with a recursive
Green's function based implementation of the Landauer-B\"uttiker formalism, an
efficient method for studying Anderson localization in quasi-one-dimensional
and two-dimensional systems using the Kubo-Greenwood formalism. Although the
recursive Green's function method can be used to obtain the localization length
of a mesoscopic conductor, it is numerically very expensive for systems that
contain a large number of atoms transverse to the transport direction. On the
other hand, linear-scaling has been achieved with the Kubo-Greenwood method,
enabling the study of effectively two-dimensional systems. While the
propagating length of the charge carriers will eventually saturate to a finite
value in the localized regime, the conductances given by the Kubo-Greenwood
method and the recursive Green's function method agree before the saturation.
The converged value of the propagating length is found to be directly
proportional to the localization length obtained from the exponential decay of
the conductance.Comment: 7 pages, 6 figure
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