113 research outputs found
Numerical Analysis of Quasiholes of the Moore-Read Wavefunction
We demonstrate numerically that non-Abelian quasihole excitations of the fractional quantum Hall state have some of the key properties necessary
to support quantum computation. We find that as the quasihole spacing is
increased, the unitary transformation which describes winding two quasiholes
around each other converges exponentially to its asymptotic limit and that the
two orthogonal wavefunctions describing a system with four quasiholes become
exponentially degenerate. We calculate the length scales for these two decays
to be and
respectively. Additionally we determine which fusion channel is lower in energy
when two quasiholes are brought close together.Comment: 4 pages, 3 figure
Resources Required for Topological Quantum Factoring
We consider a hypothetical topological quantum computer where the qubits are
comprised of either Ising or Fibonacci anyons. For each case, we calculate the
time and number of qubits (space) necessary to execute the most computationally
expensive step of Shor's algorithm, modular exponentiation. For Ising anyons,
we apply Bravyi's distillation method [S. Bravyi, Phys. Rev. A 73, 042313
(2006)] which combines topological and non-topological operations to allow for
universal quantum computation. With reasonable restrictions on the physical
parameters we find that factoring a 128 bit number requires approximately 10^3
Fibonacci anyons versus at least 3 x 10^9 Ising anyons. Other distillation
algorithms could reduce the resources for Ising anyons substantially.Comment: 4+epsilon pages, 4 figure
Coulomb drag at \nu = 1/2: Composite fermion pairing fluctuations
We consider the Coulomb drag between two two-dimensional electron layers at
filling factor \nu = 1/2 each, using a strong coupling approach within the
composite fermion picture. Due to an attractive interlayer interaction,
composite fermions are expected to form a paired state below a critical
temperature T_c. We find that above T_c pairing fluctuations make the
longitudinal transresistivity \rho_D increase with decreasing temperature. The
pairing mechanism we study is very sensitive to density variations in the two
layers, and to an applied current. We discuss possible relation to an
experiment by Lilly et al. [Phys. Rev. Lett. 80, 1714 (1998)].Comment: REVTeX, 4 pages, 1 figur
Spin-pairing instabilities at the coincidence of two Landau levels
The effect of interactions near the coincidence of two Landau levels with
opposite spins at filling factor 1/2 is investigated. By mapping to Composite
Fermions it is shown that the fluctuations of the gauge field induces an
effective attractive Fermion interaction. This can lead to a spin-singlet
ground state that is separated from the excited states by a gap. The magnitude
of the gap is evaluated. The results are consistent with the recently observed
half-polarized states in the FQHE at a fixed filling factor. It is suggested
that similar anomalies exist for other spin configurations in degenerate
spin-up and spin-down Landau levels. An experiment for testing the spin-singlet
state is proposed.Comment: to be published in Physical Review
Topological Quantum Computing with Only One Mobile Quasiparticle
In a topological quantum computer, universal quantum computation is performed
by dragging quasiparticle excitations of certain two dimensional systems around
each other to form braids of their world lines in 2+1 dimensional space-time.
In this paper we show that any such quantum computation that can be done by
braiding identical quasiparticles can also be done by moving a single
quasiparticle around n-1 other identical quasiparticles whose positions remain
fixed.Comment: 4 pages, 5 figure
Coulomb drag as a signature of the paired quantum Hall state
Motivated by the recent Coulomb drag experiment of M. P. Lilly et. al, we
study the Coulomb drag in a two-layer system with Landau level filling factor
. We find that the drag conductivity in the incompressible paired
quantum Hall state at zero temperature can be finite. The drag conductivity is
also greatly enhanced above , at which the transition between the weakly
coupled compressible liquids and the paired quantum Hall liquid takes place. We
discuss the implications of our results for the recent experiment.Comment: 4 pages, 1 figure included, replaced by the published versio
Braid Topologies for Quantum Computation
In topological quantum computation, quantum information is stored in states
which are intrinsically protected from decoherence, and quantum gates are
carried out by dragging particle-like excitations (quasiparticles) around one
another in two space dimensions. The resulting quasiparticle trajectories
define world-lines in three dimensional space-time, and the corresponding
quantum gates depend only on the topology of the braids formed by these
world-lines. We show how to find braids that yield a universal set of quantum
gates for qubits encoded using a specific kind of quasiparticle which is
particularly promising for experimental realization.Comment: 4 pages, 4 figures, minor revision
Topological Quantum Compiling
A method for compiling quantum algorithms into specific braiding patterns for
non-Abelian quasiparticles described by the so-called Fibonacci anyon model is
developed. The method is based on the observation that a universal set of
quantum gates acting on qubits encoded using triplets of these quasiparticles
can be built entirely out of three-stranded braids (three-braids). These
three-braids can then be efficiently compiled and improved to any required
accuracy using the Solovay-Kitaev algorithm.Comment: 20 pages, 20 figures, published versio
Universal Leakage Elimination
``Leakage'' errors are particularly serious errors which couple states within
a code subspace to states outside of that subspace thus destroying the error
protection benefit afforded by an encoded state. We generalize an earlier
method for producing leakage elimination decoupling operations and examine the
effects of the leakage eliminating operations on decoherence-free or noiseless
subsystems which encode one logical, or protected qubit into three or four
qubits. We find that by eliminating the large class of leakage errors, under
some circumstances, we can create the conditions for a decoherence free
evolution. In other cases we identify a combination decoherence-free and
quantum error correcting code which could eliminate errors in solid-state
qubits with anisotropic exchange interaction Hamiltonians and enable universal
quantum computing with only these interactions.Comment: 14 pages, no figures, new version has references updated/fixe
The J_1-J_2 antiferromagnet with Dzyaloshinskii-Moriya interaction on the square lattice: An exact diagonalization study
We examine the influence of an anisotropic interaction term of
Dzyaloshinskii-Moriya (DM) type on the groundstate ordering of the J_1-J_2
spin-1/2-Heisenberg antiferromagnet on the square lattice. For the DM term we
consider several symmetries corresponding to different crystal structures. For
the pure J_1-J_2 model there are strong indications for a quantum spin liquid
in the region of 0.4 < J_2/J_1 < 0.65. We find that a DM interaction influences
the breakdown of the conventional antiferromagnetic order by i) shifting the
spin liquid region, ii) changing the isotropic character of the groundstate
towards anisotropic correlations and iii) creating for certain symmetries a net
ferromagnetic moment.Comment: 7 pages, RevTeX, 6 ps-figures, to appear in J. Phys.: Cond. Ma
- …