11,009 research outputs found
Anyonic interferometry and protected memories in atomic spin lattices
Strongly correlated quantum systems can exhibit exotic behavior called
topological order which is characterized by non-local correlations that depend
on the system topology. Such systems can exhibit remarkable phenomena such as
quasi-particles with anyonic statistics and have been proposed as candidates
for naturally fault-tolerant quantum computation. Despite these remarkable
properties, anyons have never been observed in nature directly. Here we
describe how to unambiguously detect and characterize such states in recently
proposed spin lattice realizations using ultra-cold atoms or molecules trapped
in an optical lattice. We propose an experimentally feasible technique to
access non-local degrees of freedom by performing global operations on trapped
spins mediated by an optical cavity mode. We show how to reliably read and
write topologically protected quantum memory using an atomic or photonic qubit.
Furthermore, our technique can be used to probe statistics and dynamics of
anyonic excitations.Comment: 14 pages, 6 figure
Holonomic quantum computing in symmetry-protected ground states of spin chains
While solid-state devices offer naturally reliable hardware for modern
classical computers, thus far quantum information processors resemble vacuum
tube computers in being neither reliable nor scalable. Strongly correlated many
body states stabilized in topologically ordered matter offer the possibility of
naturally fault tolerant computing, but are both challenging to engineer and
coherently control and cannot be easily adapted to different physical
platforms. We propose an architecture which achieves some of the robustness
properties of topological models but with a drastically simpler construction.
Quantum information is stored in the symmetry-protected degenerate ground
states of spin-1 chains, while quantum gates are performed by adiabatic
non-Abelian holonomies using only single-site fields and nearest-neighbor
couplings. Gate operations respect the symmetry, and so inherit some protection
from noise and disorder from the symmetry-protected ground states.Comment: 19 pages, 4 figures. v2: published versio
Accidental Degeneracy and Berry Phase of Resonant States
We study the complex geometric phase acquired by the resonant states of an
open quantum system which evolves irreversibly in a slowly time dependent
environment. In analogy with the case of bound states, the Berry phase factors
of resonant states are holonomy group elements of a complex line bundle with
structure group C*. In sharp contrast with bound states, accidental
degeneracies of resonances produce a continuous closed line of singularities
formally equivalent to a continuous distribution of "magnetic" charge on a
"diabolical" circle, in consequence, we find different classes of topologically
inequivalent non-trivial closed paths in parameter space.Comment: 23 pages, 2 Postscript figures, LaTex, to be published in: Group 21:
Symposium on Semigroups and Quantum Irreversibility (Proc. of the XXI Int.
Colloquium on Group Theoretical Methods in Physics
Refocusing schemes for holonomic quantum computation in presence of dissipation
The effects of dissipation on a holonomic quantum computation scheme are
analyzed within the quantum-jump approach. We extend to the non-Abelian case
the refocusing strategies formerly introduced for (Abelian) geometric
computation. We show how double loop symmetrization schemes allow one to get
rid of the unwanted influence of dissipation in the no-jump trajectory.Comment: 4 pages, revtex
The Final Remnant of Binary Black Hole Mergers: Multipolar Analysis
Methods are presented to define and compute source multipoles of dynamical
horizons in numerical relativity codes, extending previous work from the
isolated and dynamical horizon formalisms in a manner that allows for the
consideration of horizons that are not axisymmetric. These methods are then
applied to a binary black hole merger simulation, providing evidence that the
final remnant is a Kerr black hole, both through the (spatially)
gauge-invariant recovery of the geometry of the apparent horizon, and through a
detailed extraction of quasinormal ringing modes directly from the strong-field
region.Comment: 12 pages, 13 figures. Published version. Some references have been
added and reordered, and the figures cleaned up
Topological Protection and Quantum Noiseless Subsystems
Encoding and manipulation of quantum information by means of topological
degrees of freedom provides a promising way to achieve natural fault-tolerance
that is built-in at the physical level. We show that this topological approach
to quantum information processing is a particular instance of the notion of
computation in a noiseless quantum subsystem. The latter then provide the most
general conceptual framework for stabilizing quantum information and for
preserving quantum coherence in topological and geometric systems.Comment: 4 Pages LaTeX. Published versio
Almost any quantum spin system with short-range interactions can support toric codes
Inspired by Kitaev's argument that physical error correction is possible in a
system of interacting anyons, we demonstrate that such "self-correction" is
fairly common in spin systems with classical Hamiltonians that admit the
Peierls argument and where errors are modelled by quantum perturbations.Comment: 8 pages; elsart.sty; revised version submitted to Phys. Lett.
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