81,275 research outputs found
Thermalization, Error-Correction, and Memory Lifetime for Ising Anyon Systems
We consider two-dimensional lattice models that support Ising anyonic
excitations and are coupled to a thermal bath. We propose a phenomenological
model for the resulting short-time dynamics that includes pair-creation,
hopping, braiding, and fusion of anyons. By explicitly constructing topological
quantum error-correcting codes for this class of system, we use our
thermalization model to estimate the lifetime of the quantum information stored
in the encoded spaces. To decode and correct errors in these codes, we adapt
several existing topological decoders to the non-Abelian setting. We perform
large-scale numerical simulations of these two-dimensional Ising anyon systems
and find that the thresholds of these models range between 13% to 25%. To our
knowledge, these are the first numerical threshold estimates for quantum codes
without explicit additive structure.Comment: 34 pages, 9 figures; v2 matches the journal version and corrects a
misstatement about the detailed balance condition of our Metropolis
simulations. All conclusions from v1 are unaffected by this correctio
Complexity, parallel computation and statistical physics
The intuition that a long history is required for the emergence of complexity
in natural systems is formalized using the notion of depth. The depth of a
system is defined in terms of the number of parallel computational steps needed
to simulate it. Depth provides an objective, irreducible measure of history
applicable to systems of the kind studied in statistical physics. It is argued
that physical complexity cannot occur in the absence of substantial depth and
that depth is a useful proxy for physical complexity. The ideas are illustrated
for a variety of systems in statistical physics.Comment: 21 pages, 7 figure
Parallel Algorithm and Dynamic Exponent for Diffusion-limited Aggregation
A parallel algorithm for ``diffusion-limited aggregation'' (DLA) is described
and analyzed from the perspective of computational complexity. The dynamic
exponent z of the algorithm is defined with respect to the probabilistic
parallel random-access machine (PRAM) model of parallel computation according
to , where L is the cluster size, T is the running time, and the
algorithm uses a number of processors polynomial in L\@. It is argued that
z=D-D_2/2, where D is the fractal dimension and D_2 is the second generalized
dimension. Simulations of DLA are carried out to measure D_2 and to test
scaling assumptions employed in the complexity analysis of the parallel
algorithm. It is plausible that the parallel algorithm attains the minimum
possible value of the dynamic exponent in which case z characterizes the
intrinsic history dependence of DLA.Comment: 24 pages Revtex and 2 figures. A major improvement to the algorithm
and smaller dynamic exponent in this versio
Stochastic gauge: a new technique for quantum simulations
We review progress towards direct simulation of quantum dynamics in many-body
systems, using recently developed stochastic gauge techniques. We consider
master equations, canonical ensemble calculations and reversible quantum
dynamics are compared, as well the general question of strategies for choosing
the gauge.Comment: 11 pages, 2 figures, to be published in Proceedings of the 16th
International Conference on Laser Spectroscopy (ICOLS), Palm Cove, Australia
(2003
Track clustering with a quantum annealer for primary vertex reconstruction at hadron colliders
Clustering of charged particle tracks along the beam axis is the first step
in reconstructing the positions of hadronic interactions, also known as primary
vertices, at hadron collider experiments. We use a 2036 qubit D-Wave quantum
annealer to perform track clustering in a limited capacity on artificial events
where the positions of primary vertices and tracks resemble those measured by
the Compact Muon Solenoid experiment at the Large Hadron Collider. The
algorithm, which is not a classical-quantum hybrid but relies entirely on
quantum annealing, is tested on a variety of event topologies from 2 primary
vertices and 10 tracks up to 5 primary vertices and 15 tracks. It is
benchmarked against simulated annealing executed on a commercial CPU
constrained to the same processor time per anneal as time in the physical
annealer, and performance is found to be comparable for small numbers of
vertices with an intriguing advantage noted for 2 vertices and 16 tracks
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