3,001 research outputs found
An algorithm for simulating the Ising model on a type-II quantum computer
Presented here is an algorithm for a type-II quantum computer which simulates
the Ising model in one and two dimensions. It is equivalent to the Metropolis
Monte-Carlo method and takes advantage of quantum superposition for random
number generation. This algorithm does not require the ensemble of states to be
measured at the end of each iteration, as is required for other type-II
algorithms. Only the binary result is measured at each node which means this
algorithm could be implemented using a range of different quantum computing
architectures. The Ising model provides an example of how cellular automata
rules can be formulated to be run on a type-II quantum computer.Comment: 14 pages, 11 figures. Accepted for publication in Computer Physics
Communication
Simulating Ising Spin Glasses on a Quantum Computer
A linear-time algorithm is presented for the construction of the Gibbs
distribution of configurations in the Ising model, on a quantum computer. The
algorithm is designed so that each run provides one configuration with a
quantum probability equal to the corresponding thermodynamic weight. The
partition function is thus approximated efficiently. The algorithm neither
suffers from critical slowing down, nor gets stuck in local minima. The
algorithm can be A linear-time algorithm is presented for the construction of
the Gibbs distribution of configurations in the Ising model, on a quantum
computer. The algorithm is designed so that each run provides one configuration
with a quantum probability equal to the corresponding thermodynamic weight. The
partition function is thus approximated efficiently. The algorithm neither
suffers from critical slowing down, nor gets stuck in local minima. The
algorithm can be applied in any dimension, to a class of spin-glass Ising
models with a finite portion of frustrated plaquettes, diluted Ising models,
and models with a magnetic field. applied in any dimension, to a class of
spin-glass Ising models with a finite portion of frustrated plaquettes, diluted
Ising models, and models with a magnetic field.Comment: 24 pages, 3 epsf figures, replaced with published and significantly
revised version. More info available at http://www.fh.huji.ac.il/~dani/ and
http://www.fiz.huji.ac.il/staff/acc/faculty/biha
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
Chaos and Complexity of quantum motion
The problem of characterizing complexity of quantum dynamics - in particular
of locally interacting chains of quantum particles - will be reviewed and
discussed from several different perspectives: (i) stability of motion against
external perturbations and decoherence, (ii) efficiency of quantum simulation
in terms of classical computation and entanglement production in operator
spaces, (iii) quantum transport, relaxation to equilibrium and quantum mixing,
and (iv) computation of quantum dynamical entropies. Discussions of all these
criteria will be confronted with the established criteria of integrability or
quantum chaos, and sometimes quite surprising conclusions are found. Some
conjectures and interesting open problems in ergodic theory of the quantum many
problem are suggested.Comment: 45 pages, 22 figures, final version, at press in J. Phys. A, special
issue on Quantum Informatio
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