659 research outputs found
Proposed experiments to probe the non-abelian \nu=5/2 quantum Hall state
We propose several experiments to test the non-abelian nature of
quasi-particles in the fractional quantum Hall state of \nu=5/2. One set of
experiments studies interference contribution to back-scattering of current,
and is a simplified version of an experiment suggested recently. Another set
looks at thermodynamic properties of a closed system. Both experiments are only
weakly sensitive to disorder-induced distribution of localized quasi-particles.Comment: Additional references and an improved figure, 5 page
Connection Formulae for Asymptotics of Solutions of the Degenerate Third Painlev\'{e} Equation. I
The degenerate third Painlev\'{e} equation, , where ,
and , and the associated tau-function are studied via the
Isomonodromy Deformation Method. Connection formulae for asymptotics of the
general as and solution and general regular as and solution are obtained.Comment: 40 pages, LaTeX2
Quantum simulators, continuous-time automata, and translationally invariant systems
The general problem of finding the ground state energy of lattice
Hamiltonians is known to be very hard, even for a quantum computer. We show
here that this is the case even for translationally invariant systems. We also
show that a quantum computer can be built in a 1D chain with a fixed,
translationally invariant Hamitonian consisting of nearest--neighbor
interactions only. The result of the computation is obtained after a prescribed
time with high probability.Comment: partily rewritten and important references include
Entanglement purification for Quantum Computation
We show that thresholds for fault-tolerant quantum computation are solely
determined by the quality of single-system operations if one allows for
d-dimensional systems with . Each system serves to store one
logical qubit and additional auxiliary dimensions are used to create and purify
entanglement between systems. Physical, possibly probabilistic two-system
operations with error rates up to 2/3 are still tolerable to realize
deterministic high quality two-qubit gates on the logical qubits. The
achievable error rate is of the same order of magnitude as of the single-system
operations. We investigate possible implementations of our scheme for several
physical set-ups.Comment: 4 pages, 1 figure; V2: references adde
An Isomonodromy Cluster of Two Regular Singularities
We consider a linear matrix ODE with two coalescing regular
singularities. This coalescence is restricted with an isomonodromy condition
with respect to the distance between the merging singularities in a way
consistent with the ODE. In particular, a zero-distance limit for the ODE
exists. The monodromy group of the limiting ODE is calculated in terms of the
original one. This coalescing process generates a limit for the corresponding
nonlinear systems of isomonodromy deformations. In our main example the latter
limit reads as , where is the -th Painlev\'e equation. We
also discuss some general problems which arise while studying the
above-mentioned limits for the Painlev\'e equations.Comment: 44 pages, 8 figure
Exploring Contractor Renormalization: Tests on the 2-D Heisenberg Antiferromagnet and Some New Perspectives
Contractor Renormalization (CORE) is a numerical renormalization method for
Hamiltonian systems that has found applications in particle and condensed
matter physics. There have been few studies, however, on further understanding
of what exactly it does and its convergence properties. The current work has
two main objectives. First, we wish to investigate the convergence of the
cluster expansion for a two-dimensional Heisenberg Antiferromagnet(HAF). This
is important because the linked cluster expansion used to evaluate this formula
non-perturbatively is not controlled by a small parameter. Here we present a
study of three different blocking schemes which reveals some surprises and in
particular, leads us to suggest a scheme for defining successive terms in the
cluster expansion. Our second goal is to present some new perspectives on CORE
in light of recent developments to make it accessible to more researchers,
including those in Quantum Information Science. We make some comparison to
entanglement-based approaches and discuss how it may be possible to improve or
generalize the method.Comment: Completely revised version accepted by Phy Rev B; 13 pages with added
material on entropy in COR
Detecting Non-Abelian Statistics in the nu=5/2 Fractional Quantum Hall State
In this letter we propose an interferometric experiment to detect non-Abelian
quasiparticle statistics -- one of the hallmark characteristics of the
Moore-Read state expected to describe the observed FQHE plateau at nu=5/2. The
implications for using this state for constructing a topologically protected
qubit as has been recently proposed by Das Sarma et. al. are also addressed.Comment: 5 pages, 2 eps figures v2: A few minor changes and citation
corrections. In particular, the connection to cond-mat/9711087 has been
clarified. v3: Minor changes: fixed references to Fig. 2, updated citations,
changed a few words to conform to the version published in PR
Topological entropy of realistic quantum Hall wave functions
The entanglement entropy of the incompressible states of a realistic quantum
Hall system are studied by direct diagonalization. The subdominant term to the
area law, the topological entanglement entropy, which is believed to carry
information about topologic order in the ground state, was extracted for
filling factors 1/3, 1/5 and 5/2. The results for 1/3 and 1/5 are consistent
with the topological entanglement entropy for the Laughlin wave function. The
5/2 state exhibits a topological entanglement entropy consistent with the
Moore-Read wave function.Comment: 6 pages, 6 figures; improved computations and graphics; added
reference
Simple proof of equivalence between adiabatic quantum computation and the circuit model
We prove the equivalence between adiabatic quantum computation and quantum
computation in the circuit model. An explicit adiabatic computation procedure
is given that generates a ground state from which the answer can be extracted.
The amount of time needed is evaluated by computing the gap. We show that the
procedure is computationally efficient.Comment: 5 pages, 2 figures. v2: improved gap estimates and added some more
detail
- …