103 research outputs found
Global symmetries of quantum Hall systems: lattice description
I analyze non-local symmetries of finite-size Euclidean 3D lattice
Chern-Simons models in the presence of an external magnetic field and non-zero
average current. It is shown that under very general assumptions the
particle-vortex duality interchanges the total Euclidean magnetic flux Phi/(2
Pi) and the total current I in a given direction, while the flux attachment
transformation increases the flux in a given direction by the corresponding
component of the current, Phi -> Phi+4 Pi I, independently of the disorder. In
the language of 2+1 dimensional models, appropriate for describing quantum Hall
systems, these transformations are equivalent to the symmetries of the phase
diagram known as the Correspondence Laws, and the non-linear current-voltage
mapping between mutually dual points, recently observed near the quantum Hall
liquid-insulator transitions.Comment: 14 pages, 3 ps figures include
Quantum degenerate Bose-Fermi mixtures on 1-D optical lattices
We combine model mapping, exact spectral bounds, and a quantum Monte Carlo
method to study the ground state phases of a mixture of ultracold bosons and
spin-polarized fermions in a one-dimensional optical lattice. The exact
boundary of the boson-demixing transition is obtained from the Bethe Ansatz
solution of the standard Hubbard model. We prove that along a symmetry plane in
the parameter space, the boson-fermion mixed phase is stable at all densities.
This phase is a two-component Luttinger liquid for weak couplings or for
incommensurate total density, otherwise it has a charge gap but retains a
gapless mode of mixture composition fluctuations. The static density
correlations are studied in these two limits and shown to have markedly
different features.Comment: 4 pages, 4 figure
Dynamically corrected gates for qubits with always-on Ising couplings: Error model and fault-tolerance with the toric code
We describe how a universal set of dynamically-corrected quantum gates can be
implemented using sequences of shaped decoupling pulses on any qubit network
forming a sparse bipartite graph with always-on Ising interactions. These
interactions are constantly decoupled except when they are needed for two-qubit
gates. We analytically study the error operators associated with the
constructed gates up to third order in the Magnus expansion, analyze these
errors numerically in the unitary time evolution of small qubit clusters, and
give a bound on high-order errors for qubits on a large square lattice. We
prove that with a large enough toric code the present gate set can be used to
implement a fault-tolerant quantum memory
Universal set of Dynamically Protected Gates for Bipartite Qubit Networks II: Soft Pulse Implementation of the [[5,1,3]] Quantum Error Correcting Code
We model repetitive quantum error correction (QEC) with the
single-error-correcting five-qubit code on a network of individually-controlled
qubits with always-on Ising couplings, using our previously designed universal
set of quantum gates based on sequences of shaped decoupling pulses. In
addition to serving as accurate quantum gates, the sequences also provide
dynamical decoupling (DD) of low-frequency phase noise. The simulation involves
integrating unitary dynamics of six qubits over the duration of tens of
thousands of control pulses, using classical stochastic phase noise as a source
of decoherence. The combined DD/QEC protocol dramatically improves the
coherence, with the QEC alone responsible for more than an order of magnitude
infidelity reduction.Comment: 12 pages, 9 figure
Holons on a meandering stripe
To study a possible effect of transverse fluctuations of a stripe in a 2D
antiferromagnet on its charge dynamics, we identify elementary excitations of a
weakly doped domain wall in the Hubbard model. Hartree-Fock numerics and
analysis of fermion zero modes suggest that for U>=3t charged excitations are
mobile holons, Q=1, S=0. Each holon resides on a kink in the position of the
domain wall. We construct a simple model in which transverse stripe dynamics is
induced solely by motion of the holons. In the absence of spin excitations
(spinons, Q=0, S=1/2), stripe fluctuations DO NOT suppress a tendency to form a
global charge-density order.Comment: REVTeX, 4 two-column pages, 4 eps figures with epsf.st
Refocusing of a qubit system coupled to an oscillator
Refocusing, or dynamical decoupling, is a coherent control technique where
the internal dynamics of a quantum system is effectively averaged out by an
application of specially designed driving fields. The method has originated in
nuclear magnetic resonance, but it was independently discovered in atomic
physics as a ``coherent destruction of tunneling''. Present work deals with the
analysis of the performance of ``soft'' refocusing pulses and pulse sequences
in protecting the coherence of a qubit system coupled to a quantum oscillator.Comment: 2.5pages Conference proceedings for Nanostructures: Physics and
Technology, Novosibirsk (2007). Macros file nano2cmr.sty include
Higher-dimensional quantum hypergraph-product codes
We describe a family of quantum error-correcting codes which generalize both
the quantum hypergraph-product (QHP) codes by Tillich and Z\'emor, and all
families of toric codes on -dimensional hypercubic lattices. Similar to the
latter, our codes form -complexes , with . These are
defined recursively, with obtained as a tensor product of a
complex with a -complex parameterized by a binary matrix.
Parameters of the constructed codes are given explicitly in terms of those of
binary codes associated with the matrices used in the construction.Comment: 6 pages, no figures. In version 2, a hole in the proof and several
typos are correcte
Network of edge states: random Josephson junction array description
We construct a generalization of the Chalker-Coddington network model to the
case of fractional quantum Hall effect, which describes the tunneling between
multiple chiral edges. We derive exact local and global duality symmetries of
this model, and show that its infrared properties are identical to those of
disordered planar Josephson junction array (JJA) in a weak magnetic field,
which implies the same universality class. The zero frequency Hall resistance
of the system, which was expressed through exact correlators of the tunneling
fields, is shown to be quantized both in the quantum Hall limit and in the
limit of perfect Hall insulator.Comment: revtex, 4 double-column pages, 2 ps figures included with epsf. To be
published in PRL. Changes include: clarified the concept of duality, added
one reference, and substantially rewritten the ending of the manuscrip
Universal set of scalable dynamically corrected gates for quantum error correction with always-on qubit couplings
We construct a universal set of high fidelity quantum gates to be used on a
sparse bipartite lattice with always-on Ising couplings. The gates are based on
dynamical decoupling sequences using shaped pulses, they protect against
low-frequency phase noise, and can be run in parallel on non-neighboring
qubits. This makes them suitable for implementing quantum error correction with
low-density parity check codes like the surface codes and their finite-rate
generalizations. We illustrate the construction by simulating quantum Zeno
effect with the toric code on a spin chain
Algebraic bounds for heterogeneous site percolation on directed and undirected graphs
We analyze site percolation on directed and undirected graphs with
site-dependent open-site probabilities. We construct upper bounds on cluster
susceptibilities, vertex connectivity functions, and the expected number of
simple open cycles through a chosen arc; separate bounds are given on finite
and infinite (di)graphs. These produce lower bounds for percolation and
uniqueness transitions in infinite (di)graphs, and for the formation of a giant
component in finite (di)graphs. The bounds are formulated in terms of
appropriately weighted adjacency and non-backtracking (Hashimoto) matrices. It
turns out to be the uniqueness criterion that is most closely associated with
an asymptotically vanishing probability of forming a giant strongly-connected
component on a large finite (di)graph.Comment: 16 pages, 3 figures. In v5, significant revision of text, expansion
of uniqueness discussion, vertex connectivity and infinite graph bound
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