12,750 research outputs found
Error tolerance in an NMR Implementation of Grover's Fixed-Point Quantum Search Algorithm
We describe an implementation of Grover's fixed-point quantum search
algorithm on a nuclear magnetic resonance (NMR) quantum computer, searching for
either one or two matching items in an unsorted database of four items. In this
new algorithm the target state (an equally weighted superposition of the
matching states) is a fixed point of the recursive search operator, and so the
algorithm always moves towards the desired state. The effects of systematic
errors in the implementation are briefly explored.Comment: 5 Pages RevTex4 including three figures. Changes made at request of
referees; now in press at Phys Rev
Algorithms for Lattice QCD with Dynamical Fermions
We consider recent progress in algorithms for generating gauge field
configurations that include the dynamical effects of light fermions. We survey
what has been achieved in recent state-of-the-art computations, and examine the
trade-offs between performance and control of systematic errors. We briefly
review the use of polynomial and rational approximations in Hybrid Monte Carlo
algorithms, and some of the theory of on-shell chiral fermions on the lattice.
This provides a theoretical framework within which we compare algorithmic
alternatives for their implementation; and again we examine the trade-offs
between speed and error control.Comment: Review presented at Lattice2004(plenary), Fermilab, June 21-26, 2004.
14 pages, 8 figure
Topological Flat Band Models and Fractional Chern Insulators
Topological insulators and their intriguing edge states can be understood in
a single-particle picture and can as such be exhaustively classified.
Interactions significantly complicate this picture and can lead to entirely new
insulating phases, with an altogether much richer and less explored
phenomenology. Most saliently, lattice generalizations of fractional quantum
Hall states, dubbed fractional Chern insulators, have recently been predicted
to be stabilized by interactions within nearly dispersionless bands with
non-zero Chern number, . Contrary to their continuum analogues, these states
do not require an external magnetic field and may potentially persist even at
room temperature, which make these systems very attractive for possible
applications such as topological quantum computation. This review recapitulates
the basics of tight-binding models hosting nearly flat bands with non-trivial
topology, , and summarizes the present understanding of interactions
and strongly correlated phases within these bands. Emphasis is made on
microscopic models, highlighting the analogy with continuum Landau level
physics, as well as qualitatively new, lattice specific, aspects including
Berry curvature fluctuations, competing instabilities as well as novel
collective states of matter emerging in bands with . Possible
experimental realizations, including oxide interfaces and cold atom
implementations as well as generalizations to flat bands characterized by other
topological invariants are also discussed.Comment: Invited review. 46 pages, many illustrations and references. V2:
final version with minor improvements and added reference
Hidden Non-Abelian Gauge Symmetries in Doped Planar Antiferromagnets
We investigate the possibility of hidden non-Abelian Local Phase symmetries
in large-U doped planar Hubbard antiferromagnets, believed to simulate the
physics of two-dimensional (magnetic) superconductors. We present a spin-charge
separation ansatz, appropriate to incorporate holon spin flip, which allows for
such a hidden local gauge symmetry to emerge in the effective action. The group
is of the form , where SU(2) is a local
non-Abelian group associated with the spin degrees of freedom, U_E(1) is that
of ordinary electromagnetism, associated with the electric charge of the holes,
and U_S(1) is a `statistical' Abelian gauge group pertaining to the fractional
statistics of holes on the spatial plane. In a certain regime of the parameters
of the model, namely strong U_S(1) and weak SU(2), there is the possibility of
dynamical formation of a holon condensate. This leads to a dynamical breaking
of . The resulting Abelian effective theory is closely related
to an earlier model proposed as the continuum limit of large-spin planar doped
antiferromagnets, which lead to an unconventional scenario for two-dimensional
parity-invariant superconductivity.Comment: 32 pages LATEX, one figure. (More details given in the passage from
the Hubbard model to the long wavelength lattice gauge theory; one figure
added; no changes in the conclusions.
A precise CNOT gate in the presence of large fabrication induced variations of the exchange interaction strength
We demonstrate how using two-qubit composite rotations a high fidelity
controlled-NOT (CNOT) gate can be constructed, even when the strength of the
interaction between qubits is not accurately known. We focus on the exchange
interaction oscillation in silicon based solid-state architectures with a
Heisenberg Hamiltonian. This method easily applies to a general two-qubit
Hamiltonian. We show how the robust CNOT gate can achieve a very high fidelity
when a single application of the composite rotations is combined with a modest
level of Hamiltonian characterisation. Operating the robust CNOT gate in a
suitably characterised system means concatenation of the composite pulse is
unnecessary, hence reducing operation time, and ensuring the gate operates
below the threshold required for fault-tolerant quantum computation.Comment: 9 pages, 8 figure
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