393 research outputs found
How large can the electron to proton mass ratio be in Particle-In-Cell simulations of unstable systems?
Particle-in-cell (PIC) simulations are widely used as a tool to investigate
instabilities that develop between a collisionless plasma and beams of charged
particles. However, even on contemporary supercomputers, it is not always
possible to resolve the ion dynamics in more than one spatial dimension with
such simulations. The ion mass is thus reduced below 1836 electron masses,
which can affect the plasma dynamics during the initial exponential growth
phase of the instability and during the subsequent nonlinear saturation. The
goal of this article is to assess how far the electron to ion mass ratio can be
increased, without changing qualitatively the physics. It is first demonstrated
that there can be no exact similarity law, which balances a change of the mass
ratio with that of another plasma parameter, leaving the physics unchanged.
Restricting then the analysis to the linear phase, a criterion allowing to
define a maximum ratio is explicated in terms of the hierarchy of the linear
unstable modes. The criterion is applied to the case of a relativistic electron
beam crossing an unmagnetized electron-ion plasma.Comment: To appear in Physics of Plasma
Intermediate quantum maps for quantum computation
We study quantum maps displaying spectral statistics intermediate between
Poisson and Wigner-Dyson. It is shown that they can be simulated on a quantum
computer with a small number of gates, and efficiently yield information about
fidelity decay or spectral statistics. We study their matrix elements and
entanglement production, and show that they converge with time to distributions
which differ from random matrix predictions. A randomized version of these maps
can be implemented even more economically, and yields pseudorandom operators
with original properties, enabling for example to produce fractal random
vectors. These algorithms are within reach of present-day quantum computers.Comment: 4 pages, 4 figures, research done at
http://www.quantware.ups-tlse.fr
Multiparticle Entanglement in the Lipkin-Meshkov-Glick Model
The multiparticle entanglement in the Lipkin-Meshkov-Glick model has been
discussed extensively in this paper. Measured by the global entanglement and
its generalization, our calculation shows that the multiparticle entanglement
can faithfully detect quantum phase transitions. For an antiferromagnetic case
the multiparticle entanglement reaches the maximum at the transition point,
whereas for ferromagnetic coupling, two different behaviors of multiparticle
entanglement can be identified, dependent on the anisotropic parameter in the
coupling.Comment: 7 pages and 5 figure
Quantum Logic for Trapped Atoms via Molecular Hyperfine Interactions
We study the deterministic entanglement of a pair of neutral atoms trapped in
an optical lattice by coupling to excited-state molecular hyperfine potentials.
Information can be encoded in the ground-state hyperfine levels and processed
by bringing atoms together pair-wise to perform quantum logical operations
through induced electric dipole-dipole interactions. The possibility of
executing both diagonal and exchange type entangling gates is demonstrated for
two three-level atoms and a figure of merit is derived for the fidelity of
entanglement. The fidelity for executing a CPHASE gate is calculated for two
87Rb atoms, including hyperfine structure and finite atomic localization. The
main source of decoherence is spontaneous emission, which can be minimized for
interaction times fast compared to the scattering rate and for sufficiently
separated atomic wavepackets. Additionally, coherent couplings to states
outside the logical basis can be constrained by the state dependent trapping
potential.Comment: Submitted to Physical Review
Lower bounds on entanglement measures from incomplete information
How can we quantify the entanglement in a quantum state, if only the
expectation value of a single observable is given? This question is of great
interest for the analysis of entanglement in experiments, since in many
multiparticle experiments the state is not completely known. We present several
results concerning this problem by considering the estimation of entanglement
measures via Legendre transforms. First, we present a simple algorithm for the
estimation of the concurrence and extensions thereof. Second, we derive an
analytical approach to estimate the geometric measure of entanglement, if the
diagonal elements of the quantum state in a certain basis are known. Finally,
we compare our bounds with exact values and other estimation methods for
entanglement measures.Comment: 9 pages, 4 figures, v2: final versio
On fault-tolerance with noisy and slow measurements
It is not so well-known that measurement-free quantum error correction
protocols can be designed to achieve fault-tolerant quantum computing. Despite
the potential advantages of using such protocols in terms of the relaxation of
accuracy, speed and addressing requirements on the measurement process, they
have usually been overlooked because they are expected to yield a very bad
threshold as compared to error correction protocols which use measurements.
Here we show that this is not the case. We design fault-tolerant circuits for
the 9 qubit Bacon-Shor code and find a threshold for gates and preparation of
(30% of the best known result for the
same code using measurement based error correction) while admitting up to 1/3
error rates for measurements and allocating no constraints on measurement
speed. We further show that demanding gate error rates sufficiently below the
threshold one can improve the preparation threshold to .
We also show how these techniques can be adapted to other
Calderbank-Shor-Steane codes.Comment: 11 pages, 7 figures. v3 has an extended exposition and several
simplifications that provide for an improved threshold value and resource
overhea
Efficient generation of random multipartite entangled states using time optimal unitary operations
We review the generation of random pure states using a protocol of repeated
two qubit gates. We study the dependence of the convergence to states with Haar
multipartite entanglement distribution. We investigate the optimal generation
of such states in terms of the physical (real) time needed to apply the
protocol, instead of the gate complexity point of view used in other works.
This physical time can be obtained, for a given Hamiltonian, within the
theoretical framework offered by the quantum brachistochrone formalism. Using
an anisotropic Heisenberg Hamiltonian as an example, we find that different
optimal quantum gates arise according to the optimality point of view used in
each case. We also study how the convergence to random entangled states depends
on different entanglement measures.Comment: 5 pages, 2 figures. New title, improved explanation of the algorithm.
To appear in Phys. Rev.
Entanglement Measures for Intermediate Separability of Quantum States
We present a family of entanglement measures R_m which act as indicators for
separability of n-qubit quantum states into m subsystems for arbitrary 2 \leq m
\leq n. The measure R_m vanishes if the state is separable into m subsystems,
and for m = n it gives the Meyer-Wallach measure while for m = 2 it reduces, in
effect, to the one introduced recently by Love et al. The measures R_m are
evaluated explicitly for the GHZ state and the W state (and its modifications,
the W_k states) to show that these globally entangled states exhibit rather
distinct behaviors under the measures, indicating the utility of the measures
R_m for characterizing globally entangled states as well.Comment: 8 pages, 8 figure
Multi-partite entanglement and quantum phase transition in the one-, two-, and three-dimensional transverse field Ising model
In this paper we consider the quantum phase transition in the Ising model in
the presence of a transverse field in one, two and three dimensions from a
multi-partite entanglement point of view. Using \emph{exact} numerical
solutions, we are able to study such systems up to 25 qubits. The Meyer-Wallach
measure of global entanglement is used to study the critical behavior of this
model. The transition we consider is between a symmetric GHZ-like state to a
paramagnetic product-state. We find that global entanglement serves as a good
indicator of quantum phase transition with interesting scaling behavior. We use
finite-size scaling to extract the critical point as well as some critical
exponents for the one and two dimensional models. Our results indicate that
such multi-partite measure of global entanglement shows universal features
regardless of dimension . Our results also provides evidence that
multi-partite entanglement is better suited for the study of quantum phase
transitions than the much studied bi-partite measures.Comment: 7 pages, 8 Figures. To appear in Physical Review
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