260 research outputs found
Irreversible Quantum Baker Map
We propose a generalization of the model of classical baker map on the torus,
in which the images of two parts of the phase space do overlap. This
transformation is irreversible and cannot be quantized by means of a unitary
Floquet operator. A corresponding quantum system is constructed as a completely
positive map acting in the space of density matrices. We investigate spectral
properties of this super-operator and their link with the increase of the
entropy of initially pure states.Comment: 4 pages, 3 figures include
Dynamical localization simulated on a few qubits quantum computer
We show that a quantum computer operating with a small number of qubits can
simulate the dynamical localization of classical chaos in a system described by
the quantum sawtooth map model. The dynamics of the system is computed
efficiently up to a time , and then the localization length
can be obtained with accuracy by means of order computer runs,
followed by coarse grained projective measurements on the computational basis.
We also show that in the presence of static imperfections a reliable
computation of the localization length is possible without error correction up
to an imperfection threshold which drops polynomially with the number of
qubits.Comment: 8 pages, 8 figure
Decay of the classical Loschmidt echo in integrable systems
We study both analytically and numerically the decay of fidelity of classical
motion for integrable systems. We find that the decay can exhibit two
qualitatively different behaviors, namely an algebraic decay, that is due to
the perturbation of the shape of the tori, or a ballistic decay, that is
associated with perturbing the frequencies of the tori. The type of decay
depends on initial conditions and on the shape of the perturbation but, for
small enough perturbations, not on its size. We demonstrate numerically this
general behavior for the cases of the twist map, the rectangular billiard, and
the kicked rotor in the almost integrable regime.Comment: 8 pages, 3 figures, revte
Entanglement preparation using symmetric multiports
We investigate the entanglement produced by a multi-path interferometer that
is composed of two symmetric multiports, with phase shifts applied to the
output of the first multiport. Particular attention is paid to the case when we
have a single photon entering the interferometer. For this situation we derive
a simple condition that characterize the types of entanglement that one can
generate. We then show how one can use the results from the single photon case
to determine what kinds of multi-photon entangled states one can prepare using
the interferometer.Comment: 6 pages, 2 figures, accepted for publication in European Journal of
Physics
Entanglement preparation using symmetric multiports
We investigate the entanglement produced by a multi-path interferometer that
is composed of two symmetric multiports, with phase shifts applied to the
output of the first multiport. Particular attention is paid to the case when we
have a single photon entering the interferometer. For this situation we derive
a simple condition that characterize the types of entanglement that one can
generate. We then show how one can use the results from the single photon case
to determine what kinds of multi-photon entangled states one can prepare using
the interferometer.Comment: 6 pages, 2 figures, accepted for publication in European Journal of
Physics
Optimal control theory for unitary transformations
The dynamics of a quantum system driven by an external field is well
described by a unitary transformation generated by a time dependent
Hamiltonian. The inverse problem of finding the field that generates a specific
unitary transformation is the subject of study. The unitary transformation
which can represent an algorithm in a quantum computation is imposed on a
subset of quantum states embedded in a larger Hilbert space. Optimal control
theory (OCT) is used to solve the inversion problem irrespective of the initial
input state. A unified formalism, based on the Krotov method is developed
leading to a new scheme. The schemes are compared for the inversion of a
two-qubit Fourier transform using as registers the vibrational levels of the
electronic state of Na. Raman-like transitions through the
electronic state induce the transitions. Light fields are found
that are able to implement the Fourier transform within a picosecond time
scale. Such fields can be obtained by pulse-shaping techniques of a femtosecond
pulse. Out of the schemes studied the square modulus scheme converges fastest.
A study of the implementation of the qubit Fourier transform in the Na
molecule was carried out for up to 5 qubits. The classical computation effort
required to obtain the algorithm with a given fidelity is estimated to scale
exponentially with the number of levels. The observed moderate scaling of the
pulse intensity with the number of qubits in the transformation is
rationalized.Comment: 32 pages, 6 figure
Quantum Computing of Quantum Chaos in the Kicked Rotator Model
We investigate a quantum algorithm which simulates efficiently the quantum
kicked rotator model, a system which displays rich physical properties, and
enables to study problems of quantum chaos, atomic physics and localization of
electrons in solids. The effects of errors in gate operations are tested on
this algorithm in numerical simulations with up to 20 qubits. In this way
various physical quantities are investigated. Some of them, such as second
moment of probability distribution and tunneling transitions through invariant
curves are shown to be particularly sensitive to errors. However,
investigations of the fidelity and Wigner and Husimi distributions show that
these physical quantities are robust in presence of imperfections. This implies
that the algorithm can simulate the dynamics of quantum chaos in presence of a
moderate amount of noise.Comment: research at Quantware MIPS Center http://www.quantware.ups-tlse.fr,
revtex 11 pages, 13 figs, 2 figs and discussion adde
Entanglement and localization of wavefunctions
We review recent works that relate entanglement of random vectors to their
localization properties. In particular, the linear entropy is related by a
simple expression to the inverse participation ratio, while next orders of the
entropy of entanglement contain information about e.g. the multifractal
exponents. Numerical simulations show that these results can account for the
entanglement present in wavefunctions of physical systems.Comment: 6 pages, 4 figures, to appear in the proceedings of the NATO Advanced
Research Workshop 'Recent Advances in Nonlinear Dynamics and Complex System
Physics', Tashkent, Uzbekistan, 200
Classical Infinite-Range-Interaction Heisenberg Ferromagnetic Model: Metastability and Sensitivity to Initial Conditions
A N-sized inertial classical Heisenberg ferromagnet, which consists in a
modification of the well-known standard model, where the spins are replaced by
classical rotators, is studied in the limit of infinite-range interactions. The
usual canonical-ensemble mean-field solution of the inertial classical
-vector ferromagnet (for which recovers the particular Heisenberg
model considered herein) is briefly reviewed, showing the well-known
second-order phase transition. This Heisenberg model is studied numerically
within the microcanonical ensemble, through molecular dynamics.Comment: 18 pages text, and 7 EPS figure
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