37,845 research outputs found
Quantum Chaos & Quantum Computers
The standard generic quantum computer model is studied analytically and
numerically and the border for emergence of quantum chaos, induced by
imperfections and residual inter-qubit couplings, is determined. This
phenomenon appears in an isolated quantum computer without any external
decoherence. The onset of quantum chaos leads to quantum computer hardware
melting, strong quantum entropy growth and destruction of computer operability.
The time scales for development of quantum chaos and ergodicity are determined.
In spite the fact that this phenomenon is rather dangerous for quantum
computing it is shown that the quantum chaos border for inter-qubit coupling is
exponentially larger than the energy level spacing between quantum computer
eigenstates and drops only linearly with the number of qubits n. As a result
the ideal multi-qubit structure of the computer remains rather robust against
imperfections. This opens a broad parameter region for a possible realization
of quantum computer. The obtained results are related to the recent studies of
quantum chaos in such many-body systems as nuclei, complex atoms and molecules,
finite Fermi systems and quantum spin glass shards which are also reviewed in
the paper.Comment: Lecture at Nobel symposium on "Quantum chaos", June 2000, Sweden;
revtex, 10 pages, 9 figure
Quantum Chaos at Finite Temperature
We use the quantum action to study quantum chaos at finite temperature. We
present a numerical study of a classically chaotic 2-D Hamiltonian system -
harmonic oscillators with anharmonic coupling. We construct the quantum action
non-perturbatively and find temperature dependent quantum corrections in the
action parameters. We compare Poincar\'{e} sections of the quantum action at
finite temperature with those of the classical action.Comment: Text (LaTeX), Figs. (ps
Non-Markovian Quantum Dynamics and Classical Chaos
We study the influence of a chaotic environment in the evolution of an open
quantum system. We show that there is an inverse relation between chaos and
non-Markovianity. In particular, we remark on the deep relation of the short
time non-Markovian behavior with the revivals of the average fidelity
amplitude-a fundamental quantity used to measure sensitivity to perturbations
and to identify quantum chaos. The long time behavior is established as a
finite size effect which vanishes for large enough environments.Comment: Closest to the published versio
Quantum chaos in QCD at finite temperature
We study complete eigenvalue spectra of the staggered Dirac matrix in
quenched QCD on a lattice. In particular, we investigate the
nearest-neighbor spacing distribution for various values of both
in the confinement and deconfinement phase. In both phases except far into the
deconfinement region, the data agree with the Wigner surmise of random matrix
theory which is indicative of quantum chaos. No signs of a transition to
Poisson regularity are found, and the reasons for this result are discussed.Comment: 3 pages, 6 figures (included), poster presented by R. Pullirsch at
"Lattice 97", to appear in the proceeding
Quantum Chaos in the Yang-Mills-Higgs System at Finite Temperature
The quantum chaos in the finite-temperature Yang-Mills-Higgs system is
studied. The energy spectrum of a spatially homogeneous SU(2) Yang-Mills-Higgs
is calculated within thermofield dynamics. Level statistics of the spectra is
studied by plotting nearest-level spacing distribution histograms. It is found
that finite temperature effects lead to a strengthening of chaotic effects,
i.e. spectrum which has Poissonian distribution at zero temperature has
Gaussian distribution at finite-temperature.Comment: 6 pages, 5 figures, Revte
Quantum chaos and QCD at finite chemical potential
We investigate the distribution of the spacings of adjacent eigenvalues of
the lattice Dirac operator. At zero chemical potential , the
nearest-neighbor spacing distribution follows the Wigner surmise of
random matrix theory both in the confinement and in the deconfinement phase.
This is indicative of quantum chaos. At nonzero chemical potential, the
eigenvalues of the Dirac operator become complex. We discuss how can be
defined in the complex plane. Numerical results from an SU(3) simulation with
staggered fermions are compared with predictions from non-hermitian random
matrix theory, and agreement with the Ginibre ensemble is found for .Comment: LATTICE98(hightemp), 3 pages, 10 figure
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