18,529 research outputs found
Statistical properties of eigenvalues for an operating quantum computer with static imperfections
We investigate the transition to quantum chaos, induced by static
imperfections, for an operating quantum computer that simulates efficiently a
dynamical quantum system, the sawtooth map. For the different dynamical regimes
of the map, we discuss the quantum chaos border induced by static imperfections
by analyzing the statistical properties of the quantum computer eigenvalues.
For small imperfection strengths the level spacing statistics is close to the
case of quasi-integrable systems while above the border it is described by the
random matrix theory. We have found that the border drops exponentially with
the number of qubits, both in the ergodic and quasi-integrable dynamical
regimes of the map characterized by a complex phase space structure. On the
contrary, the regime with integrable map dynamics remains more stable against
static imperfections since in this case the border drops only algebraically
with the number of qubits.Comment: 9 pages, 10 figure
Chaos and Complexity of quantum motion
The problem of characterizing complexity of quantum dynamics - in particular
of locally interacting chains of quantum particles - will be reviewed and
discussed from several different perspectives: (i) stability of motion against
external perturbations and decoherence, (ii) efficiency of quantum simulation
in terms of classical computation and entanglement production in operator
spaces, (iii) quantum transport, relaxation to equilibrium and quantum mixing,
and (iv) computation of quantum dynamical entropies. Discussions of all these
criteria will be confronted with the established criteria of integrability or
quantum chaos, and sometimes quite surprising conclusions are found. Some
conjectures and interesting open problems in ergodic theory of the quantum many
problem are suggested.Comment: 45 pages, 22 figures, final version, at press in J. Phys. A, special
issue on Quantum Informatio
Gyrotactic suppression and emergence of chaotic trajectories of swimming particles in three-dimensional flows
We study the effects of imposed {three-dimensional flows} on the trajectories and mixing of gyrotactic swimming micro-organisms, and identify new phenomena not seen in flows restricted to two dimensions. Through numerical simulation of Taylor--Green and ABC flows, we explore the role that the flow and the cell shape play in determining the long-term configuration of the cells' trajectories, which often take the form of multiple sinuous and helical `plume-like' structures, even in the chaotic ABC flow. This gyrotactic suppression of Lagrangian chaos persists even in the presence of random noise. Analytical solutions for a number of cases reveal the how plumes form and the nature of the competition between torques acting on individual cells. \note{Furthermore, studies of Lyapunov exponents reveal that as the ratio of cell swimming speed relative to the flow speed increases from zero, the initial chaotic trajectories are first suppressed and then give way to a second unexpected window of chaotic trajectories at speeds greater than unity, before suppression of chaos at high relative swimming speeds
Characterization of complex quantum dynamics with a scalable NMR information processor
We present experimental results on the measurement of fidelity decay under
contrasting system dynamics using a nuclear magnetic resonance quantum
information processor. The measurements were performed by implementing a
scalable circuit in the model of deterministic quantum computation with only
one quantum bit. The results show measurable differences between regular and
complex behaviour and for complex dynamics are faithful to the expected
theoretical decay rate. Moreover, we illustrate how the experimental method can
be seen as an efficient way for either extracting coarse-grained information
about the dynamics of a large system, or measuring the decoherence rate from
engineered environments.Comment: 4pages, 3 figures, revtex4, updated with version closer to that
publishe
Distribution of "level velocities" in quasi 1D disordered or chaotic systems with localization
The explicit analytical expression for the distribution function of
parametric derivatives of energy levels ("level velocities") with respect to a
random change of scattering potential is derived for the chaotic quantum
systems belonging to the quasi 1D universality class (quantum kicked rotator,
"domino" billiard, disordered wire, etc.).Comment: 11 pages, REVTEX 3.
Exponential Gain in Quantum Computing of Quantum Chaos and Localization
We present a quantum algorithm which simulates the quantum kicked rotator
model exponentially faster than classical algorithms. This shows that important
physical problems of quantum chaos, localization and Anderson transition can be
modelled efficiently on a quantum computer. We also show that a similar
algorithm simulates efficiently classical chaos in certain area-preserving
maps.Comment: final published versio
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