299 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
PageRank model of opinion formation on Ulam networks
We consider a PageRank model of opinion formation on Ulam networks, generated
by the intermittency map and the typical Chirikov map. The Ulam networks
generated by these maps have certain similarities with such scale-free networks
as the World Wide Web (WWW), showing an algebraic decay of the PageRank
probability. We find that the opinion formation process on Ulam networks have
certain similarities but also distinct features comparing to the WWW. We
attribute these distinctions to internal differences in network structure of
the Ulam and WWW networks. We also analyze the process of opinion formation in
the frame of generalized Sznajd model which protects opinion of small
communities.Comment: 7 pages, 6 figures. Updated version for publicatio
Schrodinger cat animated on a quantum computer
We present a quantum algorithm which allows to simulate chaos-assisted
tunneling in deep semiclassical regime on existing quantum computers. This
opens new possibilities for investigation of macroscopic quantum tunneling and
realization of semiclassical Schr\"odinger cat oscillations. Our numerical
studies determine the decoherence rate induced by noisy gates for these
oscillations and propose a suitable parameter regime for their experimental
implementation.Comment: research at Quantware MIPS Center http://www.quantware.ups-tlse.fr ;
revtex, 4 pages, 4 figure
Floquet theory of microwave absorption by an impurity in two dimensional electron gas
We investigate the dynamics of a two-dimensional electron gas (2DEG) under
circular polarized microwave radiation in presence of dilute localized
impurities. Inspired by recent developments on Floquet topological insulators
we obtain the Floquet wavefunctions of this system which allow us to predict
the microwave absorption and charge density responses of the electron gas, we
demonstrate how these properties can be understood from the underlying
semiclassical dynamics even for impurities with a size of around a magnetic
length. The charge density response takes the form of a rotating charge density
vortex around the impurity that can lead to a significant renormalization of
the external microwave field which becomes strongly inhomogeneous on the scale
of a cyclotron radius around the impurity. We show that this in-homogeneity can
suppress the circular polarization dependence which is theoretically expected
for MIRO but which was not observed in MIRO experiments on semiconducting
2DEGs. Our explanation, for this so far unexplained polarization independence,
has close similarities with the Azbel'-Kaner effect in metals where the
interaction length between the microwave field and conduction electrons is much
smaller than the cyclotron radius due to skin effect generating harmonics of
the cyclotron resonance
Quantum computer inverting time arrow for macroscopic systems
A legend tells that once Loschmidt asked Boltzmann on what happens to his
statistical theory if one inverts the velocities of all particles, so that, due
to the reversibility of Newton's equations, they return from the equilibrium to
a nonequilibrium initial state. Boltzmann only replied ``then go and invert
them''. This problem of the relationship between the microscopic and
macroscopic descriptions of the physical world and time-reversibility has been
hotly debated from the XIXth century up to nowadays. At present, no modern
computer is able to perform Boltzmann's demand for a macroscopic number of
particles. In addition, dynamical chaos implies exponential growth of any
imprecision in the inversion that leads to practical irreversibility. Here we
show that a quantum computer composed of a few tens of qubits, and operating
even with moderate precision, can perform Boltzmann's demand for a macroscopic
number of classical particles. Thus, even in the regime of dynamical chaos, a
realistic quantum computer allows to rebuild a specific initial distribution
from a macroscopic state given by thermodynamic laws.Comment: revtex, 4 pages, 4 figure
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