128 research outputs found
Efficient quantum computation of high harmonics of the Liouville density distribution
We show explicitly that high harmonics of the classical Liouville density
distribution in the chaotic regime can be obtained efficiently on a quantum
computer [1,2]. As was stated in [1], this provides information unaccessible
for classical computer simulations, and replies to the questions raised in
[3,4].Comment: revtex, 2 pages, 1 figure; related to [1] quant-ph/0101004, [2]
quant-ph/0102082, [8] quant-ph/0105149, [4] quant-ph/0110019, [3]
quant-ph/011002
Comment on "Stable Quantum Computation of Unstable Classical Chaos"
I think the title and content of the recent Letter by Georgeot and
Shepelyanski [PRL 86, 5393 (2001), also quant-ph/0101004)] are not correct. As
long as the classical Arnold map is considered, the classical computational
algorithm can be made exactly equivalent with the quantum one. The claimed
advantage of the Letter's quantum algorithm disappears if we correctly restrict
the statistical analysis for the classical Arnold system.Comment: 1 page, PRL version + footnote [2] + refs.[3,5
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
Inertial waves in a rotating spherical shell: attractors and asymptotic spectrum
We investigate the asymptotic properties of inertial modes confined in a
spherical shell when viscosity tends to zero. We first consider the mapping
made by the characteristics of the hyperbolic equation (Poincar\'e's equation)
satisfied by inviscid solutions. Characteristics are straight lines in a
meridional section of the shell, and the mapping shows that, generically, these
lines converge towards a periodic orbit which acts like an attractor.
We then examine the relation between this characteristic path and
eigensolutions of the inviscid problem and show that in a purely
two-dimensional problem, convergence towards an attractor means that the
associated velocity field is not square-integrable. We give arguments which
generalize this result to three dimensions. We then consider the viscous
problem and show how viscosity transforms singularities into internal shear
layers which in general betray an attractor expected at the eigenfrequency of
the mode. We find that there are nested layers, the thinnest and most internal
layer scaling with -scale, being the Ekman number. Using an
inertial wave packet traveling around an attractor, we give a lower bound on
the thickness of shear layers and show how eigenfrequencies can be computed in
principle. Finally, we show that as viscosity decreases, eigenfrequencies tend
towards a set of values which is not dense in , contrary to the
case of the full sphere ( is the angular velocity of the system).
Hence, our geometrical approach opens the possibility of describing the
eigenmodes and eigenvalues for astrophysical/geophysical Ekman numbers
(), which are out of reach numerically, and this for a wide
class of containers.Comment: 42 pages, 20 figures, abstract shortene
Distinguishing humans from computers in the game of go: a complex network approach
We compare complex networks built from the game of go and obtained from
databases of human-played games with those obtained from computer-played games.
Our investigations show that statistical features of the human-based networks
and the computer-based networks differ, and that these differences can be
statistically significant on a relatively small number of games using specific
estimators. We show that the deterministic or stochastic nature of the computer
algorithm playing the game can also be distinguished from these quantities.
This can be seen as tool to implement a Turing-like test for go simulators.Comment: 7 pages, 6 figure
Move ordering and communities in complex networks describing the game of go
We analyze the game of go from the point of view of complex networks. We
construct three different directed networks of increasing complexity, defining
nodes as local patterns on plaquettes of increasing sizes, and links as actual
successions of these patterns in databases of real games. We discuss the
peculiarities of these networks compared to other types of networks. We explore
the ranking vectors and community structure of the networks and show that this
approach enables to extract groups of moves with common strategic properties.
We also investigate different networks built from games with players of
different levels or from different phases of the game. We discuss how the study
of the community structure of these networks may help to improve the computer
simulations of the game. More generally, we believe such studies may help to
improve the understanding of human decision process.Comment: 14 pages, 21 figure
Quantum computation of multifractal exponents through the quantum wavelet transform
We study the use of the quantum wavelet transform to extract efficiently
information about the multifractal exponents for multifractal quantum states.
We show that, combined with quantum simulation algorithms, it enables to build
quantum algorithms for multifractal exponents with a polynomial gain compared
to classical simulations. Numerical results indicate that a rough estimate of
fractality could be obtained exponentially fast. Our findings are relevant e.g.
for quantum simulations of multifractal quantum maps and of the Anderson model
at the metal-insulator transition.Comment: 9 pages, 9 figure
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