共查询到20条相似文献,搜索用时 15 毫秒
1.
G. Benenti G. Casati S. Montangero D.L. Shepelyansky 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2003,22(2):285-293
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.
Received 19 June 2002 / Received in final form 30 September 2002 Published online 17 Decembre 2002
RID="a"
ID="a"e-mail: dima@irsamc.ups-tlse.fr
RID="b"
ID="b"UMR 5626 du CNRS 相似文献
2.
G. Benenti G. Casati D.L. Shepelyansky 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2001,17(2):265-272
We model an isolated quantum computer as a two-dimensional lattice of qubits (spin halves) with fluctuations in individual
qubit energies and residual short-range inter-qubit couplings. In the limit when fluctuations and couplings are small compared
to the one-qubit energy spacing, the spectrum has a band structure and we study the quantum computer core (central band) with
the highest density of states. Above a critical inter-qubit coupling strength, quantum chaos sets in, leading to quantum ergodicity
of eigenstates in an isolated quantum computer. The onset of chaos results in the interaction induced dynamical thermalization
and the occupation numbers well described by the Fermi-Dirac distribution. This thermalization destroys the noninteracting
qubit structure and sets serious requirements for the quantum computer operability.
Received 3 July 2001 and Received in final form 9 September 2001 相似文献
3.
G. Benenti G. Casati S. Montangero D.L. Shepelyansky 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2002,20(2):293-296
We study the properties of eigenstates of an operating quantum computer which simulates the dynamical evolution in the regime
of quantum chaos. Even if the quantum algorithm is polynomial in number of qubits nq, it is shown that the ideal eigenstates become mixed and strongly modified by static imperfections above a certain threshold
which drops exponentially with nq. Above this threshold the quantum eigenstate entropy grows linearly with nq but the computation remains reliable during a time scale which is polynomial in the imperfection strength and in nq.
Received 7 March 2002/ Received in final form 3 May 2002 Published online 19 July 2002 相似文献
4.
M. Terraneo B. Georgeot D.L. Shepelyansky 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2003,22(1):127-130
We show that dissipative classical dynamics converging to a strange attractor can be simulated on a quantum computer. Such
quantum computations allow to investigate efficiently the small scale structure of strange attractors, yielding new information
inaccessible to classical computers. This opens new possibilities for quantum simulations of various dissipative processes
in nature.
Received 10 August 2002 Published online 29 October 2002
RID="a"
ID="a"e-mail: dima@irsamc.ups-tlse.fr
RID="b"
ID="b"UMR 5626 du CNRS 相似文献
5.
V. Pascalutsa 《The European Physical Journal A - Hadrons and Nuclei》2003,16(2):149-153
The nearest-neighbor mass-spacing distribution of the meson and baryon spectrum (up to 2.5 GeV) is described by the Wigner surmise corresponding to the statistics of the Gaussian orthogonal ensemble of random matrix theory. This can be viewed as a manifestation of quantum chaos in hadrons.
Received: 30 September 2002 / Accepted: 21 November 2002 / Published online: 4 February 2003
RID="a"
ID="a"Present address: Department of Physics and Astronomy, Ohio University, Athens, OH 45701, USA; e-mail: vlad@phy.ohiou.edu
Communicated by G. Orlandini 相似文献
6.
Peter A. Braun Stefan Heusler Sebastian Müller Fritz Haake 《The European Physical Journal B - Condensed Matter and Complex Systems》2002,30(2):189-206
Employing symbolic dynamics for geodesic motion on the tesselated pseudosphere, the so-called Hadamard-Gutzwiller model, we
construct extremely long periodic orbits without compromising accuracy. We establish criteria for such long orbits to behave
ergodically and to yield reliable statistics for self-crossings and avoided crossings. Self-encounters of periodic orbits
are reflected in certain patterns within symbol sequences, and these allow for analytic treatment of the crossing statistics.
In particular, the distributions of crossing angles and avoided-crossing widths thus come out as related by analytic continuation.
Moreover, the action difference for Sieber-Richter pairs of orbits (one orbit has a self-crossing which the other narrowly
avoids and otherwise the orbits look very nearly the same) results to all orders in the crossing angle. These findings may
be helpful for extending the work of Sieber and Richter towards a fuller understanding of the classical basis of quantum spectral
fluctuations.
Received 17 July 2002 Published online 29 November 2002 相似文献
7.
H. Schomerus 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2000,10(1):5-8
We investigate broken rational tori consisting of a chain of four (rather than two) periodic orbits. The normal form that
describes this configuration is identified and used to construct a uniform semiclassical approximation, which can be utilized
to improve trace formulae. An accuracy gain can be achieved even for the situation when two of the four orbits are ghosts.
This is illustrated for a model system, the kicked top.
Received 3 August 1999 相似文献
8.
D. Braun 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2000,11(1):3-12
I investigate the propagator of the Wigner function for a dissipative chaotic quantum map. I show that a small amount of dissipation
reduces the propagator of sufficiently smooth Wigner functions to its classical counterpart, the Frobenius-Perron operator,
if . Several consequences arise: the Wigner transform of the invariant density matrix is a smeared out version of the classical
strange attractor; time dependent expectation values and correlation functions of observables can be evaluated via hybrid quantum-classical formulae in which the quantum character enters only via the initial Wigner function. If a classical phase-space distribution is chosen for the latter or if the map is iterated sufficiently
many times the formulae become entirely classical, and powerful classical trace formulae apply.
Received 7 October 1999 相似文献
9.
O. Brodier T. Neicu A. Kudrolli 《The European Physical Journal B - Condensed Matter and Complex Systems》2001,23(3):365-372
We report a numerical study of the flexural modes of a plate using semi-classical analysis developed in the context of quantum
systems. We first introduce the Clover billiard as a paradigm for a system inside which rays exhibit stable and chaotic trajectories.
The resulting phase space explored by the ray trajectories is illustrated using the Poincare surface of section, and shows
that it has both integrable and chaotic regions. Examples of the stable and the unstable periodic orbits in the geometry are
presented. We numerically solve the biharmonic equation for the flexural vibrations of the Clover shaped plate with clamped
boundary conditions. The first few hundred eigenvalues and the eigenfunctions are obtained using a boundary elements method.
The Fourier transform of the eigenvalues show strong peaks which correspond to ray periodic orbits. However, the peaks corresponding
to the shortest stable periodic orbits are not stronger than the peaks associated with unstable periodic orbits. We also perform
statistics on the obtained eigenvalues and the eigenfunctions. The eigenvalue spacing distribution P(s) shows a strong peak and therefore deviates from both the Poisson and the Wigner distribution of random matrix theory at
small spacings because of the C4v symmetry of the Clover geometry. The density distribution of the eigenfunctions is observed to agree with the Porter-Thomas
distribution of random matrix theory.
Received 12 February 2001 and Received in final form 17 April 2001 相似文献
10.
Quantum spin dynamics as a model for quantum computer operation 总被引:1,自引:0,他引:1
H. De Raedt K. Michielsen A. Hams S. Miyashita K. Saito 《The European Physical Journal B - Condensed Matter and Complex Systems》2002,27(1):15-28
We study effects of the physical realization of quantum computers on their logical operation. Through simulation of physical
models of quantum computer hardware, we analyze the difficulties that are encountered in programming physical realizations
of quantum computers. Examples of logically identical implementations of the controlled-NOT operation and Grover's database
search algorithm are used to demonstrate that the results of a quantum computation are unstable with respect to the physical
realization of the quantum computer. We discuss the origin of these instabilities and discuss possibilities to overcome this,
for practical purposes, fundamental limitation of quantum computers.
Received 5 November 2001 and Received in final form 8 February 2002 相似文献
11.
I.O. Kulik T. Hakioğlu A. Barone 《The European Physical Journal B - Condensed Matter and Complex Systems》2002,30(2):219-226
We examine a generic three level mechanism of quantum computation in which all fundamental single and double qubit quantum
logic gates are operating under the effect of adiabatically controllable static (radiation free) bias couplings between the
states. Under the time evolution imposed by these bias couplings the quantum state cycles between the two degenerate levels
in the ground state and the quantum gates are realized by changing Hamiltonian at certain time intervals when the system collapses
to a two state subspace. We propose a physical implementation of the mechanism using Aharonov-Bohm persistent-current loops
in crossed electric and magnetic fields, with the output of the loop read out by using a quantum Hall effect aided mechanism.
Received 26 March 2002 / Received in final form 8 July 2002
Published online 19 November 2002 相似文献
12.
J. Bhattacharya P.P. Kanjilal 《The European Physical Journal B - Condensed Matter and Complex Systems》2000,13(2):399-403
The correlation coefficient vs. prediction time profile has been widely used to distinguish chaos from noise. The correlation coefficient remains initially
high, gradually decreasing as prediction time increases for chaos and remains low for all prediction time for noise. We here
show that for some chaotic series with dominant embedded cyclical component(s), when modelled through a newly developed scheme
of periodic decomposition, will yield high correlation coefficient even for long prediction time intervals, thus leading to
a wrong assessment of inherent chaoticity. But if this profile of correlation coefficient vs. prediction horizon is compared with the profile obtained from the surrogate series, correct interpretations about the underlying
dynamics are very much likely.
Received 8 March 1999 相似文献
13.
A. Politi S. Ruffo L. Tessieri 《The European Physical Journal B - Condensed Matter and Complex Systems》2000,14(4):673-679
We have investigated numerically the quantum evolution of a -like wave-packet in a quenched disordered medium described by a tight-binding Hamiltonian with long-range hopping (band random
matrix approach). We have obtained clean data for the scaling properties in time and in the bandwidth b of the packet width and its fluctuations with respect to disorder realizations. We confirm that the fluctuations of the packet width in the steady-state show an anomalous
scaling [0pt] with [0pt] . This can be related to the presence of non-Gaussian tails in the distribution of [0pt]. Finally, we have analysed the steady state probability profile and we have found 1/b corrections with respect to the theoretical formula derived by Zhirov in the limit, except at the origin, where the corrections are .
Received 6 August 1999 and Received in final form 22 October 1999 相似文献
14.
J.O. Andersen 《The European Physical Journal B - Condensed Matter and Complex Systems》2002,28(4):389-396
We consider an interacting homogeneous Bose gas at zero temperature in two spatial dimensions. The properties of the system
can be calculated as an expansion in powers of g, where g is the coupling constant. We calculate the ground state pressure and the ground state energy density to second order in the
quantum loop expansion. The renormalization group is used to sum up leading and subleading logarithms from all orders in perturbation
theory. In the dilute limit, the renormalization group improved pressure and energy density are expansions in powers of the
T
2B and T
2Bln(T
2B), respectively, where T
2B is the two-body T-matrix.
Received 19 April 2002 Published online 13 August 2002 相似文献
15.
G. Vilasi 《The European Physical Journal B - Condensed Matter and Complex Systems》2002,30(2):207-210
Melnikov-method-based theoretical results are demonstrated concerning the relative effectiveness of any two weak excitations in suppressing homoclinic/heteroclinic chaos of a relevant class of dissipative, low-dimensional and
non-autonomous systems for the main resonance between the chaos-inducing and chaos-suppressing excitations. General analytical
expressions are derived from the analysis of generic Melnikov functions providing the boundaries of the regions as well as
the enclosed area in the amplitude/initial phase plane of the chaos-suppressing excitation where homoclinic/heteroclinic chaos
is inhibited. The relevance of the theoretical results on chaotic attractor elimination is confirmed by means of Lyapunov
exponent calculations for a two-well Duffing oscillator.
Received 21 May 2002 / Received in final form 13 September 2002 Published online 29 November 2002 相似文献
16.
P. Schlagheck A. Buchleitner 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2003,22(3):401-415
We provide a detailed quantum treatment of the spectral characteristics and of the dynamics of nondispersive two-electron
wave packets along the periodically driven, collinear frozen planet configuration of helium. These highly correlated, long-lived
wave packets arise as a quantum manifestation of regular islands in a mixed classical phase space, which are induced by nonlinear
resonances between the external driving and the unperturbed dynamics of the frozen-planet configuration. Particular emphasis
is given to the dependence of the ionization rates of the wave packet states on the driving field parameters and on the quantum
mechanical phase space resolution, preceded by a comparison of 1D and 3D life times of the unperturbed frozen planet. Furthermore,
we study the effect of a superimposed static electric field component, which, on the grounds of classical considerations,
is expected to stabilize the real 3D dynamics against large (and possibly ionizing) deviations from collinearity.
Received 7 November 2002 / Received in final form 2 December 2002 Published online 28 January 2003 相似文献
17.
Pil H. Song ILki Kim 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2003,23(2):299-303
We study the effects of dissipation or leakage on the time evolution of Grover's algorithm for a quantum computer. We introduce
an effective two-level model with dissipation and randomness (imperfections), which is based upon the idea that ideal Grover's
algorithm operates in a 2-dimensional Hilbert space. The simulation results of this model and Grover's algorithm with imperfections
are compared, and it is found that they are in good agreement for appropriately tuned parameters. It turns out that the main
features of Grover's algorithm with imperfections can be understood in terms of two basic mechanisms, namely, a diffusion
of probability density into the full Hilbert space and a stochastic rotation within the original 2-dimensional Hilbert space.
Received 12 August 2002 / Received in final form 14 October 2002 Published online 4 February 2003 相似文献
18.
G.N. Katomeris S.N. Evangelou 《The European Physical Journal B - Condensed Matter and Complex Systems》2000,16(1):133-136
We examine the validity of the recently proposed semi-Poisson level spacing distribution function P(S), which characterizes “critical quantum chaos”, in 2D disordered systems with spin-orbit coupling. At the Anderson transition
we show that the semi-Poisson P(S) can describe closely the critical distribution obtained with averaged boundary conditions, over Dirichlet in one direction
with periodic in the other and Dirichlet in both directions. We also obtain a sub-Poisson linear number variance , with asymptotic value . The obtained critical statistics, intermediate between Wigner and Poisson, is discussed for disordered systems and chaotic
models.
Received 1 September 1999 相似文献
19.
L.G.G.V. Dias da Silva M.A.M. de Aguiar 《The European Physical Journal B - Condensed Matter and Complex Systems》2000,16(4):719-728
We propose a simple method to calculate periodic orbits in two-dimensional systems with no symbolic dynamics. The method is
based on a line by line scan of the Poincaré surface of section and is particularly useful for billiards. We have applied
it to the Square and Sinai's billiards subjected to a uniform orthogonal magnetic field and we obtained about 2000 orbits
for both systems using absolutely no information about their symbolic dynamics.
Received 21 September 1999 and Received in final form 13 April 2000 相似文献
20.
P.J. Edwards G.H. Pollard W.N. Cheung 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2002,18(2):147-153
Quantum key exchanges using weak coherent (Poissonian) single-photon sources are open to attack by a variety of eavesdropping
techniques. Quantum-correlated photon sources provide a means of flagging potentially insecure multiple-photon emissions and
thus extending the secure quantum key channel capacity and the secure key distribution range. We present indicative photon-counting
statistics for a fully correlated Poissonian multibeam photon source in which the transmitted beam is conditioned by photon
number measurements on the remaining beams with non-ideal multiphoton counters. We show that significant rejection of insecure
photon pulses from a twin-beam source cannot be obtained with a detector having a realistic quantum efficiency. However quantum-correlated
(quadruplet or octuplet) multiplet photon sources conditioned by high efficiency multiphoton counters could provide large
improvements in the secure channel capacity and the secure distribution range of high loss systems such as those using the
low earth orbit satellite links proposed for global quantum key distribution.
Received 14 July and Received in final form 20 November 2001 相似文献