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1.
B. Georgeot D.L. Shepelyansky 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2002,19(2):263-266
Since Boltzmann developed the statistical theory for macroscopic thermodynamics the question has relentlessly been put forward
of how time-reversibility at microscopic level is compatible with macroscopic irreversibility. Here we show that a quantum
computer can efficiently simulate a macroscopic thermodynamic process with chaotic microscopic dynamics and invert the time
arrow even in presence of quantum errors. In contrast, small errors in classical computer simulation of this dynamics grow
exponentially with time and rapidly destroy time-reversibility.
Received 31 October 2001 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.
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
5.
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
6.
A quasi-crisis in a quasi-dissipative system 总被引:3,自引:0,他引:3
X. -M. Wang Y. -M. Wang K. Zhang W. -X. Wang H. Chen Y. -M. Jiang Y. -Q. Lu J. -S. Mao D. -R. He 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2002,19(1):119-124
A system concatenated by two area-preserving maps may be addressed as “quasi-dissipative", since such a system can display
dissipative behaviors. This is due to noninvertibility induced by discontinuity in the system function. In such a system,
the image set of the discontinuous border forms a chaotic quasi-attractor. At a critical control parameter value the quasi-attractor
suddenly vanishes. The chaotic iterations escape, via a leaking hole, to an emergent period-8 elliptic island. The hole is the intersection of the chaotic quasi-attractor and
the period-8 island. The chaotic quasi-attractor thus changes to chaotic quasi-transients. The scaling behavior that drives
the quasi-crisis has been investigated numerically.
Received 29 May 2001 and Received in final form 6 November 2001 相似文献
7.
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
8.
A. Laforgia X. Leoncini L. Kuznetsov G.M. Zaslavsky 《The European Physical Journal B - Condensed Matter and Complex Systems》2001,20(3):427-440
The advection of passive tracers in a system of 4 identical point vortices is studied when the motion of the vortices is chaotic.
The phenomenon of vortex-pairing has been observed and statistics of the pairing time is computed. The distribution exhibits
a power-law tail with exponent ∼ 3.6 implying finite average pairing time. This exponents is in agreement with its computed
analytical estimate of 3.5. Tracer motion is studied for a chosen initial condition of the vortex system. Accessible phase
space is investigated. The size of the cores around the vortices is well approximated by the minimum inter-vortex distance
and stickiness to these cores is observed. We investigate the origin of stickiness which we link to the phenomenon of vortex
pairing and jumps of tracers between cores. Motion within the core is considered and fluctuations are shown to scale with
tracer-vortex distance r as r
6. No outward or inward diffusion of tracers are observed. This investigation allows the separation of the accessible phase
space in four distinct regions, each with its own specific properties: the region within the cores, the reunion of the periphery
of all cores, the region where vortex motion is restricted and finally the far-field region. We speculate that the stickiness
to the cores induced by vortex-pairings influences the long-time behavior of tracers and their anomalous diffusion.
Received 28 September 2000 and Received in final form 9 February 2001 相似文献
9.
X.-M. Wang Z.-J. Fang J.-F. Zhang 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2006,37(3):417-422
The multiple Devil's staircase, which describes phase-locking
behavior, is observed in a discontinuous nonlinear circle map.
Phase-locked steps form many towers with similar structure in
winding number(W)-parameter(k) space. Each step belongs to a
certain period-adding sequence that exists in a smooth curve. The
Collision modes that determine steps and the sequence of mode
transformations create a variety of tower structures and their
particular characteristics. Numerical results suggest a scaling
law for the width of phase-locked steps in the
period-adding (W=n/(n+i), n,i∈int) sequences, that is,
Δk(n)∝n-τ (τ>0). And the study indicates
that the multiple Devil's staircase
may be common in a class of discontinuous circle maps. 相似文献
10.
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
11.
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
12.
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
13.
P. Navez 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2002,18(2):219-228
We describe a cryptographic protocol consisting of two entangled beams of squeezed light which makes use of statistical tests
to deduce the secret key bit. The sender (Alice) encrypts a secret key by modulating the phase of the beam sent in public
by the receiver (Bob) who keeps the other beam private. The knowledge of the degree of non classical correlation between the
beam quadrature components measured in private and in public allows only Bob to decrypt the secret key. With a view towards
absolute security, we formally prove that any external intervention from an eavesdropper (Eve) during the communication process
introduces necessarily some modification susceptible to be detected. Statistical confidentiality tests are proposed to detect
the presence of Eve.
Received 12 July 2001 and Received in final form 11 November 2001 相似文献
14.
We discuss strange nonchaotic attractors (SNAs) in addition to chaotic and regular attractors in a quasiperiodically driven system with time delays. A route and the associated mechanism are described for a special type of attractor called strange-nonchaotic-attractor-like (SNA-like) through T2 torus bifurcation. The type of attractor can be observed in large parameter domains and it is easily mistaken for a true SNA judging merely from the phase portrait, power spectrum and the largest Lyapunov exponent. SNA-like attractor is not strange and has no phase sensitivity. Conditions for Neimark-Sacker bifurcation are obtained by theoretical analysis for the unforced system. Complicated and interesting dynamical transitions are investigated among the different tongues. 相似文献
15.
G.F. Mkrtchian 《Physics letters. A》2008,372(32):5270-5273
We consider the model of quantum computer, which is represented as a Ising spin lattice, where qubits (spin-half systems) are separated by the isolators (two spin-half systems). In the idle mode or at the single bit operations the total spin of isolators is 0. There are no need of complicated protocols for correcting the phase and probability errors due to permanent interaction between the qubits. We present protocols for implementation of universal quantum gates with the rectangular radio-frequency pulses. 相似文献
16.
A.N. Pisarchik R. Meucci F.T. Arecchi 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2001,13(3):385-391
The discrete distribution of homoclinic orbits has been investigated numerically and experimentally in a CO2 laser with feedback. The narrow chaotic ranges appear consequently when a laser parameter (bias voltage or feedback gain)
changes exponentially. Up to six consecutive chaotic windows have been observed in the numerical simulation as well as in
the experiments. Every subsequent increase in the number of loops in the upward spiral around the saddle focus is accompanied
by the appearance of the corresponding chaotic window. The discrete character of homoclinic chaos is also demonstrated through
bifurcation diagrams, eigenvalues of the fixed point, return maps, and return times of the return maps.
Received 28 September 2000 and 27 October 2000 相似文献
17.
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
18.
Crystal lattice quantum computer 总被引:2,自引:0,他引:2
31 P nucleus can be used to represent a quantum bit (‘qubit’) with a relatively long relaxation time. In a CeP crystal lattice,
31P nuclei are periodically situated in three dimensions at distances of about 6 Å. The application of a static magnetic field
gradient in one direction causes differences in the Zeemanfrequencies of separate nuclei. This allows thousands of distinct
qubits to be individually addressed. Initializations of the qubits can be done efficiently by the Pound–Overhauser double
resonance effect on the nuclear spins and the antiferromagnetically ordered 4f electron spins of cerium ions. Logic operations
can be performed by simple pulse sequences, and computational results after logic operations can be measured by the nuclear
magnetic resonance of neighboring nuclei, or the electron resonance of neighboring 4f electrons of cerium ions.
Received: 26 October 1998/Accepted: 29 October 1998 相似文献
19.
M. Genovese C. Novero 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2002,21(1):109-113
We propose a quantum transmission based on bi-photons, which are doubly-entangled both in polarisation and phase. This scheme
finds a natural application in quantum cryptography, where we show that an eventual eavesdropper is bound to introduce a larger
error on the quantum communication than for a single entangled bi-photon communication, when he steels the same information.
Received 23 July 2001 / Received in final form 30 November 2001 Published online 24 September 2002 相似文献
20.
U. Yurtsever D. Strekalov J.P. Dowling 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2003,22(3):365-371
A quantum gravity-gradiometer consists of two spatially separated ensembles of atoms interrogated by pulses of a common laser
beam. The laser pulses cause the probability amplitudes of atomic ground-state hyperfine levels to interfere, producing two,
motion-sensitive, phase shifts, which allow the measurement of the average acceleration of each ensemble, and, via simple
differencing, of the acceleration gradient. Here we propose entangling the quantum states of atoms from the two ensembles
prior to the pulse sequence, and show that entanglement encodes their relative acceleration in a single interference phase
which can be measured directly, with no need for differencing.
Received 6 June 2002 / Received in final form 25 October 2002 Published online 28 January 2003 相似文献