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61.
P. J. Salas 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2008,46(2):365-373
The decoherence effect on Grover algorithm has been studied numerically
through a noise modelled by a depolarizing channel. Two types of error are
introduced characterizing the qubit time evolution and gate application, so
the noise is directly related to the quantum network construction. The
numerical simulation concludes an exponential damping law for the successive
probability of the maxima as time increases. We have obtained an
allowed-error law for the algorithm: the error threshold for the allowed
noise behaves as εth(N) ∼1/N1.1 (N being the
size of the data set). As the power of N is almost one, we consider the
Grover algorithm as robust to a certain extent against decoherence. This law
also provides an absolute threshold: if the free evolution error is greater
than 0.043, Grover algorithm does not work for any number of qubits affected
by the present error model. The improvement in the probability of success,
in the case of two qubits has been illustrated by using a fault-tolerant
encoding of the initial state by means of the [[7,1,3]] quantum code. 相似文献
62.
Dave KIELPINSKI 《Frontiers of Physics in China》2008,3(4):365-381
Atomic ions trapped in ultra-high vacuum form an especially well-understood and useful physical system for quantum information
processing. They provide excellent shielding of quantum information from environmental noise, while strong, well-controlled
laser interactions readily provide quantum logic gates. A number of basic quantum information protocols have been demonstrated
with trapped ions. Much current work aims at the construction of large-scale ion-trap quantum computers using complex microfabricated
trap arrays. Several groups are also actively pursuing quantum interfacing of trapped ions with photons.
相似文献
63.
Integral representations are considered of solutions of the Airy differential equation w
–zw=0 for computing Airy functions for complex values of z. In a first method contour integral representations of the Airy functions are written as non-oscillating integrals for obtaining stable representations, which are evaluated by the trapezoidal rule. In a second method an integral representation is evaluated by using generalized Gauss–Laguerre quadrature; this approach provides a fast method for computing Airy functions to a predetermined accuracy. Comparisons are made with well-known algorithms of Amos, designed for computing Bessel functions of complex argument. Several discrepancies with Amos' code are detected, and it is pointed out for which regions of the complex plane Amos' code is less accurate than the quadrature algorithms. Hints are given in order to build reliable software for complex Airy functions. 相似文献
64.
一类描述混沌映射的符号动力系统 总被引:11,自引:0,他引:11
本文定义了符号空间上的拟移位映射,并用该类映射描述了Cantor集及平面Cantor集上的混沌映射,本文结果可看作Smale马蹄模型的简化。 相似文献
65.
N.M. Temme 《Numerical Algorithms》1997,15(2):207-225
Airy-type asymptotic representations of a class of special functions are considered from a numerical point of view. It is well known that the evaluation of the coefficients of the asymptotic series near the transition point is a difficult problem. We discuss two methods for computing the asymptotic series. One method is based on expanding the coefficients of the asymptotic series in Maclaurin series. In the second method we consider auxiliary functions that can be computed more efficiently than the coefficients in the first method, and we do not need the tabulation of many coefficients. The methods are quite general, but the paper concentrates on Bessel functions, in particular on the differential equation of the Bessel functions, which has a turning point character when order and argument of the Bessel functions are equal. 相似文献
66.
Iain A. Stewart 《Mathematical Logic Quarterly》1997,43(1):1-21
We investigate the definability in monadic ∑11 and monadic Π11 of the problems REGk, of whether there is a regular subgraph of degree k in some given graph, and XREGk, of whether, for a given rooted graph, there is a regular subgraph of degree k in which the root has degree k, and their restrictions to graphs in which every vertex has degree at most k, namely REGkk and XREGkk, respectively, for k ≥ 2 (all our graphs are undirected). Our motivation partly stems from the fact (which we prove here) that REGkk and XREGkk are logspace equivalent to CONN and REACH, respectively, for k ≥ 3, where CONN is the problem of whether a given graph is connected and REACH is the problem of whether a given graph has a path joining two given vertices. We use monadic first - order reductions, monadic ∑11 games and a recent technique due to Fagin, Stockmeyer and Vardi to almost completely classify whether these problems are definable in monadic ∑11 and monadic Π11, and we compare the definability of these problems (in monadic ∑11 and monadic Π11 with their computational complexity (which varies from solvable using logspace to NP - complete). 相似文献
67.
Wei Shyy 《国际流体数值方法杂志》1988,8(4):475-489
Recently the concept of adaptive grid computation has received much attention in the computational fluid dynamics research community. This paper continues the previous efforts of multiple one-dimensional procedures in developing and asessing the ideas of adaptive grid computation. The focus points here are the issue of numerical stability induced by the grid distribution and the accuracy comparison with previously reported work. Two two-dimensional problems with complicated characteristics—namely, flow in a channel with a sudden expansion and natural convection in an enclosed square cavity—are used to demonstrate some salient features of the adaptive grid method. For the channel flow, by appropriate distribution of the grid points the numerical algorithm can more effectively dampen out the instabilities, especially those related to artificial boundary treatments, and hence can converge to a steady-state solution more rapidly. For a more accurate finite difference operator, which contains less undesirable numerical diffusion, the present adaptive grid method can yield a steady-state and convergent solution, while uniform grids produce non-convergent and numerically oscillating solutions. Furthermore, the grid distribution resulting from the adaptive procedure is very responsive to the different characteristics of laminar and turbulent flows. For the problem of natural convection, a combination of a multiple one-dimensional adaptive procedure and a variational formulation is found very useful. Comparisons of the solutions on uniform and adaptive grids with the reported benchmark calculations demonstrate the important role that the adaptive grid computation can play in resolving complicated flow characteristics. 相似文献
68.
We experimentally show that computing with attractors leads to fast adaptive behavior in which dynamical associations can be made between different inputs which initially produce sharply distinct outputs. We do so by first defining a set of simple local procedures which allow a computing array to change its state in time so as to produce classical Pavlovian conditioning. We then examine the dynamics of coalescence and dissociation of attractors with a number of quantitative experiments. We also show how such arrays exhibit generalization and differentiation of inputs in their behavior. 相似文献
69.
The paper reports the results of work on the construction of LISP programs for various symbolic operations in complex analysis, including the evaluation of integrals around closed contours by the use of Cauchy's Theorem. It is concluded that the only difficulty in the way of the preparation of programs for all of the important and useful textbook calculations in complex analysis is that large amounts of fast storage in the computer are needed. 相似文献
70.
Das R Kumar SK Kumar A 《Journal of magnetic resonance (San Diego, Calif. : 1997)》2005,177(2):318-328
Geometric phases have stimulated researchers for its potential applications in many areas of science. One of them is fault-tolerant quantum computation. A preliminary requisite of quantum computation is the implementation of controlled dynamics of qubits. In controlled dynamics, one qubit undergoes coherent evolution and acquires appropriate phase, depending on the state of other qubits. If the evolution is geometric, then the phase acquired depend only on the geometry of the path executed, and is robust against certain types of error. This phenomenon leads to an inherently fault-tolerant quantum computation. Here we suggest a technique of using non-adiabatic geometric phase for quantum computation, using selective excitation. In a two-qubit system, we selectively evolve a suitable subsystem where the control qubit is in state |1, through a closed circuit. By this evolution, the target qubit gains a phase controlled by the state of the control qubit. Using the non-adiabatic geometric phase we demonstrate implementation of Deutsch-Jozsa algorithm and Grover's search algorithm in a two-qubit system. 相似文献