6,132 research outputs found
Can epidemic models describe the diffusion of topics across disciplines?
This paper introduces a new approach to describe the spread of research topics across disciplines using epidemic models. The approach is based on applying individual-based models from mathematical epidemiology to the diffusion of a research topic over a contact network that represents knowledge flows over the map of science—as obtained from citations between ISI Subject Categories. Using research publications on the protein class kinesin as a case study, we report a better fit between model and empirical data when using the citation-based contact network. Incubation periods on the order of 4–15.5 years support the view that, whilst research topics may grow very quickly, they face difficulties to overcome disciplinary boundaries
Complex chaos in conditional qubit dynamics and purification protocols
Selection of an ensemble of equally prepared quantum systems, based on
measurements on it, is a basic step in quantum state purification. For an
ensemble of single qubits, iterative application of selective dynamics has been
shown to lead to complex chaos, which is a novel form of quantum chaos with
true sensitivity to the initial conditions. The Julia set of initial valuse
with no convergence shows a complicated structre on the complex plane. The
shape of the Julia set varies with the parameter of the dynamics. We present
here results for the two qubit case demonstrating how a purification process
can be destroyed with chaotic oscillations
Complex chaos in the conditional dynamics of qubits
We analyze the consequences of iterative measurement-induced nonlinearity on
the dynamical behavior of qubits. We present a one-qubit scheme where the
equation governing the time evolution is a complex-valued nonlinear map with
one complex parameter. In contrast to the usual notion of quantum chaos,
exponential sensitivity to the initial state occurs here. We calculate
analytically the Lyapunov exponent based on the overlap of quantum states, and
find that it is positive. We present a few illustrative examples of the
emerging dynamics.Comment: 4 pages, 3 figure
Optimized quantum random-walk search algorithms
Shenvi, Kempe and Whaley's quantum random-walk search (SKW) algorithm [Phys.
Rev. A 67, 052307 (2003)] is known to require number of oracle
queries to find the marked element, where is the size of the search space.
The overall time complexity of the SKW algorithm differs from the best
achievable on a quantum computer only by a constant factor. We present
improvements to the SKW algorithm which yield significant increase in success
probability, and an improvement on query complexity such that the theoretical
limit of a search algorithm succeeding with probability close to one is
reached. We point out which improvement can be applied if there is more than
one marked element to find.Comment: 7 pages, 2 figures. Major revision according to referee repor
Scattering quantum random-walk search with errors
We analyze the realization of a quantum-walk search algorithm in a passive,
linear optical network. The specific model enables us to consider the effect of
realistic sources of noise and losses on the search efficiency. Photon loss
uniform in all directions is shown to lead to the rescaling of search time.
Deviation from directional uniformity leads to the enhancement of the search
efficiency compared to uniform loss with the same average. In certain cases
even increasing loss in some of the directions can improve search efficiency.
We show that while we approach the classical limit of the general search
algorithm by introducing random phase fluctuations, its utility for searching
is lost. Using numerical methods, we found that for static phase errors the
averaged search efficiency displays a damped oscillatory behaviour that
asymptotically tends to a non-zero value.Comment: 10 pages, 10 figures. Two figures added for clarity, also made
improvements to the tex
Directional correlations in quantum walks with two particles
Quantum walks on a line with a single particle possess a classical analogue. Involving more walkers opens up the possibility of studying collective quantum effects, such as many-particle correlations. In this context, entangled initial states and the indistinguishability of the particles play a role. We consider the directional correlations between two particles performing a quantum walk on a line. For non-interacting particles, we find analytic asymptotic expressions and give the limits of directional correlations. We show that by introducing delta-interaction between the particles, one can exceed the limits for non-interacting particles
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