7 research outputs found
Quantum Walk with Jumps
We analyze a special class of 1-D quantum walks (QWs) realized using optical
multi-ports. We assume non-perfect multi-ports showing errors in the
connectivity, i.e. with a small probability the multi- ports can connect not to
their nearest neighbor but to another multi-port at a fixed distance - we call
this a jump. We study two cases of QW with jumps where multiple displacements
can emerge at one timestep. The first case assumes time-correlated jumps
(static disorder). In the second case, we choose the positions of jumps
randomly in time (dynamic disorder). The probability distributions of position
of the QW walker in both instances differ significantly: dynamic disorder leads
to a Gaussian-like distribution, while for static disorder we find two distinct
behaviors depending on the parity of jump size. In the case of even-sized
jumps, the distribution exhibits a three-peak profile around the position of
the initial excitation, whereas the probability distribution in the odd case
follows a Laplace-like discrete distribution modulated by additional
(exponential) peaks for long times. Finally, our numerical results indicate
that by an appropriate mapping an universal functional behavior of the variance
of the long-time probability distribution can be revealed with respect to the
scaled average of jump size.Comment: 11 pages, 13 figure
Quantum walks: a comprehensive review
Quantum walks, the quantum mechanical counterpart of classical random walks,
is an advanced tool for building quantum algorithms that has been recently
shown to constitute a universal model of quantum computation. Quantum walks is
now a solid field of research of quantum computation full of exciting open
problems for physicists, computer scientists, mathematicians and engineers.
In this paper we review theoretical advances on the foundations of both
discrete- and continuous-time quantum walks, together with the role that
randomness plays in quantum walks, the connections between the mathematical
models of coined discrete quantum walks and continuous quantum walks, the
quantumness of quantum walks, a summary of papers published on discrete quantum
walks and entanglement as well as a succinct review of experimental proposals
and realizations of discrete-time quantum walks. Furthermore, we have reviewed
several algorithms based on both discrete- and continuous-time quantum walks as
well as a most important result: the computational universality of both
continuous- and discrete- time quantum walks.Comment: Paper accepted for publication in Quantum Information Processing
Journa
A Model of the Distribution of Wealth in Society
A model of the distribution of wealth in society will be presented. The model is based on an agent-based Monte Carlo simulation where interaction (exchange of wealth) is allowed along the edges of a small-world network. The interaction is like inelastic scattering and it is characterized by two constants. Simulations of the model show that the distribution behaves as a power-law and it agrees with results of Pareto.
Evolution of imitation networks in Minority Game model
The Minority Game is adapted to study the “imitation dilemma”, i.e. the tradeoff between local benefit and global harm coming from imitation. The agents are placed on a substrate network and are allowed to imitate more successful neighbours. Imitation domains, which are oriented trees, are formed. We investigate size distribution of the domains and in-degree distribution within the trees. We use four types of substrate: one-dimensional chain; Erdös-Rényi graph; Barabási-Albert scale-free graph; Barabási-Albert 'model A' graph. The behaviour of some features of the imitation network strongly depend on the information cost epsilon, which is the percentage of gain the imitators must pay to the imitated. Generally, the system tends to form a few domains of equal size. However, positive epsilon makes the system stay in a long-lasting metastable state with complex structure. The in-degree distribution is found to follow a power law in two cases of those studied: for Erdös-Rényi substrate for any epsilon and for Barabási-Albert scale-free substrate for large enough epsilon. A brief comparison with empirical data is provided. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 200789.65.-s Social and economic systems, 05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion, 02.50.-r Probability theory, stochastic processes, and statistics,