We apply results of [BP07, BBBP08] to compute limiting probability profiles for various quantum random walks in one and two dimensions. Using analytic machinery we show some features of the limit distribution that are not evident in an empirical intensity plot of the time 10,000 distribution. Some conjecutres are stated and computational techniques are discussed as well.

QSW_MPI is a python package developed for time-series simulation of continuous-time quantum stochastic walks. This model allows the study Markovian open systems in Lindblad formalism, including generalisation random walk and walk. Consisting interface accessing parallelised Fortran libraries utilising sparse data structures, scalable to massively parallel computers, which makes possible wide ra...

We analyze in detail the discrete–time quantum walk on the line by separating the quantum evolution equation into Markovian and interference terms. As a result of this separation, it is possible to show analytically that the quadratic increase in the variance of the quantum walker’s position with time is a direct consequence of the coherence of the quantum evolution. If the evolution is decoher...

Any positive-energy state of a free Dirac particle that is initially highly-localized, evolves in time by spreading at speeds close to the speed of light. This general phenomenon is explained by the fact that the Dirac evolution can be approximated arbitrarily closely by a quantum random walk, where the roles of coin and walker systems are naturally attributed to the spin and position degrees o...

Quantum nano-structures are likely to become primary elements of future devices. However, there are a number of significant scientific challenges to real world applications of quantum devices. These include de-coherence that erodes operation of a quantum device and control issues. In nature, certain processes have been shown to use quantum mechanical processes for overcoming these barriers. One...

We introduce memory-dependent discrete-time quantum random walk models by adding uncorrelated memory terms and also by modifying the Hamiltonian of the walker to include couplings with memory-keeping agents. We next study numerically the correlation effects in these models. We also propose a correlation exponent as a relevant and promising tool for investigation of correlation or memory (hence ...

Quantum computing became a prominent area of research with publications such as Feynman’s 1986 paper suggesting a construction for a Hamiltonian that can implement any quantum circuit [1]. Some of the key results in quantum information science such as Shor’s algorithm [2] and Grover’s algorithm [3] which show speed up over classical algorithms for integer factorisation and database searching ha...

This report presents quantum walks which are the quantum counterparts of classical random walks. Quantum walks are first defined on general graphs and the possibility of very different behavior between a classical random walk and its quantum analogue is illustrated with a simple graph. A generalization of the quantum walk protocol for a particle in a one-dimensional chain, by using several type...

The Mahler measure was introduced by in the study of number theory. It is known that appears different areas mathematics and physics. On other hand, we have been investigated a new class zeta functions for various kinds walks including quantum series our previous work on “Zeta Correspondence”. walk counterpart random walk. In this paper, present relation between function walks. Firstly consider...