2 research outputs found
Quantum stochastic walks: A generalization of classical random walks and quantum walks
We introduce the quantum stochastic walk (QSW), which determines the
evolution of generalized quantum mechanical walk on a graph that obeys a
quantum stochastic equation of motion. Using an axiomatic approach, we specify
the rules for all possible quantum, classical and quantum-stochastic
transitions from a vertex as defined by its connectivity. We show how the
family of possible QSWs encompasses both the classical random walk (CRW) and
the quantum walk (QW) as special cases, but also includes more general
probability distributions. As an example, we study the QSW on a line, the QW to
CRW transition and transitions to genearlized QSWs that go beyond the CRW and
QW. QSWs provide a new framework to the study of quantum algorithms as well as
of quantum walks with environmental effects.Comment: 5 pages, 2 figures, 1 table. Video Abstract: http://vimeo.com/474903
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