2 research outputs found
Decoherence vs entanglement in coined quantum walks
Quantum versions of random walks on the line and cycle show a quadratic
improvement in their spreading rate and mixing times respectively. The addition
of decoherence to the quantum walk produces a more uniform distribution on the
line, and even faster mixing on the cycle by removing the need for
time-averaging to obtain a uniform distribution. We calculate numerically the
entanglement between the coin and the position of the quantum walker and show
that the optimal decoherence rates are such that all the entanglement is just
removed by the time the final measurement is made.Comment: 11 pages, 6 embedded eps figures; v2 improved layout and discussio
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