2,579 research outputs found
An HHL-Based Algorithm for Computing Hitting Probabilities of Quantum Random Walks
We present a novel application of the HHL (Harrow-Hassidim-Lloyd) algorithm
-- a quantum algorithm solving systems of linear equations -- in solving an
open problem about quantum random walks, namely computing hitting (or
absorption) probabilities of a general (not only Hadamard) one-dimensional
quantum random walks with two absorbing boundaries. This is achieved by a
simple observation that the problem of computing hitting probabilities of
quantum random walks can be reduced to inverting a matrix. Then a quantum
algorithm with the HHL algorithm as a subroutine is developed for solving the
problem, which is faster than the known classical algorithms by numerical
experiments
Absorption problems for quantum walks in one dimension
This paper treats absorption problems for the one-dimensional quantum walk
determined by a 2 times 2 unitary matrix U on a state space {0,1,...,N} where N
is finite or infinite by using a new path integral approach based on an
orthonormal basis P, Q, R and S of the vector space of complex 2 times 2
matrices. Our method studied here is a natural extension of the approach in the
classical random walk.Comment: 15 pages, small corrections, journal reference adde
Analysis of Absorbing Times of Quantum Walks
Quantum walks are expected to provide useful algorithmic tools for quantum
computation. This paper introduces absorbing probability and time of quantum
walks and gives both numerical simulation results and theoretical analyses on
Hadamard walks on the line and symmetric walks on the hypercube from the
viewpoint of absorbing probability and time.Comment: LaTeX2e, 14 pages, 6 figures, 1 table, figures revised, references
added, to appear in Physical Review
Braiding Interactions in Anyonic Quantum Walks
The anyonic quantum walk is a dynamical model describing a single anyon
propagating along a chain of stationary anyons and interacting via mutual
braiding statistics. We review the recent results on the effects of braiding
statistics in anyonic quantum walks in quasi-one dimensional ladder geometries.
For anyons which correspond to spin-1/2 irreps of the quantum groups ,
the non-Abelian species gives rise to entanglement between the
walker and topological degrees of freedom which is quantified by quantum link
invariants over the trajectories of the walk. The decoherence is strong enough
to reduce the walk on the infinite ladder to classical like behaviour. We also
present numerical results on mixing times of or Ising model anyon
walks on cyclic graphs. Finally, the possible experimental simulation of the
anyonic quantum walk in Fractional Quantum Hall systems is discussed.Comment: 13 pages, submitted to Proceedings of the 2nd International
Conference on Theoretical Physics (ICTP 2012
Quantum walks on two kinds of two-dimensional models
In this paper, we numerically study quantum walks on two kinds of
two-dimensional graphs: cylindrical strip and Mobius strip. The two kinds of
graphs are typical two-dimensional topological graph. We study the crossing
property of quantum walks on these two models. Also, we study its dependence on
the initial state, size of the model. At the same time, we compare the quantum
walk and classical walk on these two models to discuss the difference of
quantum walk and classical walk
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