Inhomogeneous quantum walks

Noah Linden; James Sharam

doi:10.1103/PhysRevA.80.052327

Inhomogeneous quantum walks

Noah Linden^*, James Sharam

^*Corresponding author for this work

Research output: Contribution to journal › Article (Academic Journal) › peer-review

35 Citations (Scopus)

Abstract

We study a natural construction of a general class of inhomogeneous quantum walks (namely, walks whose transition probabilities depend on position). Within the class we analyze walks that are periodic in position and show that, depending on the period, such walks can be bounded or unbounded in time; in the latter case we analyze the asymptotic speed. We compare the construction to others in the existing literature. As an example we give a quantum version of a nonirreducible classical walk: the Poacutelya Urn.

Original language	English
Article number	052327
Number of pages	11
Journal	Physical Review A: Atomic, Molecular and Optical Physics
Volume	80
Issue number	5
DOIs	https://doi.org/10.1103/PhysRevA.80.052327
Publication status	Published - Nov 2009

Keywords

ALGORITHMS
random processes
CELLULAR-AUTOMATA
graph theory
probability
quantum theory
Markov processes

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title = "Inhomogeneous quantum walks",

abstract = "We study a natural construction of a general class of inhomogeneous quantum walks (namely, walks whose transition probabilities depend on position). Within the class we analyze walks that are periodic in position and show that, depending on the period, such walks can be bounded or unbounded in time; in the latter case we analyze the asymptotic speed. We compare the construction to others in the existing literature. As an example we give a quantum version of a nonirreducible classical walk: the Poacutelya Urn.",

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AB - We study a natural construction of a general class of inhomogeneous quantum walks (namely, walks whose transition probabilities depend on position). Within the class we analyze walks that are periodic in position and show that, depending on the period, such walks can be bounded or unbounded in time; in the latter case we analyze the asymptotic speed. We compare the construction to others in the existing literature. As an example we give a quantum version of a nonirreducible classical walk: the Poacutelya Urn.

KW - ALGORITHMS

KW - random processes

KW - CELLULAR-AUTOMATA

KW - graph theory

KW - probability

KW - quantum theory

KW - Markov processes

U2 - 10.1103/PhysRevA.80.052327

DO - 10.1103/PhysRevA.80.052327

M3 - Article (Academic Journal)

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VL - 80

JO - Physical Review A: Atomic, Molecular and Optical Physics

JF - Physical Review A: Atomic, Molecular and Optical Physics

IS - 5

M1 - 052327

ER -

Inhomogeneous quantum walks

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Keywords

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