Quantum walks based on an interferometric analogy

Journal Article · Mon Sep 01 04:00:00 EDT 2003 · Physical Review. A

DOI:https://doi.org/10.1103/PhysRevA.68.032314· OSTI ID:20640158

Hillery, Mark; Bergou, Janos ^[1]; Feldman, Edgar ^[2]

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1. Department of Physics, Hunter College of CUNY, 695 Park Avenue, New York, New York 10021, USA (United States)
2. Department of Mathematics, Graduate Center of the City University of New York, 365 Fifth Avenue, New York, New York 10016, USA (United States)

There are presently two models for quantum walks on graphs. The ''coined'' walk uses discrete-time steps, and contains, besides the particle making the walk, a second quantum system, the coin, that determines the direction in which the particle will move. The continuous walk operates with continuous time. Here a third model for quantum walks is proposed, which is based on an analogy to optical interferometers. It is a discrete-time model, and the unitary operator that advances the walk one step depends only on the local structure of the graph on which the walk is taking place. This type of walk also allows us to introduce elements, such as phase shifters, that have no counterpart in classical random walks. Several examples are discussed.

• OSTI ID: 20640158
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 3 Vol. 68; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
GRAPH THEORY
INTERFEROMETERS
PHASE SHIFT
PROBABILITY
QUANTUM MECHANICS
RANDOMNESS