Quantum stochastic walks: A generalization of classical random walks and quantum walks

Journal Article · Mon Feb 15 00:00:00 EST 2010 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.81.022323· OSTI ID:21408212

Whitfield, James D; Rodriguez-Rosario, Cesar A; Aspuru-Guzik, Alan ^[1]

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1. Department of Chemistry and Chemical Biology and Center for Excitonics, Harvard University, Cambridge, Massachusetts 02138 (United States)

We introduce the quantum stochastic walk (QSW), which determines the evolution of a 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 and the glued tree of depth three to observe the behavior of the QW-to-CRW transition.

• OSTI ID: 21408212
• Journal Information: Physical Review. A, Vol. 81, Issue 2; Other Information: DOI: 10.1103/PhysRevA.81.022323; (c) 2010 The American Physical Society; ISSN 1050-2947
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
EQUATIONS OF MOTION
EVOLUTION
GRAPH THEORY
PROBABILITY
QUANTUM MECHANICS
RANDOMNESS
STOCHASTIC PROCESSES
DIFFERENTIAL EQUATIONS
EQUATIONS
MATHEMATICS
MECHANICS
PARTIAL DIFFERENTIAL EQUATIONS