Group velocity of discrete-time quantum walks

Journal Article · Fri May 15 00:00:00 EDT 2009 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.79.052317· OSTI ID:21300825

Kempf, A ^[1]; Portugal, R ^[2]

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1. Department of Physics, University of Queensland, St. Lucia, Queensland 4072 (Australia)
2. Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1 (Canada)

We show that certain types of quantum walks can be modeled as waves that propagate in a medium with phase and group velocities that are explicitly calculable. Since the group and phase velocities indicate how fast wave packets can propagate causally, we propose the use of these wave velocities in our definition for the hitting time of quantum walks. Our definition of hitting time has the advantage that it requires neither the specification of a walker's initial condition nor of an arrival probability threshold. We give full details for the case of quantum walks on the Cayley graphs of Abelian groups. This includes the special cases of quantum walks on the line and on hypercubes.

• OSTI ID: 21300825
• Journal Information: Physical Review. A, Vol. 79, Issue 5; Other Information: DOI: 10.1103/PhysRevA.79.052317; (c) 2009 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 1050-2947
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
GRAPH THEORY
GROUP THEORY
PHASE VELOCITY
PROBABILITY
QUANTUM COMPUTERS
SCHROEDINGER EQUATION
SPECIFICATIONS
WAVE PACKETS