Weak Limit of the 3-State Quantum Walk on the Line

Abstract

We revisit the one dimensional discrete time quantum walk with 3 states and the Grover coin. We derive analytic expressions for observed the localization, an long time approximation for the probability density function (PDF). We also connect the time averaged approximation to the PDF found by Inui et. al. to a spatial average of the walk. We show that this smooth approximation constitutes a proper PDF that predicts moments of the real PDF accurately.

8 pages, revtex, for related information see http://www.physics.emory.edu/faculty/boettcher/ v2: minor changes, references added

References in corpus (2)

• Universal computation by quantum walk
• Spatial search by quantum walk

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