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arXiv · 1111.5032

Single-qubit unitary gates by graph scattering

Benjamin A. Blumer·Michael S. Underwood·David L. Feder
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Abstract

We consider the effects of plane-wave states scattering off finite graphs, as an approach to implementing single-qubit unitary operations within the continuous-time quantum walk framework of universal quantum computation. Four semi-infinite tails are attached at arbitrary points of a given graph, representing the input and output registers of a single qubit. For a range of momentum eigenstates, we enumerate all of the graphs with up to $n=9$ vertices for which the scattering implements a single-qubit gate. As $n$ increases, the number of new unitary operations increases exponentially, and for $n>6$ the majority correspond to rotations about axes distributed roughly uniformly across the Bloch sphere. Rotations by both rational and irrational multiples of $π$ are found.

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Benjamin A. Blumer, Michael S. Underwood, David L. Feder. 2011-11-21. Single-qubit unitary gates by graph scattering. https://doi.org/10.1103/physreva.84.062302

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