Single-qubit unitary gates by graph scattering

Details Single-qubit unitary gates by graph scattering Single-qubit unitary gates by graph scattering

2011-11-21

arxiv.org/abs/1111.5032v1

Phys. Rev. A 84, 062302 (2011)

Physics

Quantum Physics

8 pages, 7 figures

Scientific paper

10.1103/PhysRevA.84.062302

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 $\pi$ are found.

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