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arXiv · 0906.3094

Quantum search algorithms on the hypercube

Birgit Hein·Gregor Tanner
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Abstract

We investigate a set of discrete-time quantum search algorithms on the n-dimensional hypercube following a proposal by Shenvi, Kempe and Whaley. We show that there exists a whole class of quantum search algorithms in the symmetry reduced space which perform a search of a marked vertex in time of order $\sqrt{N}$ where $N = 2^n$, the number of vertices. In analogy to Grover's algorithm, the spatial search is effectively facilitated through a rotation in a two-level sub-space of the full Hilbert space. In the hypercube, these two-level systems are introduced through avoided crossings. We give estimates on the quantum states forming the 2-level sub-spaces at the avoided crossings and derive improved estimates on the search times.

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Birgit Hein, Gregor Tanner. 2009-06-17. Quantum search algorithms on the hypercube. https://doi.org/10.1088/1751-8113/42/8/085303

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