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arXiv · 1509.05806

Abelian Hypergroups and Quantum Computation

Juan Bermejo-Vega·Kevin C. Zatloukal
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Abstract

Motivated by a connection, described here for the first time, between the hidden normal subgroup problem (HNSP) and abelian hypergroups (algebraic objects that model collisions of physical particles), we develop a stabilizer formalism using abelian hypergroups and an associated classical simulation theorem (a la Gottesman-Knill). Using these tools, we develop the first provably efficient quantum algorithm for finding hidden subhypergroups of nilpotent abelian hypergroups and, via the aforementioned connection, a new, hypergroup-based algorithm for the HNSP on nilpotent groups. We also give efficient methods for manipulating non-unitary, non-monomial stabilizers and an adaptive Fourier sampling technique of general interest.

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Juan Bermejo-Vega, Kevin C. Zatloukal. 2015-09-18. Abelian Hypergroups and Quantum Computation. https://arxiv.org/abs/1509.05806

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