Abelian Hypergroups and Quantum Computation

Abelian Hypergroups and Quantum Computation

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...

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Hauptverfasser: Bermejo-Vega, Juan, Zatloukal, Kevin C
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Sprache:eng
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Computer Science - Computational Complexity
Mathematics - Mathematical Physics
Physics - Mathematical Physics
Physics - Quantum Physics
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description 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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subjects Computer Science - Computational Complexity
Mathematics - Mathematical Physics
Physics - Mathematical Physics
Physics - Quantum Physics
title Abelian Hypergroups and Quantum Computation
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