Abelian Hypergroups and Quantum Computation

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