2014/06/30 by William Zeng, Jamie Vicary
Physics and Astronomy · Computer Science · Mathematics · #quant-ph #cs.LO #math.CT
paper · pdf · doi:10.4204/eptcs.172.19
published as EPTCS 172, 2014, pp. 270-284 · In Proceedings QPL 2014, arXiv:1412.8102
arxiv created 2014/12/30 · arxiv updated 2014/12/31
We show that a pair of complementary dagger-Frobenius algebras, equipped with a self-conjugate comonoid homomorphism onto one of the algebras, produce a nontrivial unitary morphism on the product of the algebras. This gives an abstract understanding of the structure of an oracle in a quantum computation, and we apply this understanding to develop a new algorithm for the deterministic identification of group homomorphisms into abelian groups. We also discuss an application to the categorical theory of signal-flow networks.