Abstract structure of unitary oracles for quantum algorithms
  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. 
William Zeng (University of Oxford), Jamie Vicary (University of   Singapore and University of Oxford)
quant-ph cs.LO math.CT