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Abstract structure of unitary oracles for quantum algorithms

Research paper by William Zeng, Jamie Vicary

Indexed on: 29 Dec '14Published on: 29 Dec '14Published in: Quantum Physics



Abstract

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.