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arXiv · 1406.1278

Abstract structure of unitary oracles for quantum algorithms

William Zeng·Jamie Vicary
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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.

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William Zeng, Jamie Vicary. 2014-06-05. Abstract structure of unitary oracles for quantum algorithms. https://doi.org/10.4204/eptcs.172.19

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