Abstract structure of unitary oracles for quantum algorithms
Quantum Physics
2014-12-31 v3 Logic in Computer Science
Category Theory
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.
Cite
@article{arxiv.1406.1278,
title = {Abstract structure of unitary oracles for quantum algorithms},
author = {William Zeng and Jamie Vicary},
journal= {arXiv preprint arXiv:1406.1278},
year = {2014}
}
Comments
In Proceedings QPL 2014, arXiv:1412.8102