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arXiv · 1209.3917

The Topology of Quantum Algorithms

Jamie Vicary
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Abstract

We use a categorical topological semantics to examine the Deutsch-Jozsa, hidden subgroup and single-shot Grover algorithms. This reveals important structures hidden by conventional algebraic presentations, and allows novel proofs of correctness via local topological operations, giving for the first time a satisfying high-level explanation for why these procedures work. We also investigate generalizations of these algorithms, providing improved analyses of those already in the literature, and a new generalization of the single-shot Grover algorithm.

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Jamie Vicary. 2012-09-18. The Topology of Quantum Algorithms. https://doi.org/10.1109/lics.2013.14

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