Topological Structure of Quantum Algorithms

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...

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Bibliographic Details
Published in:2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science pp. 93 - 102
Main Author: Vicary, Jamie
Format: Conference Proceeding
Language:English
Published: IEEE 01.06.2013
Subjects:
Algebra
Algorithm design and analysis
category theory
Equations
Finite element analysis
Fourier transforms
Heuristic algorithms
Protocols
quantum algorithms
quantum computing
topology
ISBN:1479904139, 9781479904136
ISSN:1043-6871
Online Access:Get full text
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Summary: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.
ISBN:1479904139
9781479904136
ISSN:1043-6871
DOI:10.1109/LICS.2013.14