Normal subgroup reconstruction and quantum computation using group representations
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Quantum computation and quantum information
Quantum computation and quantum information
Quantum Database Search by a Single Query
QCQC '98 Selected papers from the First NASA International Conference on Quantum Computing and Quantum Communications
A Categorical Semantics of Quantum Protocols
LICS '04 Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science
Environment and classical channels in categorical quantum mechanics
CSL'10/EACSL'10 Proceedings of the 24th international conference/19th annual conference on Computer science logic
Higher Semantics of Quantum Protocols
LICS '12 Proceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science
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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.