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The Toffoli-Hadamard Gate System: an Algebraic Approach.

Shi and Aharonov have shown that the Toffoli gate and the Hadamard gate give rise to an approximately universal set of quantum computational gates. The basic algebraic properties of this system have been studied in Dalla Chiara et al. (Foundations of Physics 39(6):559-572, ), where we have introduce...

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Published in:Journal of Philosophical Logic Vol. 42; no. 3; pp. 467 - 482
Main Authors: Dalla Chiara, M., Ledda, A., Sergioli, G., Giuntini, R.
Format: Article
Published: Springer Nature Jun2013
Subjects:
Quantum computing
Quantum theory
Algebra
Quantum logic
Hilbert space
Notions (Philosophy)
Abstract algebra
Online Access:View this record in EBSCOhost
Summary:Shi and Aharonov have shown that the Toffoli gate and the Hadamard gate give rise to an approximately universal set of quantum computational gates. The basic algebraic properties of this system have been studied in Dalla Chiara et al. (Foundations of Physics 39(6):559-572, ), where we have introduced the notion of Shi-Aharonov quantum computational structure. In this paper we propose an algebraic abstraction from the Hilbert-space quantum computational structures, by introducing the notion of Toffoli-Hadamard algebra. From an intuitive point of view, such abstract algebras represent a natural quantum generalization of both classical and fuzzy-like structures.