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Journal of Logic and Computation Advance Access published online on February 27, 2009
Journal of Logic and Computation, doi:10.1093/logcom/exp008
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© The Author, 2009. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Original Papers

An Axiomatic System Suggested by Quantum Computation1

C. Bertini and R. Leporini

Dipartimento di Matematica, Statistica, Informatica e Applicazioni, Università degli Studi di Bergamo, Via dei Caniana 2, Bergamo, 24127, Italy.
E-mail: roberto.leporini{at}unibg.it; cesarino.bertini{at}unibg.it

Received 14 January 2009.


  Abstract

The theory of logical gates in quantum computation has suggested new forms of quantum logic, called quantum computational logics. The basic semantic idea is the following: the meaning of a sentence is identified with a quregister (a system of qubits in a pure state) or, more generally, with a mixture of quregisters (called qumix). Following an approach proposed by Domenech and Freytes, we apply residuated structures associated with fuzzy logic to develop certain aspects of information processing in quantum computing from a logical perspective. For this purpose, we introduce an axiomatic system whose natural interpretation is the irreversible quantum Poincaré algebra. Such a system allows to establish a completeness theorem.

Keywords: Quantum computation; quantum logic; quantum algebra; product Lukasiewicz logic; PMV algebra

1 This work has been supported by MIUR\PRIN project ‘Aspetti matematici e applicazioni emergenti degli automi e dei linguaggi formali’.


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