On Multiplicative Linear Logic, Modality and Quantum Circuits

Ugo Dal Lago
(Università di Bologna & INRIA Sophia Antipolis)
Claudia Faggian
(CNRS & Université Denis-Diderot Paris 7)

A logical system derived from linear logic and called QMLL is introduced and shown able to capture all unitary quantum circuits. Conversely, any proof is shown to compute, through a concrete GoI interpretation, some quantum circuits. The system QMLL, which enjoys cut-elimination, is obtained by endowing multiplicative linear logic with a quantum modality.

In Bart Jacobs, Peter Selinger and Bas Spitters: Proceedings 8th International Workshop on Quantum Physics and Logic (QPL 2011), Nijmegen, Netherlands, October 27-29, 2011, Electronic Proceedings in Theoretical Computer Science 95, pp. 55–66.
Published: 1st October 2012.

ArXived at: http://dx.doi.org/10.4204/EPTCS.95.6 bibtex PDF
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