On Multiplicative Linear Logic, Modality and Quantum Circuits
Ugo Dal Lago, Claudia Faggian · Electronic Proceedings in Theoretical Computer Science · 2012
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.