On Multiplicative Linear Logic, Modality and Quantum Circuits
  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. 
Ugo Dal Lago (Universit\`a di Bologna & INRIA Sophia Antipolis),   Claudia Faggian (CNRS & Universit\'e Denis-Diderot Paris 7)
cs.LO quant-ph