On Multiplicative Linear Logic, Modality and Quantum Circuits

Abstract

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 Proceedings QPL 2011, arXiv:1210.0298

References in corpus (2)

• A Lambda Calculus for Quantum Computation
• Generalised Proof-Nets for Compact Categories with Biproducts

Cited by in corpus (1)

• Wave-Style Token Machines and Quantum Lambda Calculi