The Geometry of Parallelism. Classical, Probabilistic, and Quantum Effects
Abstract
We introduce a Geometry of Interaction model for higher-order quantum computation, and prove its adequacy for a full quantum programming language in which entanglement, duplication, and recursion are all available. Our model comes with a multi-token machine, a proof net system, and a PCF-style language. The approach we develop is not specific to quantum computation, and our model is an instance of a new framework whose main feature is the ability to model commutative effects in a parallel setting. Being based on a multi-token machine equipped with a memory, it has a concrete nature which makes it well suited for building low-level operational descriptions of higher-order languages.
Cite
@article{arxiv.1610.09629,
title = {The Geometry of Parallelism. Classical, Probabilistic, and Quantum Effects},
author = {Ugo Dal Lago and Claudia Faggian and Benoit Valiron and Akira Yoshimizu},
journal= {arXiv preprint arXiv:1610.09629},
year = {2017}
}
Comments
21 pages, extended version of the conference paper ; July 2017: removed a spurious and unused lemma