The Geometry of Parallelism. Classical, Probabilistic, and Quantum Effects

TL;DR

This paper develops a Geometry of Interaction model for higher-order quantum computation, incorporating entanglement, duplication, and recursion, and introduces a multi-token machine, proof net system, and a PCF-style language.

Contribution

It presents a novel Geometry of Interaction framework for quantum programming that models commutative effects in parallel, applicable beyond quantum computation.

Findings

Model is adequate for a full quantum programming language

Includes a multi-token machine with memory for operational descriptions

Framework can model 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.