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arXiv · 1610.09629

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

Ugo Dal Lago·Claudia Faggian·Benoit Valiron·Akira Yoshimizu
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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.

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Ugo Dal Lago, Claudia Faggian, Benoit Valiron, Akira Yoshimizu. 2016-10-30. The Geometry of Parallelism. Classical, Probabilistic, and Quantum Effects. https://arxiv.org/abs/1610.09629

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