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.
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Submitted on : Friday, June 14, 2019 - 9:38:12 AM
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Ugo Dal Lago, Claudia Faggian, Benoît Valiron, Akira Yoshimizu. The Geometry of Parallelism: Classical, Probabilistic, and Quantum Effects. POPL 2017 - 44th ACM SIGPLAN Symposium on Principles of Programming Languages, Jan 2017, Paris, France. pp.833-845, ⟨10.1145/3009837.3009859⟩. ⟨hal-01474620⟩

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