A Categorical Model for a Quantum Circuit Description Language (Extended Abstract) release_bmzlejavc5do7iayvfsyb3bbqa

by Francisco Rios, Peter Selinger

Released as a article .

2018  

Abstract

Quipper is a practical programming language for describing families of quantum circuits. In this paper, we formalize a small, but useful fragment of Quipper called Proto-Quipper-M. Unlike its parent Quipper, this language is type-safe and has a formal denotational and operational semantics. Proto-Quipper-M is also more general than Quipper, in that it can describe families of morphisms in any symmetric monoidal category, of which quantum circuits are but one example. We design Proto-Quipper-M from the ground up, by first giving a general categorical model of parameters and state. The distinction between parameters and state is also known from hardware description languages. A parameter is a value that is known at circuit generation time, whereas a state is a value that is known at circuit execution time. After finding some interesting categorical structures in the model, we then define the programming language to fit the model. We cement the connection between the language and the model by proving type safety, soundness, and adequacy properties.
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Type  article
Stage   accepted
Date   2018-03-02
Version   v2
Language   en ?
arXiv  1706.02630v2
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