A Categorical Model for a Quantum Circuit Description Language (Extended Abstract). Rios, F. & Selinger, P. In Proceedings 14th international conference on quantum physics and logic, QPL 2017, volume 266, pages 164–178, July, 2017. arXiv: 1706.02630
A Categorical Model for a Quantum Circuit Description Language (Extended Abstract) [link]Paper  doi  abstract   bibtex   
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.
@inproceedings{rios_categorical_2017,
	title = {A {Categorical} {Model} for a {Quantum} {Circuit} {Description} {Language} ({Extended} {Abstract})},
	volume = {266},
	url = {https://doi.org/10.4204/EPTCS.266.11},
	doi = {10/gf8skw},
	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.},
	booktitle = {Proceedings 14th international conference on quantum physics and logic, {QPL} 2017},
	author = {Rios, Francisco and Selinger, Peter},
	month = jul,
	year = {2017},
	note = {arXiv: 1706.02630},
	keywords = {cs.PL, math.CT, quant-ph},
	pages = {164--178}
}

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