Concrete Categorical Model of a Quantum Circuit Description Language with Measurement

• URL: http://arxiv.org/abs/2110.02691v1
• Date: Wed, 6 Oct 2021 12:29:03 GMT
• Title: Concrete Categorical Model of a Quantum Circuit Description Language with Measurement
• Authors: Dongho Lee, Valentin Perrelle, Beno\^it Valiron and Zhaowei Xu
• Abstract summary: We introduce dynamic lifting to a quantum circuit-description language, following the Proto-Quipper language approach. We propose a type system and an operational semantics for the language and we state safety properties. Our approach is to construct on top of a concrete category of circuits with measurements a Kleisli category, capturing as a side effect the action of retrieving classical content out of a quantum memory.
• Score: 7.439160287320074
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In this paper, we introduce dynamic lifting to a quantum circuit-description language, following the Proto-Quipper language approach. Dynamic lifting allows programs to transfer the result of measuring quantum data -- qubits -- into classical data -- booleans -- . We propose a type system and an operational semantics for the language and we state safety properties. Next, we introduce a concrete categorical semantics for the proposed language, basing our approach on a recent model from Rios\&Selinger for Proto-Quipper-M. Our approach is to construct on top of a concrete category of circuits with measurements a Kleisli category, capturing as a side effect the action of retrieving classical content out of a quantum memory. We then show a soundness result for this semantics.

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