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On Dynamic Lifting and Effect Typing in Circuit Description Languages

Authors Andrea Colledan , Ugo Dal Lago

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Author Details

Andrea Colledan
  • University of Bologna, Italy
  • INRIA Sophia Antipolis, France
Ugo Dal Lago
  • University of Bologna, Italy
  • INRIA Sophia Antipolis, France

Funding

The research leading to these results has received funding from the European Union - NextGenerationEU through the Italian Ministry of University and Research under PNRR - M4C2 - I1.4 Project CN00000013 "National Centre for HPC, Big Data and Quantum Computing".

Cite As Get BibTex

Andrea Colledan and Ugo Dal Lago. On Dynamic Lifting and Effect Typing in Circuit Description Languages. In 28th International Conference on Types for Proofs and Programs (TYPES 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 269, pp. 3:1-3:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023) https://doi.org/10.4230/LIPIcs.TYPES.2022.3

Abstract

In the realm of quantum computing, circuit description languages represent a valid alternative to traditional QRAM-style languages. They indeed allow for finer control over the output circuit, without sacrificing flexibility nor modularity. We introduce a generalization of the paradigmatic lambda-calculus Proto-Quipper-M, which models the core features of the quantum circuit description language Quipper. The extension, called Proto-Quipper-K, is meant to capture a very general form of dynamic lifting. This is made possible by the introduction of a rich type and effect system in which not only computations, but also the very types are effectful. The main results we give for the introduced language are the classic type soundness results, namely subject reduction and progress.

Subject Classification

ACM Subject Classification
  • Theory of computation → Operational semantics
  • Theory of computation → Type theory
  • Hardware → Quantum computation
Keywords
  • Circuit-Description Languages
  • λ-calculus
  • Dynamic lifting
  • Type and effect systems

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References

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