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Two linearities for quantum computing in the lambda calculus

Alejandro Díaz-Caro, Gilles Dowek B, Juan Pablo Rinaldi

arXiv:1601.04294BiosystemsNov 19, 201918 citations

A fully abstract model for quantum controlled lambda calculus

Alejandro Díaz-Caro, Octavio Malherbe

Jun 1, 20181 citation

A Double Effect λ-calculus for Quantum Computation

Juliana Kaizer Vizzotto, Bruno Crestani Calegaro, Eduardo Kessler Piveta

Lecture notes in computer scienceJan 1, 20136 citations

A Quantum-Control Lambda-Calculus with Multiple Measurement Bases

Alejandro Díaz-Caro, Nicolas A. Monzon

arXiv:2506.16244Lecture notes in computer scienceOct 30, 20250 citations

Higher-order semantics for quantum programming languages with classical control

Philip Atzemoglou

This thesis studies the categorical formalisation of quantum computing, through the prism of type theory, in a three-tier process. The first stage of our investigation involves the creation of the dagger lambda calculus, a lambda calculus for dagger compact categories. Our second contribution lifts the expressive power of the dagger lambda calculus, to that of a quantum programming language, by adding classical control in the form of complementary classical structures and dualisers. Finally, our third contribution demonstrates how our lambda calculus can be applied to various well known problems in quantum computation.This thesis studies the categorical formalisation of quantum computing, through the prism of type theory, in a three-tier process. The first stage of our investigation involves the creation of the dagger lambda calculus, a lambda calculus for dagger compact categories. Our second contribution lifts the expressive power of the dagger lambda calculus, to that of a quantum programming language, by adding classical control in the form of complementary classical structures and dualisers. Finally, our third contribution demonstrates how our lambda calculus can be applied to various well known problems in quantum computation.

arXiv:1311.6563Nov 26, 20131 citation

Higher-order semantics for quantum programming languages with classical control

George Philip Atzemoglou

This thesis studies the categorical formalisation of quantum computing, through the prism of type theory, in a three-tier process. The first stage of our investigation involves the creation of the dagger lambda calculus, a lambda calculus for dagger compact categories. Our second contribution lifts the expressive power of the dagger lambda calculus, to that of a quantum programming language, by adding classical control in the form of complementary classical structures and dualisers. Finally, our third contribution demonstrates how our lambda calculus can be applied to various well known problems in quantum computation: Quantum Key Distribution, the quantum Fourier transform, and the teleportation protocol./This thesis studies the categorical formalisation of quantum computing, through the prism of type theory, in a three-tier process. The first stage of our investigation involves the creation of the dagger lambda calculus, a lambda calculus for dagger compact categories. Our second contribution lifts the expressive power of the dagger lambda calculus, to that of a quantum programming language, by adding classical control in the form of complementary classical structures and dualisers. Finally, our third contribution demonstrates how our lambda calculus can be applied to various well known problems in quantum computation: Quantum Key Distribution, the quantum Fourier transform, and the teleportation protocol./

Jan 1, 20121 citation

A Lambda Calculus for Quantum Computation with Classical Control

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