Research Article
A Review of Quantum Lambda Calculi: Linearity, Semantics, and Programming Models
@ARTICLE{10.4108/eetcasa.9668, author={Tran Ngoc Dan and Nguyen Thi Kim Phung and Nguyen Thi Hong Tu and Nguyen Van Han}, title={A Review of Quantum Lambda Calculi: Linearity, Semantics, and Programming Models}, journal={EAI Endorsed Transactions on Contex-aware Systems and Applications}, volume={10}, number={1}, publisher={EAI}, journal_a={CASA}, year={2025}, month={7}, keywords={Quantum Lambda Calculus, Quantum Programming Lanugages, Quantum Circuits , Formal Semantics}, doi={10.4108/eetcasa.9668} }- Tran Ngoc Dan
Nguyen Thi Kim Phung
Nguyen Thi Hong Tu
Nguyen Van Han
Year: 2025
A Review of Quantum Lambda Calculi: Linearity, Semantics, and Programming Models
CASA
EAI
DOI: 10.4108/eetcasa.9668
Abstract
Quantum lambda calculi extend classical lambda calculus to model quantum computation by integrating linear types, quantum operations, and classical control. This paper surveys key calculi—including QΛ, QLC, Proto-Quipper, and QML—highlighting their design principles, type systems, and semantic foundations. By comparing their approaches to handling quantum data, control flow, and circuit construction, we provide insights into the current state and future directions of quantum programming language research.
Copyright © 2025 Tran Ngoc Dan et al., licensed to EAI. This is an open access article distributed under the terms of the CC BY-NC-SA 4.0, which permits copying, redistributing, remixing, transformation, and building upon the material in any medium so long as the original work is properly cited.
