Quantum programming languages permit a hardware independent, high-level description of quantum algorithms. In particular, the quantum lambda-calculus is a higher-order programming language with quantum primitives, mixing quantum data and classical control. Giving satisfactory denotational semantics to the quantum lambda-calculus is a challenging problem that has attracted significant interest in the past few years. Several models have been proposed but for those that address the whole quantum lambda-calculus, they either do not represent the dynamics of computation, or they lack the compositionality one often expects from denotational models.
In this paper, we give the first compositional and interactive model of the full quantum lambda-calculus, based on game semantics. To achieve this we introduce a model of quantum games and strategies, combining quantum data with a representation of the dynamics of computation inspired from causal models of concurrent systems. In this category we first give a computationally adequate interpretation of the affine fragment. Then, we extend the model with a notion of symmetry, allowing us to deal with replication. In this refined setting, we interpret and prove adequacy for the full quantum lambda-calculus. We do this both from a sequential and a parallel interpretation, the latter representing faithfully the causal independence between sub-computations.
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|Quantitative Robustness Analysis of Quantum Programs|
Shih-Han Hung University of Maryland, Kesha Hietala University of Maryland, Shaopeng Zhu University of Maryland, Mingsheng Ying University of Technology Sydney, Michael Hicks University of Maryland, College Park, Xiaodi Wu University of Oregon, USALink to publication DOI Media Attached
|Game Semantics for Quantum Programming|
Research PapersLink to publication DOI Media Attached
|Quantum Relational Hoare Logic|
Dominique Unruh University of TartuLink to publication DOI Pre-print Media Attached File Attached