A probabilistic powerdomain of evaluations
Proceedings of the Fourth Annual Symposium on Logic in computer science
Types as abstract interpretations
Proceedings of the 24th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Quantum computation and quantum information
Quantum computation and quantum information
Constructive design of a hierarchy of semantics of a transition system by abstract interpretation
Theoretical Computer Science
Towards a quantum programming language
Mathematical Structures in Computer Science
Quantum programming languages: survey and bibliography
Mathematical Structures in Computer Science
Dagger Compact Closed Categories and Completely Positive Maps
Electronic Notes in Theoretical Computer Science (ENTCS)
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Several domains [S. Abramsky. A Cook's tour of a simple quantum programming language. 3rd International Symposium on Domain Theory, Xi'an, China, May 2004; B. Coecke and K. Martin. A partial order on classical and quantum states. Technical report, PRG-RR-02-07, 2002; Ph. Jorrand and S. Perdrix. Towards a quantum calculus. In To appear in Proceedings of the 4th International Workshop on Quantum Programming Languages, ENTCS, 2006; P. Selinger. Towards a quantum programming language. Mathematical Structures in Computer Science, 14(4):527-586, 2004] can be used to define the semantics of quantum programs. Among them Abramsky [S. Abramsky. A Cook's tour of a simple quantum programming language. 3rd International Symposium on Domain Theory, Xi'an, China, May 2004] has introduced a semantics based on probabilistic power domains, whereas the one by Selinger [P. Selinger. Towards a quantum programming language. Mathematical Structures in Computer Science, 14(4):527-586, 2004] associates with every program a completely positive map. In this paper, we mainly introduce a semantical domain based on admissible transformations, i.e. multisets of linear operators. In order to establish a comparison with existing domains, we introduce a simple quantum imperative language (QIL), equipped with three different denotational semantics, called pure, observable, and admissible respectively. The pure semantics is a natural extension of probabilistic (classical) semantics and is similar to the semantics proposed by Abramsky [S. Abramsky. A Cook's tour of a simple quantum programming language. 3rd International Symposium on Domain Theory, Xi'an, China, May 2004]. The observable semantics, a la Selinger [P. Selinger. Towards a quantum programming language. Mathematical Structures in Computer Science, 14(4):527-586, 2004], associates with any program a superoperator over density matrices. Finally, we introduce an admissible semantics which associates with any program an admissible transformation. These semantics are not equivalent, but exact abstraction [P. Cousot. Types as abstract interpretations. In POPL, pages 316-331, 1997] or interpretation relations are established between them, leading to a hierarchy of quantum semantics.