Semantics for Variational Quantum Programming
| Autor: | Xiaodong Jia, Andre Kornell, Bert Lindenhovius, Michael Mislove, Vladimir Zamdzhiev |
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| Přispěvatelé: | Hunan University [Changsha] (HNU), Tulane University, Johannes Kepler Universität Linz (JKU), Designing the Future of Computational Models (MOCQUA), Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Department of Formal Methods (LORIA - FM), Laboratoire Lorrain de Recherche en Informatique et ses Applications (LORIA), Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Laboratoire Lorrain de Recherche en Informatique et ses Applications (LORIA), Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS) |
| Jazyk: | angličtina |
| Rok vydání: | 2022 |
| Předmět: |
FOS: Computer and information sciences
Computer Science - Logic in Computer Science Computer Science - Programming Languages 010102 general mathematics Mathematics - Operator Algebras [INFO.INFO-LO]Computer Science [cs]/Logic in Computer Science [cs.LO] Mathematics - Category Theory 0102 computer and information sciences 01 natural sciences Logic in Computer Science (cs.LO) 010201 computation theory & mathematics FOS: Mathematics Computer Science::Programming Languages Category Theory (math.CT) 0101 mathematics Operator Algebras (math.OA) Safety Risk Reliability and Quality Software Programming Languages (cs.PL) |
| Zdroj: | 49th ACM SIGPLAN Symposium on Principles of Programming Languages (POPL 2022) 49th ACM SIGPLAN Symposium on Principles of Programming Languages (POPL 2022), Jan 2022, Philadelphia, United States. ⟨10.1145/3498687⟩ POPL 2022-49th ACM SIGPLAN Symposium on Principles of Programming Languages POPL 2022-49th ACM SIGPLAN Symposium on Principles of Programming Languages, Jan 2022, Philadelphia, United States. ⟨10.1145/3498687⟩ |
| DOI: | 10.1145/3498687⟩ |
| Popis: | We consider a programming language that can manipulate both classical and quantum information. Our language is type-safe and designed for variational quantum programming, which is a hybrid classical-quantum computational paradigm. The classical subsystem of the language is the Probabilistic FixPoint Calculus (PFPC), which is a lambda calculus with mixed-variance recursive types, term recursion and probabilistic choice. The quantum subsystem is a first-order linear type system that can manipulate quantum information. The two subsystems are related by mixed classical/quantum terms that specify how classical probabilistic effects are induced by quantum measurements, and conversely, how classical (probabilistic) programs can influence the quantum dynamics. We also describe a sound and computationally adequate denotational semantics for the language. Classical probabilistic effects are interpreted using a recently-described commutative probabilistic monad on DCPO. Quantum effects and resources are interpreted in a category of von Neumann algebras that we show is enriched over (continuous) domains. This strong sense of enrichment allows us to develop novel semantic methods that we use to interpret the relationship between the quantum and classical probabilistic effects. By doing so we provide a very detailed denotational analysis that relates domain-theoretic models of classical probabilistic programming to models of quantum programming. |
| Databáze: | OpenAIRE |
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