On a measurement-free quantum lambda calculus with classical control

We study a measurement-free, untyped λ-calculus with quantum data and classical control. This work arises from previous proposals by Selinger and Valiron, and Van Tonder. We focus on operational and expressiveness issues, rather than (denotational) semantics. We prove subject reduction and confluenc...

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Bibliographic Details
Published inMathematical structures in computer science Vol. 19; no. 2; pp. 297 - 335
Main Authors LAGO, UGO DAL, MASINI, ANDREA, ZORZI, MARGHERITA
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 01.04.2009
Subjects
Calculus
Computer science
Logic programming
Theorems
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ISSN0960-1295
1469-8072
DOI10.1017/S096012950800741X

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Summary:We study a measurement-free, untyped λ-calculus with quantum data and classical control. This work arises from previous proposals by Selinger and Valiron, and Van Tonder. We focus on operational and expressiveness issues, rather than (denotational) semantics. We prove subject reduction and confluence, and a standardisation theorem. Moreover, we prove the computational equivalence of the proposed calculus with a suitable class of quantum circuit families.
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ISSN:0960-1295
1469-8072
DOI:10.1017/S096012950800741X