On a measurement-free quantum lambda calculus with classical control

Authors:
Ugo dal Lago;Andrea Masini;Margherita Zorzi
Affiliations:
Dipartimento di scienze dell'informazione, università di bologna email: dallago@cs.unibo.it;Dipartimento di informatica, università di verona email: andrea.masini@univr.it;Dipartimento di informatica, università di verona email: margherita.zorzi@univr.it
Venue:
Mathematical Structures in Computer Science
Year:
2009

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Abstract

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.