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On a measurement-free quantum lambda calculus with classical control

Published online by Cambridge University Press:  01 April 2009

UGO DAL LAGO ,
ANDREA MASINI  and
MARGHERITA ZORZI
UGO DAL LAGO
Affiliation:
Dipartimento di Scienze dell'Informazione, Università di Bologna Email: dallago@cs.unibo.it
ANDREA MASINI
Affiliation:
Dipartimento di Informatica, Università di Verona Email: andrea.masini@univr.it
MARGHERITA ZORZI
Affiliation:
Dipartimento di Informatica, Università di Verona Email: margherita.zorzi@univr.it
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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.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 19 , Issue 2 , April 2009 , pp. 297 - 335
Copyright
Copyright © Cambridge University Press 2009

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