Applying quantitative semantics to higher-order quantum computing

Authors:
Michele Pagani;Peter Selinger;Benoît Valiron
Affiliations:
Université Paris 13, Sorbonne Paris Cité, Villetaneuse, France;Dalhousie University, Halifax, Canada;University of Pennsylvania, Philadelphia, USA
Venue:
Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages
Year:
2014

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Abstract

Finding a denotational semantics for higher order quantum computation is a long-standing problem in the semantics of quantum programming languages. Most past approaches to this problem fell short in one way or another, either limiting the language to an unusably small finitary fragment, or giving up important features of quantum physics such as entanglement. In this paper, we propose a denotational semantics for a quantum lambda calculus with recursion and an infinite data type, using constructions from quantitative semantics of linear logic.