Adding measurement to quantum λ-calculi
Last week in Grenoble we were visited by Alejandro Diaz-Caro from Argentina. Alejandro has been working on adding measurement to van Tonder’s quantum λ-calculus as part of his masters thesis. Details of this can be found in the slides for the talk he gave while here.
Alejandro, Pablo and I had interesting discussions about adding measurement, and possibly also a type system, to Pablo’s linear algebra λ-calculus, amongst other interesting discussions (including QML.) We also went over Alejandro’s proof that adding measurement to van Tonder’s calculus preserved confluence for the language.
Alejandro is working on a paper presenting this work, and I’ll post it here when it’s completed.
UPDATE: “Extended abstract” now available. See comment below for details.
April 7th, 2008 at 3:02 pm
Measurements and confluence in quantum lambda calculi
with explicit qubits by Alejandro Díaz-Caro, Pablo Arrighi, Manuel Gadella and Jonathan Grattage
Submitted to Quantum Physics and Logic (QPL) 2008.
This paper shows how to add measurement to a quantum lambda calculus with explicit qubits, in an elegant manner. This is done with full details for van Tonder’s λq-calculus, with a proof that confluence, and hence the consistency of the operational semantics, is preserved by this extension. The methods illustrated here are general, and applying these techniques to QML and Arrighi and Dowek’s Lineal is currently ongoing.