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Programming by Examples: PL Meets ML Read chapter Read first chapter

2017 | OriginalPaper | Chapter

A Lambda Calculus for Density Matrices with Classical and Probabilistic Controls

Author : Alejandro Díaz-Caro

Published in: Programming Languages and Systems

Publisher: Springer International Publishing

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Abstract

In this paper we present two flavors of a quantum extension to the lambda calculus. The first one, \(\lambda _\rho \), follows the approach of classical control/quantum data, where the quantum data is represented by density matrices. We provide an interpretation for programs as density matrices and functions upon them. The second one, \(\lambda _\rho ^\circ \), takes advantage of the density matrices presentation in order to follow the mixed trace of programs in a kind of generalised density matrix. Such a control can be seen as a weaker form of the quantum control and data approach.

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Footnotes
1
A generalisation to any arbitrary measurement can be considered in a future, however, for the sake of simplicity in the classical control, we consider only measurements in the computational basis, which is a common practice in quantum lambda calculi [11, 17, 19, 21, 22, 31].
 
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Metadata
Title
A Lambda Calculus for Density Matrices with Classical and Probabilistic Controls
Author
Alejandro Díaz-Caro
Copyright Year
2017
Book
Programming Languages and Systems

Print ISBN: 978-3-319-71236-9

Electronic ISBN: 978-3-319-71237-6

Copyright Year: 2017

DOI
https://doi.org/10.1007/978-3-319-71237-6_22

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