A Quick Overview on the Quantum Control Approach to the Lambda Calculus

TL;DR

This paper reviews over a decade of research on quantum control within lambda calculus, highlighting the differences between quantum and classical paradigms and summarizing key developments from foundational work to advanced models.

Contribution

It provides a comprehensive overview of quantum control approaches in lambda calculus, covering untyped calculi, categorical, and realisability models, consolidating 10+ years of research.

Findings

Summarizes key developments in quantum control and lambda calculus.

Highlights the evolution from foundational to advanced models.

Provides insights into the differences between quantum and classical control.

Abstract

In this short overview, we start with the basics of quantum computing, explaining the difference between the quantum and the classical control paradigms. We give an overview of the quantum control line of research within the lambda calculus, ranging from untyped calculi up to categorical and realisability models. This is a summary of the last 10+ years of research in this area, starting from Arrighi and Dowek's seminal work until today.