Topos logic in measurement-based quantum computation

TL;DR

This paper explores how non-classical topos logic relates to measurement-based quantum computation, revealing that classical universality in certain MBQC models depends on non-classical logic, which is used up during computation.

Contribution

It establishes a connection between topos-theoretic logic and MBQC, identifying non-classical logic as a resource for quantum computation.

Findings

Classical universality in some MBQC models requires non-classical logic.

Non-classical logic is 'consumed' during the computation process.

Highlights a potential new quantum computational resource.

Abstract

We report first steps towards elucidating the relationship between contextuality, measurement-based quantum computation (MBQC) and the non-classical logic of a topos associated with the computation. We show that, in a class of MBQC, classical universality requires non-classical logic, which is 'consumed' during the course of the computation, thereby pinpointing another potential quantum computational resource.