Putting paradoxes to work: contextuality in measurement-based quantum computation

TL;DR

This paper introduces a cohomological framework linking measurement-based quantum computation with contextuality proofs, providing a mathematical tool to analyze quantum computations and their inherent contextuality.

Contribution

It develops a cohomological approach to characterize MBQC and contextuality, focusing on the second cohomology group as a key analytical object.

Findings

Cohomological framework unifies computation and contextuality analysis.

Second cohomology group encodes the computed function and contextuality witness.

Framework currently applies to temporally flat MBQCs, with extensions proposed.

Abstract

We describe a joint cohomological framework for measurement-based quantum computation (MBQC) and the corresponding contextuality proofs. The central object in this framework is an element in the second cohomology group of the chain complex describing a given MBQC. It contains the function computed, up to gauge equivalence, and at the same time is a contextuality witness. The present cohomological description only applies to temporally flat MBQCs, and we outline an approach for extending it to the temporally ordered case.