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

2022/08/13 by Robert Raussendorf, Raussendorf, Robert · 2 citations
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #FOS: Physical sciences #Homotopy and Cohomology in Algebraic Topology #Quantum Physics (quant-ph) #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2208.06624

openalex publication_date 2022/08/13 · openalex created_date 2022/08/17 · openalex updated_date 2026/07/28

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.

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