Simulation and Hardware Realisation of Non-Abelian Topological Order

This project was carried out under the auspices of QPurpose, following its collaboration with Quantinuum to explore Topological Quantum Field Theory computations on quantum devices and related error-correcting properties. We focus on the study and extension of Quantinuum’s work presented in [1], where non-abelian topological order was realised on Quantinuum's H2 device. The objective of the project is to analyse the theoretical framework presented, link it to the experimental results, and build upon these experimentally. To this end, we present a review of the relevant background literature to aid the reader, a breakdown of the methods and results of the foundational paper, and an elaboration on the proposed extensions. For this work, we first replicate the results of [1]. Then, we inspect Hopf-links between different fluxes under distinct orderings and spatial configurations, we analyse unpaired anyons via non-ground state logical sectors, and we attempt to create and manipulate semions to detect unique phases induced under twisting.