In 1997, Alexei Kitaev proposed that non-abelian anyons could be used as qubits in quantum computers. These quasiparticles have the potential to perform calculations beyond the limits of traditional computers. Unlike traditional qubits, non-abelian anyons have the unique ability to change their state through the process of “braiding” and can retain their state without being affected by external factors. However, efforts to create and manipulate non-abelian anyons have proven challenging, with researchers still struggling to demonstrate successful braiding. Quantum processors have provided an alternative approach to studying anyons, allowing researchers to simulate and correct errors in qubits through measurements. Google and other companies have made progress in quantum error correction by implementing the toric code and creating non-abelian defects in qubit grids. Theorists are also exploring the creation of more complex phases of quantum matter where true non-abelian anyons can naturally emerge. This field of research is still largely unexplored, but recent advancements show promise in understanding and utilizing the topological landscape of non-abelian anyons.
https://www.quantamagazine.org/physicists-create-elusive-particles-that-remember-their-pasts-20230509/