Quantum picturalism for topological cluster-state computing

Abstract

Topological quantum computing (QC) is a way of allowing recise quantum computations to run on noisy and imperfect hardware. One mplementation uses surface codes created by forming defects in a highlyentangled uster state. Such a method of computing is a leading candidate for rge-scale QC. However, there has been a lack of sufficiently powerful highlevel anguages to describe computing in this form without resorting to singlequbit perations, which quickly become prohibitively complex as the system size ncreases. In this paper, we apply the category-theoretic work of Abramsky and oecke to the topological cluster-state model of QC to give a high-level graphical anguage that enables direct translation between quantum processes and physical tterns of measurement in a computer-a 'compiler language'. We give the quivalence between the graphical and topological information flows, and show he applicable rewrite algebra for this computing model. We show that this gives s a native graphical language for the design and analysis of topological quantum lgorithms, and finish by discussing the possibilities for automating this process a large scale. © lishing Ltd and Deutsche Physikalische Gesellschaft.