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Topological quantum computing is a way of allowing precise quantumcomputations to run on noisy and imperfect hardware. One implementation usessurface codes created by forming defects in a highly-entangled cluster state.Such a method of computing is a leading candidate for large-scale quantumcomputing. However, there has been a lack of sufficiently powerful high-levellanguages to describe computing in this form without resorting to single-qubitoperations, which quickly become prohibitively complex as the system sizeincreases. In this paper we apply the category-theoretic work of Abramsky andCoecke to the topological cluster-state model of quantum computing to give ahigh-level graphical language that enables direct translation between quantumprocesses and physical patterns of measurement in a computer - a "compilerlanguage". We give the equivalence between the graphical and topologicalinformation flows, and show the applicable rewrite algebra for this computingmodel. We show that this gives us a native graphical language for the designand analysis of topological quantum algorithms, and finish by discussing thepossibilities for automating this process on a large scale.

Quantum picturalism for topological cluster-state computing