Strictly local Union-Find

Fault-tolerant quantum computing requires classical hardware to perform the decoding necessary for error correction. The Union-Find decoder is one of the best candidates for this. It has remarkably organic characteristics, involving the growth and merger of data structures through nearest-neighbour steps; this naturally suggests the possibility of realising Union-Find using a lattice of very simple processors with strictly nearest-neighbour links. In this way the computational load can be distributed with near-ideal parallelism. Here we build on earlier work to show for the first time that this strict (rather than partial) locality is practical, with a worst-case runtime $\mathcal O(d^3)$ and mean runtime subquadratic in $d$ where $d$ is the surface code distance. A novel parity-calculation scheme is employed, which can also simplify previously proposed architectures. We compare our strictly local realisation with one augmented by long-range links; while the latter is of course faster, we note that local asynchronous logic could largely negate the difference.Comment: 15 pages, 12 figure

Advances in quantum machine learning

Here we discuss advances in the field of quantum machine learning. The following document offers a hybrid discussion; both reviewing the field as it is currently, and suggesting directions for further research. We include both algorithms and experimental implementations in the discussion. The field's outlook is generally positive, showing significant promise. However, we believe there are appreciable hurdles to overcome before one can claim that it is a primary application of quantum computation.Comment: 38 pages, 17 Figure