Graph processors such as Graphcore's Intelligence Processing Unit (IPU) are part of the major new wave of novel computer architecture for AI, and have a general design with massively parallel computation, distributed on-chip memory and very high inter-core communication bandwidth which allows breakthrough performance for message passing algorithms on arbitrary graphs. We show for the first time that the classical computer vision problem of bundle adjustment (BA) can be solved extremely fast on a graph processor using Gaussian Belief Propagation. Our simple but fully parallel implementation uses the 1216 cores on a single IPU chip to, for instance, solve a real BA problem with 125 keyframes and 1919 points in under 40ms, compared to 1450ms for the Ceres CPU library. Further code optimisation will surely increase this difference on static problems, but we argue that the real promise of graph processing is for flexible in-place optimisation of general, dynamically changing factor graphs representing Spatial AI problems. We give indications of this with experiments showing the ability of GBP to efficiently solve incremental SLAM problems, and deal with robust cost functions and different types of factors.