Tales told by coloured tangles

Tangle machines are a topologically inspired diagrammatic formalism to describe information flow in networks. This paper begins with an expository account of tangle machines, motivated by the problem of describing how Gaussian estimators with unknown error correlations can be fused in networks. Tangle machines may be used to describe classical computations and quantum computations. Invariants of tangle machines provide ‘intrinsic’ information about the computations that they describe. Two examples are presented in which tangle machines tell stories of adiabatic quantum computations. The paper concludes with a preliminary discussion of how tangle machines may be learned from data by adapting existing causality-detection algorithms.