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Complex contour deformations of the path integral have been demonstrated tosignificantly improve the signal-to-noise ratio of observables in previousstudies of two-dimensional gauge theories with open boundary conditions. Inthis work, new developments based on gauge fixing and a neural networkdefinition of the deformation are introduced, which enable an effectiveapplication to theories in higher dimensions and with generic boundaryconditions. Improvements of the signal-to-noise ratio by up to three orders ofmagnitude for Wilson loop measurements are shown in $SU(2)$ lattice gaugetheory in three spacetime dimensions.

Signal-to-noise improvement through neural network contour deformations for 3D $SU(2)$ lattice gauge theory