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Evaluating gravitational path integrals in the Lorentzian has been along-standing challenge due to the numerical sign problem. We show that thischallenge can be overcome in simplicial quantum gravity. By deforming theintegration contour into the complex, the sign fluctuations can be suppressed,for instance using the holomorphic gradient flow algorithm. Working throughsimple models, we show that this algorithm enables efficient Monte Carlosimulations for Lorentzian simplicial quantum gravity.  In order to allow complex deformations of the integration contour, we providea manifestly holomorphic formula for Lorentzian simplicial gravity. This leadsto a complex version of simplicial gravity that generalizes the Euclidean andLorentzian cases. Outside the context of numerical computation, complexsimplicial gravity is also relevant to studies of singularity resolvingprocesses with complex semi-classical solutions. Along the way, we prove acomplex version of the Gauss-Bonnet theorem, which may be of independentinterest.

Complex, Lorentzian, and Euclidean simplicial quantum gravity: numerical methods and physical prospects