  Evaluating gravitational path integrals in the Lorentzian has been a
long-standing challenge due to the numerical sign problem. We show that this
challenge can be overcome in simplicial quantum gravity. By deforming the
integration contour into the complex, the sign fluctuations can be suppressed,
for instance using the holomorphic gradient flow algorithm. Working through
simple models, we show that this algorithm enables efficient Monte Carlo
simulations for Lorentzian simplicial quantum gravity.
  In order to allow complex deformations of the integration contour, we provide
a manifestly holomorphic formula for Lorentzian simplicial gravity. This leads
to a complex version of simplicial gravity that generalizes the Euclidean and
Lorentzian cases. Outside the context of numerical computation, complex
simplicial gravity is also relevant to studies of singularity resolving
processes with complex semi-classical solutions. Along the way, we prove a
complex version of the Gauss-Bonnet theorem, which may be of independent
interest.
