  Quantum cosmology aims at elucidating the beginning of our Universe. Back in
early 80's, Vilenkin and Hartle-Hawking put forward the "tunneling from
nothing" and "no boundary" proposals. Recently there has been renewed interest
in this subject from the viewpoint of defining the oscillating path integral
for Lorentzian quantum gravity using the Picard-Lefschetz theory. Aiming at
going beyond the mini-superspace and saddle-point approximations, we perform
Monte Carlo calculations using the generalized Lefschetz thimble method to
overcome the sign problem. In particular, we confirm that either Vilenkin or
Hartle-Hawking saddle point becomes relevant if one uses the Robin boundary
condition depending on its parameter. We also clarify some fundamental issues
in quantum cosmology, such as an issue related to the integration domain of the
lapse function and an issue related to reading off the real geometry from the
complex geometry obtained at the saddle point.
