  Quantum tunneling is a valuable resource exploited by quantum annealers to
solve complex optimization problems. Tunneling events also occur during
projective quantum Monte Carlo (PQMC) simulations, and in a class of problems
characterized by a double-well energy landscape their rate was found to scale
linearly with the first energy gap, i.e., even more favorably than in physical
quantum annealers, where the rate scales with the gap squared. Here we
investigate how a guiding wave function --- which is essential to make
many-body PQMC simulations computationally feasible --- affects the tunneling
rate. The chosen testbeds are a continuous-space double-well problem, the
ferromagnetic quantum Ising chain, and the recently introduced shamrock model.
As guiding wave function, we consider an approximate Boltzmann-type ansatz, the
numerically-exact ground state of the double-well model, and a neural-network
wave function based on a Boltzmann machine. Remarkably, for each ansatz we find
the same asymptotic linear scaling of the tunneling rate that was previously
found in the PQMC simulations performed without a guiding wave function. We
also provide a semiclassical theory for the double-well with exact guiding wave
function that explains the observed linear scaling. These findings suggest that
PQMC simulations guided by an accurate ansatz represent a valuable benchmark
for physical quantum annealers and a potentially competitive quantum-inspired
optimization technique.
