  Overlap between two neural quantum states can be computed through Monte Carlo
sampling by evaluating the unnormalized probability amplitudes on a subset of
basis configurations. Due to the presence of probability amplitude ratios in
the estimator, which are possibly unbounded, convergence of this quantity is
not immediately obvious. Our work provides a derivation of analytical error
bounds on the overlap in the Monte Carlo calculations as a function of their
fidelity and the number of samples. Special case of normalized autoregressive
neural quantum states is analyzed separately.
