Eliminate bias in Monte Carlo estimation of the quantum geometric tensor S

Develop an unbiased or provably corrected Monte Carlo estimator for the quantum geometric tensor S used in variational Monte Carlo optimization when the support of the variational wave function amplitudes does not coincide with the support of the parameter derivatives, thereby removing the bias identified under such support-mismatch conditions.

Background

In variational Monte Carlo, gradients and the quantum geometric tensor (QGT) S are estimated from samples drawn according to the variational wave function. When the support of the wave function does not match the support of its parameter derivatives, these Monte Carlo estimators become biased.

While the bias in gradient estimators can be removed, the bias in the estimator for S has not been resolved. The paper notes this as an explicit open problem and mentions overlap-optimization-based approaches as a possible workaround rather than a direct solution.