  A recent preprint by Mazzola and Carleo numerically investigates exponential
challenges that can arise for the QC-QMC algorithm introduced in our work,
"Unbiasing fermionic quantum Monte Carlo with a quantum computer." As discussed
in our original paper, we agree with this general concern. However, here we
provide further details and numerics to emphasize that the prospects for
practical quantum advantage in QC-QMC remain open. The exponential challenges
in QC-QMC are dependent on (1) the choice of QMC methods, (2) the underlying
system, and (3) the form of trial and walker wavefunctions. While one can find
difficult examples with a specific method, a specific system, and a specific
walker/trial form, for some combinations of these choices, the approach is
potentially more scalable than other near-term quantum algorithms. Future
research should aim to identify examples for which QC-QMC enables practical
quantum advantage.
