(We do not know how to implement any MA or QMA efficiently.)
QMC cannot speed up simulation of a different quantum system - unless you're simulating a strict subset of your specific machine.
Quantum simulator is not a QMC system - it is designed to exhibit same behavior as a modelled system. That makes it somewhat useless for a system whose properties you do not understand. Any grid of fermions does not act like any other - if it did, BCS version would be accurate.
Furthermore, I never said quantum simulation was QMC. I said that having quantum computers able to simulate many-body Hamiltonians would make QMC irrelevant, or at the very least would not suffer the same limitations that QMC suffers, specifically for strongly correlated fermion problems.
I suggest getting a stronger grasp on the literature before you go around making claims like this. Whether you know it or not, you're actively spreading misinformation and making the internet a worse place.
https://en.wikipedia.org/wiki/Numerical_sign_problem
https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.94...
"Computational Complexity and Fundamental Limitations to Fermionic Quantum Monte Carlo Simulations, Matthias Troyer and Uwe-Jens Wiese, Phys. Rev. Lett. 94, 170201, 4 May 2005"
"Quantum Monte Carlo simulations, while being efficient for bosons, suffer from the “negative sign problem” when applied to fermions — causing an exponential increase of the computing time with the number of particles. A polynomial time solution to the sign problem is highly desired since it would provide an unbiased and numerically exact method to simulate correlated quantum systems. Here we show that such a solution is almost certainly unattainable by proving that the sign problem is nondeterministic polynomial (NP) hard, implying that a generic solution of the sign problem would also solve all problems in the complexity class NP in polynomial time."
https://arxiv.org/abs/cond-mat/0408370