Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations

Phys Rev Lett. 2005 May 6;94(17):170201. doi: 10.1103/PhysRevLett.94.170201. Epub 2005 May 4.


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.