Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
<|reference_start|>Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations: 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 NP-hard, implying that a generic solution of the sign problem would also solve all problems in the complexity class NP (nondeterministic polynomial) in polynomial time.<|reference_end|>
@article{troyer2004computational,
    title={Computational complexity and fundamental limitations to fermionic
  quantum Monte Carlo simulations},
    author={Matthias Troyer, Uwe-Jens Wiese},
    journal={Phys.Rev.Lett. 94 (2005) 170201},
    year={2004},
    doi={10.1103/PhysRevLett.94.170201},
    archivePrefix={arXiv},
    eprint={cond-mat/0408370},
    primaryClass={cond-mat.stat-mech cond-mat.str-el cs.CC hep-lat physics.comp-ph}
}