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Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations

Matthias Troyer·Uwe-Jens Wiese
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Abstract

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.

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BibTeXRIS

Matthias Troyer, Uwe-Jens Wiese. 2004-08-16. Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations. https://doi.org/10.1103/physrevlett.94.170201

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