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Computational Complexity and Fundamental Limitations to Fermionic Quantum Monte Carlo Simulations
Open accessAbstract
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.
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“For some quantum systems, especially fermionic and frustrated systems, the numerical evaluation of the integrals encounters the problem of sampling with non-positive-semidefinite weight functions, which is the so-called sign problem [see, e.g. (Troyer and Wiese, 2005)].”
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Metadata
- Authors
- Troyer, M., & Wiese, U.-J.
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2005-05-04
- Volume
- 94
- Issue
- 17
- Pages
- 170201-170201
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2017474131
- Cited by
- 1,246
- References
- 2
- FWCI
- 14.77
- Type
- journal article
- Language
- en
- Open access
- green
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