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There are various proposals for solving systems with a severe sign problem:
* Contour deformation. The field space is complexified and the path integral contour is deformed from <math>R^N</math> to another <math>N</math>-dimensional manifold embedded in complex <math>C^N</math> space.<ref>{{Cite journal |last1=Alexandru |first1=Andrei |last2=Basar |first2=Gokce |last3=Bedaque |first3=Paulo |last4=Warrington |first4=Neill |year=2022 |title=Complex paths around the sign problem |journal=Reviews of Modern Physics |volume=94 |pages=015006 |arxiv=2007.05436 |doi=10.1103/RevModPhys.94.015006}}</ref>
* [[Meron (physics)|Meron]]-cluster algorithms. These achieve an exponential speed-up by decomposing the fermion world lines into clusters that contribute independently. Cluster algorithms have been developed for certain theories,<ref name='Wiese-cluster'>{{cite journal |doi=10.1103/PhysRevLett.83.3116 |arxiv=cond-mat/9902128 |bibcode=1999PhRvL..83.3116C |title=Meron-Cluster Solution of Fermion Sign Problems |journal=Physical Review Letters |volume=83 |issue=16 |pages=3116–3119 |year=1999 |last1=Chandrasekharan |first1=Shailesh |last2=Wiese |first2=Uwe-Jens|s2cid=119061060 }}</ref> but not for the Hubbard model of electrons, nor for [[Quantum chromodynamics|QCD]], the theory of quarks.
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