Sign problem in the Bethe approximation

@article{Ramezanpour2012SignPI,
  title={Sign problem in the Bethe approximation},
  author={Abolfazl Ramezanpour and Riccardo Zecchina},
  journal={Physical Review B},
  year={2012},
  volume={86},
  pages={155147}
}
We propose a message-passing algorithm to compute the Hamiltonian expectation with respect to an appropriate class of trial wave functions for an interacting system of fermions. To this end, we connect the quantum expectations to average quantities in a classical system with both local and global interactions, which are related to the variational parameters and use the Bethe approximation to estimate the average energy within the replica-symmetric approximation. The global interactions, which… 
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7 Citations

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References

SHOWING 1-2 OF 2 REFERENCES
Spin Glass Theory and Beyond
This book contains a detailed and self-contained presentation of the replica theory of infinite range spin glasses. The authors also explain recent theoretical developments, paying particular…
Information, physics, and computation
This paper presents several observations on the connections between information, physics, and computation. In particular, the computing power of quantum computers is examined. Quantum theory is…