Sign problem in the Bethe approximation

  title={Sign problem in the Bethe approximation},
  author={Abolfazl Ramezanpour and Riccardo Zecchina},
  journal={Physical Review B},
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… 
Low-temperature excitations within the Bethe approximation
We propose the variational quantum cavity method to construct a minimal energy subspace of wavevectors that are used to obtain some upper bounds for the energy cost of the low-temperature
Multilayer wave functions: A recursive coupling of local excitations
Finding a succinct representation to describe the ground state of a disordered interacting system could be very helpful in understanding the interplay between the interactions that is manifested in a
Enhancing the efficiency of quantum annealing via reinforcement: A path-integral Monte Carlo simulation of the quantum reinforcement algorithm
This work implements a local version of the quantum reinforcement algorithm, where the system wave function is replaced by an approximate wave function using the local expectation values of the system and uses this algorithm to find solutions to a prototypical constraint satisfaction problem (XORSAT) close to the satisfiability to unsatisfiability phase transition.
Computing loop corrections by message passing
  • A. Ramezanpour
  • Mathematics, Medicine
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2013
This work proposes an approximation loop correction algorithm for the Ising model relying on the above representation of the problem, which deals at the same time with the short and long loops, and can be used to obtain upper and lower bounds for the free energy.
Statistical physics of loopy interactions: Independent-loop approximation and beyond
This work considers an interacting system of spin variables on a loopy interaction graph, identified by a tree graph and a set of loopy interactions, and finds the sum over the loop configurations can be computed "exactly" by the belief propagation algorithm in the low orders of the approximation as long as the loops have a tree structure.


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