PolynomialTime Classical Simulation of Quantum Ferromagnets
Abstract
We consider a family of quantum spin systems which includes, as special cases, the ferromagnetic X Y model and ferromagnetic Ising model on any graph, with or without a transverse magnetic field. We prove that the partition function of any model in this family can be efficiently approximated to a given relative error ∊ using a classical randomized algorithm with runtime polynomial in ∊^{1}, system size, and inverse temperature. As a consequence, we obtain a polynomial time algorithm which approximates the free energy or ground energy to a given additive error. We first show how to approximate the partition function by the perfect matching sum of a finite graph with positive edge weights. Although the perfect matching sum is not known to be efficiently approximable in general, the graphs obtained by our method have a special structure which facilitates efficient approximation via a randomized algorithm due to Jerrum and Sinclair.
 Publication:

Physical Review Letters
 Pub Date:
 September 2017
 DOI:
 10.1103/PhysRevLett.119.100503
 arXiv:
 arXiv:1612.05602
 Bibcode:
 2017PhRvL.119j0503B
 Keywords:

 Quantum Physics;
 Condensed Matter  Strongly Correlated Electrons;
 Computer Science  Computational Complexity
 EPrint:
 Phys. Rev. Lett. 119, 100503 (2017)