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Physical Review Letters
Paper

Polynomial-Time Classical Simulation of Quantum Ferromagnets

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Abstract

We consider a family of quantum spin systems which includes, as special cases, the ferromagnetic XY 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 ϵ using a classical randomized algorithm with runtime polynomial in ϵ-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.

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Physical Review Letters

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