"Exponentially improved classical algorithm inspired by quantum computation for classical many-body systems"


Ra Kou (Univ. of Tokyo)


We present a classical algorithm to approximate the partition functions of quite a broad class of classical many-body systems: two and three dimensional Ising and Potts models on arbitrary lattices with magnetic fields. Even though this algorithm is purely classical, it is based on the concept of the stabilizer formalism of quantum computation. The algorithm suppresses error exponentially better than other approaches that utilize direct correspondence between partition functions and quantum state overlaps. In addition, we compare our algorithm with another quantum algorithm achieving exponential error-suppression both in the real and the imaginary parameter regimes. Surprisingly, we find that our classical algorithm achieves the approximation accuracy that is close to the accuracy of a quantum algorithm for a BQP-complete problem.

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