Ising models and topological codes: classical algorithms and quantum simulation

TL;DR

This paper introduces a classical algorithm for approximating partition functions of 3-body Ising models on complex 2D lattices, leveraging topological quantum systems, and proposes a quantum simulation protocol based on color codes.

Contribution

It develops a novel classical approximation algorithm for 3-body Ising models using topological quantum system connections, outperforming existing methods.

Findings

Exponential improvement over previous algorithms

Efficient quantum simulation protocol via local measurements

Applicable to arbitrary genus 2D lattices

Abstract

We present an algorithm to approximate partition functions of 3-body classical Ising models on two-dimensional lattices of arbitrary genus, in the real-temperature regime. Even though our algorithm is purely classical, it is designed by exploiting a connection to topological quantum systems, namely the color codes. The algorithm performance is exponentially better than other approaches which employ mappings between partition functions and quantum state overlaps. In addition, our approach gives rise to a protocol for quantum simulation of such Ising models by simply measuring local observables on color codes.