Efficient algorithms for approximating quantum partition functions
Ryan L. Mann, Tyler Helmuth
Abstract
We establish a polynomial-time approximation algorithm for partition functions of quantum spin models at high temperature. Our algorithm is based on the quantum cluster expansion of Netočný and Redig and the cluster expansion approach to designing algorithms due to Helmuth, Perkins, and Regts. Similar results have previously been obtained by related methods, and our main contribution is a simple and slightly sharper analysis for the case of pairwise interactions on bounded-degree graphs.
Topics & Concepts
Partition (number theory)Bounded functionCluster expansionMathematicsQuantumQuantum algorithmAlgorithmPolynomialSimple (philosophy)Approximation algorithmCluster (spacecraft)Graph partitionDiscrete mathematicsCombinatoricsGraphComputer scienceQuantum mechanicsPhysicsMathematical analysisEpistemologyPhilosophyProgramming languageMarkov Chains and Monte Carlo MethodsQuantum many-body systemsQuantum Computing Algorithms and Architecture