Related papers: The Ising model on cubic maps: arbitrary genus

A linear-time algorithm is presented for the construction of the Gibbs distribution of configurations in the Ising model, on a quantum computer. The algorithm is designed so that each run provides one configuration with a quantum…

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…

We study the problem of approximating the Ising model partition function with complex parameters on bounded degree graphs. We establish a deterministic polynomial-time approximation scheme for the partition function when the interactions…

We call an Ising model tractable when it is possible to compute its partition function value (statistical inference) in polynomial time. The tractability also implies an ability to sample configurations of this model in polynomial time. The…

We investigate quantum computational complexity of calculating partition functions of Ising models. We construct a quantum algorithm for an additive approximation of Ising partition functions on square lattices. To this end, we utilize the…

We extend the planar Pfaffian formalism for the evaluation of the Ising partition function to lattices of high topological genus g. The 3D Ising model on a cubic lattice, where g is proportional to the number of sites, is discussed in…

We present a polynomial-time Markov chain Monte Carlo algorithm for estimating the partition function of the antiferromagnetic Ising model on any line graph. The analysis of the algorithm exploits the "winding" technology devised by…

We present a novel quantum algorithm for estimating Gibbs partition functions in sublinear time with respect to the logarithm of the size of the state space. This is the first speed-up of this type to be obtained over the seminal…

We give efficient quantum algorithms to estimate the partition function of (i) the six vertex model on a two-dimensional (2D) square lattice, (ii) the Ising model with magnetic fields on a planar graph, (iii) the Potts model on a quasi 2D…

We show that the two dimensional Ising model is complete, in the sense that the partition function of any lattice model on any graph is equal to the partition function of the 2D Ising model with complex coupling. The latter model has all…

Instantaneous quantum polynomial-time (IQP) computation is a class of quantum computation consisting only of commuting two-qubit gates and is not universal in the sense of standard quantum computation. Nevertheless, it has been shown that…

We present a simple construction that maps quantum circuits to graphs and vice-versa. Inspired by the results of D.A. Lidar linking the Ising partition function with quadratically signed weight enumerators (QWGTs), we also present a…

The partition function of the two-dimensional Ising model on a square lattice with nearest-neighbour interactions and periodic boundary conditions is investigated. Kaufman [Phys. Rev. 76, 1232--1243 (1949)] gave a solution for this function…

We consider the problem of approximating partition functions for Ising models. We make use of recent tools in combinatorial optimization: the Sherali-Adams and Lasserre convex programming hierarchies, in combination with variational methods…

While the Ising model remains essential to understand physical phenomena, its natural connection to combinatorial reasoning makes it also one of the best models to probe complex systems in science and engineering. We bring a computational…

We present an algorithm to compute the number of solutions of the (constrained) number partitioning problem. A concrete implementation of the algorithm on an Ising-type quantum computer is given.

The high-performance scalable parallel algorithm for rigorous calculation of partition function of lattice systems with finite number Ising spins was developed. The parallel calculations run by C++ code with using of Message Passing…

The partition function of a factor graph and the partition function of the dual factor graph are related to each other by the normal factor graph duality theorem. We apply this result to the classical problem of computing the partition…

This paper deals with the partition function of the Ising model from statistical mechanics, which is used to study phase transitions in physical systems. A special case of interest is that of the Ising model with constant energies and…

A new and efficient algorithm is presented for the calculation of the partition function in the $S=\pm 1$ Ising model. As an example, we use the algorithm to obtain the thermal dependence of the magnetic spin susceptibility of an Ising…