Related papers: Ising Model Partition Function Computation as a We…
We consider the problem associated to recovering the block structure of an Ising model given independent observations on the binary hypercube. This new model, called the Ising blockmodel, is a perturbation of the mean field approximation of…
The forthcoming generation of wireless technology, 6G, aims to usher in an era of ubiquitous intelligent services, where everything is interconnected and intelligent. This vision requires the seamless integration of three fundamental…
We give a complexity dichotomy theorem for the counting Constraint Satisfaction Problem (#CSP in short) with complex weights. To this end, we give three conditions for its tractability. Let F be any finite set of complex-valued functions,…
We find that the overlapping of a topological quantum color code state, representing a quantum memory, with a factorized state of qubits can be written as the partition function of a 3-body classical Ising model on triangular or Union Jack…
Ising computing provides a new computing paradigm for many hard combinatorial optimization problems. Ising computing essentially tries to solve the quadratic unconstrained binary optimization problem, which is also described by the Ising…
How complex is an Ising model? Usually, this is measured by the computational complexity of its ground state energy problem. Yet, this complexity measure only distinguishes between planar and non-planar interaction graphs, and thus fails to…
SAT technology has proven to be surprisingly effective in a large variety of domains. However, for the Weighted CSP problem dedicated algorithms have always been superior. One approach not well-studied so far is the use of SAT in…
We propose a method for generalizing the Ising model in magnetic fields and calculating the partition function (exact solution) for the Ising model of an arbitrary shape. Specifically, the partition function is calculated using matrices…
Various combinatorial optimization NP-hard problems can be reduced to finding the minimizer of an Ising model, which is a discrete mathematical model. It is an intellectual challenge to develop some mathematical tools or algorithms for…
Recent years have seen significant advances in quantum/quantum-inspired technologies capable of approximately searching for the ground state of Ising spin Hamiltonians. The promise of leveraging such technologies to accelerate the solution…
The recent emergence of novel computational devices, such as adiabatic quantum computers, CMOS annealers, and optical parametric oscillators, present new opportunities for hybrid-optimization algorithms that are hardware accelerated by…
Stochastic Ising machines, sIMs, are highly promising accelerators for optimization and sampling of computational problems that can be formulated as an Ising model. Here we investigate the computational advantage of sIM for simulations of…
A powerful existing technique for evaluating statistical mechanical quantities in two-dimensional Ising models is based on constructing a matrix representing the nearest neighbor spin couplings and then evaluating the Pfaffian of the…
The mining in physics and biology for accelerating the hardcore algorithm to solve non-deterministic polynomial (NP) hard problems has inspired a great amount of special-purpose ma-chine models. Ising machine has become an efficient solver…
For multiparametric mixed-integer convex programming problems such as those encountered in hybrid model predictive control, we propose an algorithm for generating a feasible partition of a subset of the parameter space. The result is a…
Model-based clustering is a powerful tool that is often used to discover hidden structure in data by grouping observational units that exhibit similar response values. Recently, clustering methods have been developed that permit…
Partition functions, also known as homomorphism functions, form a rich family of graph invariants that contain combinatorial invariants such as the number of k-colourings or the number of independent sets of a graph and also the partition…
The weight space of the Ising perceptron in which a set of random patterns is stored is examined using the generating function of the partition function $\phi(n)=(1/N)\log [Z^n]$ as the dimension of the weight vector $N$ tends to infinity,…
Log-linear models are arguably the most successful class of graphical models for large-scale applications because of their simplicity and tractability. Learning and inference with these models require calculating the partition function,…
We study the computational complexity of approximating the partition function of the ferromagnetic Ising model with the external field parameter $\lambda$ on the unit circle in the complex plane. Complex-valued parameters for the Ising…