Related papers: Exact sampling hardness of Ising spin models
Ising and Potts models are an important class of discrete probability distributions which originated from statistical physics and since then have found applications in several disciplines. Simulation from these models is a well known…
When the problem of boson sampling was first proposed, it was assumed that little or no photon collisions occur. However, modern experimental realizations rely on setups where collisions are quite common, i.e. the number of photons $M$…
The reliable simulation of spin models is of critical importance to tackle complex optimization problems that are intractable on conventional computing machines. The recently introduced hyperspin machine, which is a network of linearly and…
Boson Sampling represents a promising approach to obtain an evidence of the supremacy of quantum systems as a resource for the solution of computational problems. The classical hardness of Boson Sampling has been related to the so called…
We propose an importance sampling (IS)-based transport map Hamiltonian Monte Carlo procedure for performing full Bayesian analysis in general nonlinear high-dimensional hierarchical models. Using IS techniques to construct a transport map,…
Classical spin models with discrete or continuous degrees of freedom arise in many studies of complex physical systems. A wide class of hard real-life optimisation problems can be formulated as a minimisation of a spin Hamiltonian. Here we…
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…
Gaussian Boson Samplers aim to demonstrate quantum advantage by performing a sampling task believed to be classically hard. The probabilities of individual outcomes in the sampling experiment are determined by the Hafnian of an…
Stoquastic Hamiltonians are characterized by the property that their off-diagonal matrix elements in the standard product basis are real and non-positive. Many interesting quantum models fall into this class including the Transverse field…
Combinatorial optimization problems are ubiquitous in industrial applications. However, finding optimal or close-to-optimal solutions can often be extremely hard. Because some of these problems can be mapped to the ground-state search of…
Optical simulators for the Ising model have demonstrated great promise for solving challenging problems in physics and beyond. Here, we develop a spatial optical simulator for a variety of classical statistical systems, including the clock,…
We introduce a general class of mean-field-like spin systems with random couplings that comprises both the Ising model on inhomogeneous dense random graphs and the randomly diluted Hopfield model. We are interested in quantitative estimates…
Efficient sampling for the conditional time integrated variance process in the Heston stochastic volatility model is key to the simulation of the stock price based on its exact distribution. We construct a new series expansion for this…
Atomistic simulations of thermodynamic properties of magnetic materials rely on an accurate modelling of magnetic interactions and an efficient sampling of the high-dimensional spin space. Recent years have seen significant progress with a…
We provide a perfect sampling algorithm for the hard-sphere model on subsets of $\mathbb{R}^d$ with expected running time linear in the volume under the assumption of strong spatial mixing. A large number of perfect and approximate sampling…
In this paper we introduce an approximate method to solve the quantum cavity equations for transverse field Ising models. The method relies on a projective approximation of the exact cavity distributions of imaginary time trajectories…
Paper: cond-mat/9311033 The Hubbard model of interacting electrons, like the Ising model of spin-spin interactions, is the simplest possible model displaying many ``real world'' features, but it is much more difficult to analyze…
Sampling problems have emerged as a central avenue for demonstrating quantum advantage on noisy intermediate-scale quantum devices. However, physical noise can fundamentally alter their computational complexity, often making them…
We present a recursive formula for the computation of the static effective Hamiltonian of a system under a fast-oscillating drive. Our analytical result is well-suited to symbolic calculations performed by a computer and can be implemented…
The `classical' model for a massive spinning particle, which was recently proposed, is derived from the isotropic rotator model. Through this derivation, we note that the spin can be understood as the relativistic extension of the isotropic…