Related papers: Optimality and annealing path planning of dynamica…
We present the mean field solution of the quantum and classical Heisenberg spin glasses, using the combination of a high precision numerical solution of the Parisi full replica symmetry breaking equations and a continuous time Quantum Monte…
Classical or quantum physical systems can simulate the Ising Hamiltonian for large-scale optimization and machine learning. However, devices such as quantum annealers and coherent Ising machines suffer an exponential drop in the probability…
We introduce a methodology for generating benchmark problem sets for Ising machines---devices designed to solve discrete optimization problems cast as Ising models. In our approach, linear systems of equations are cast as Ising cost…
The general-purpose programmable photonic processors offer a scalable and reconfigurable solution for a wide range of RF and optical applications. Therefore, implementing photonic Ising machines using programmable processors leverages the…
We study the problem of testing and recovering $k$-clique Ferromagnetic mean shift in the planted Sherrington-Kirkpatrick model (i.e., a type of spin glass model) with $n$ spins. The planted SK model -- a stylized mixture of an uncountable…
The development of physical simulators, called Ising machines, that sample from low energy states of the Ising Hamiltonian has the potential to drastically transform our ability to understand and control complex systems. However, most of…
As spin glass materials have extremely slow dynamics, devious numerical methods are needed to study low-temperature states. A simple and fast optimization version of the classical Kasteleyn treatment of the Ising model is described and…
An Ising machine is any hardware specifically designed for finding the ground state of the Ising model. Relevant examples are coherent Ising machines and quantum annealers. In this paper, we propose a new machine learning model that is…
The performance of quantum annealing for combinatorial optimization is fundamentally limited by the minimum energy gap $\Delta$ encountered at quantum phase transitions. We investigate the scaling of $\Delta$ with system size $N$ for two…
We use record dynamics (RD), a coarse-grained description of the ubiquitous relaxation phenomenology known as "aging", as a diagnostic tool to find universal features that distinguish between the energy landscapes of Ising spin models and…
We perform an in-depth comparison of quantum annealing with several classical optimisation techniques, namely thermal annealing, Nelder-Mead, and gradient descent. We begin with a direct study of the 2D Ising model on a quantum annealer,…
In this paper we study the phase diagram of a Sherrington-Kirkpatrick (SK) model where the couplings are forced to thermalize at different time scales. Besides being a challenging generalization of the SK model, such settings may arise…
Annealing algorithms such as simulated annealing and population annealing are widely used both for sampling the Gibbs distribution and solving optimization problems (i.e. finding ground states). For both statistical mechanics and…
Dynamical Ising machines are based on continuous dynamical systems evolving from a generic initial state to a state strongly related to the ground state of the classical Ising model on a graph. Reaching the ground state is equivalent to…
A novel quantum-classical hybrid scheme is proposed to efficiently solve large-scale combinatorial optimization problems. The key concept is to introduce a Hamiltonian dynamics of the classical flux variables associated with the quantum…
We revisit the problem of efficiently learning the underlying parameters of Ising models from data. Current algorithmic approaches achieve essentially optimal sample complexity when given i.i.d. samples from the stationary measure and the…
We describe and analyze some novel approaches for studying the dynamics of Ising spin glass models. We first briefly consider the variational approach based on minimizing the Kullback-Leibler divergence between independent trajectories and…
The past decade has seen the emergence of Ising machines targeting hard combinatorial optimization problems by minimizing the Ising Hamiltonian with spins represented by continuous dynamical variables. However, capabilities of these…
We propose a general learning algorithm for solving optimization problems, based on a simple strategy of trial and adaptation. The algorithm maintains a probability distribution of possible solutions (configurations), which is updated…
The statistical properties of the local optima (metastable states) of the infinite range Ising spin glass with p-spin interactions in the presence of an external magnetic field h are investigated analytically. The average number of optima…