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The versatility and wide-ranging applicability of the Ising model, originally introduced to study phase transitions in magnetic materials, have made it a cornerstone in statistical physics and a valuable tool for evaluating the performance…
Inference algorithms based on evolving interactions between replicated solutions are introduced and analyzed on a prototypical NP-hard problem - the capacity of the binary Ising perceptron. The efficiency of the algorithm is examined…
Machine learning for phase transition has received intensive research interest in recent years. However, its application in percolation still remains challenging. We propose an auxiliary Ising mapping method for machine learning study of…
We find the ground-state energy of the Ising model using the Cascaded Variational Quantum Eigensolver (CVQE) algorithm with the Guided-Sampling Ansatz (GSA) using up to 63 qubits on a quantum computer. We study a heavy-hex lattice to match…
We present an analysis of neural network-based machine learning schemes for phases and phase transitions in theoretical condensed matter research, focusing on neural networks with a single hidden layer. Such shallow neural networks were…
A pivotal task for quantum computing is to speed up solving problems that are both classically intractable and practically valuable. Among these, combinatorial optimization problems have attracted tremendous attention due to their broad…
Combinatorial optimization problems are crucial in industry. However, many COPs are NP-hard, causing the search space to grow exponentially with problem size and rendering large-scale instances computationally intractable. Conventional…
Presented here is an algorithm for a type-II quantum computer which simulates the Ising model in one and two dimensions. It is equivalent to the Metropolis Monte-Carlo method and takes advantage of quantum superposition for random number…
In recent years, the researches about solving partial differential equations (PDEs) based on artificial neural network have attracted considerable attention. In these researches, the neural network models are usually designed depend on…
We locate the phase-transition line for the Ising model on the fuzzy sphere from a finite-size scaling analysis of its ground-state energy. Our strategy is to write the latter as $E_{GS}(N_m)/N_m = E_{0} + E_1 /N_m + E_{3/2}/N_m^{3/2}+…
Simple algorithm of dynamics of Ising magnetic is described. The algorithm can be implemented on conventional digital computer and can be used for construction of specialized processor for simulation of ferromagnetic systems. The algorithm…
Recently, quantum-state representation using artificial neural networks has started to be recognized as a powerful tool. However, due to the black-box nature of machine learning, it is difficult to analyze what machine learns or why it is…
We demonstrate, by means of a convolutional neural network, that the features learned in the two-dimensional Ising model are sufficiently universal to predict the structure of symmetry-breaking phase transitions in considered systems…
We introduce a novel framework for simulating spin models using differentiable programming, an approach that leverages the advancements in machine learning and computational efficiency. We focus on three distinct spin systems: the Ising…
We propose a method to find out the community structure of a complex network. In this method the ground state problem of a ferromagnetic random field Ising model is considered on the network with the magnetic field $B_s = +\infty$, $B_{t} =…
Many tasks in our modern life, such as planning an efficient travel, image processing and optimizing integrated circuit design, are modeled as complex combinatorial optimization problems with binary variables. Such problems can be mapped to…
We present a new way to make Ising machines, i.e., using networks of coupled self-sustaining nonlinear oscillators. Our scheme is theoretically rooted in a novel result that establishes that the phase dynamics of coupled oscillator systems,…
As we approach the physical limits predicted by Moore's law, a variety of specialized hardware is emerging to tackle specialized tasks in different domains. Within combinatorial optimization, adiabatic quantum computers, CMOS annealers, and…
To tackle challenging combinatorial optimization problems, analog computing machines based on the nature-inspired Ising model are attracting increasing attentions in order to disruptively overcome the impending limitations on conventional…
We show how a conditional displacement of the vibrational mode of trapped ions can be used to simulate nonlinear collective and interacting spin systems including nonlinear tops and Ising models (a universal two qubit gate), independent of…