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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…
Random fields of scales result when the class of musical scales is thought as a set of sites, and a site can be in one of two possible states (or spins): On or Off. We present a flexible simulated annealing model that produces generic…
Energy-correction method is proposed as an addition to mainstream integrators for equations of motion of systems of classical spins. This solves the problem of non-conservation of energy in long computations and makes mainstream integrators…
Ising machines have emerged as accelerators for combinatorial optimization. To enable practical deployment, this work aims to reduce time-to-solution by addressing three challenges: (1) hardware topology, (2) spin selection and update…
In combinatorial optimization, probabilistic Ising machines (PIMs) have gained significant attention for their acceleration of Monte Carlo sampling with the potential to reduce time-to-solution in finding approximate ground states. However,…
The quantum theory of coherent Ising machines, based on degenerate optical parametric oscillators and measurement-feedback circuits, is developed using the positive $P({\alpha},{\beta})$ representation of the density operator and the master…
Finite size corrections to the pressure (free energy) of the Ising model on a 2 dimensional cylinder are calculated and shown to be consistent with the predictions of conformal field theory. The exact solution of the model is expressed in…
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…
The Ising model provides a natural mapping for many computationally hard combinatorial optimization problems (COPs). Consequently, dynamical system-inspired computing models and hardware platforms that minimize the Ising Hamiltonian, have…
Motivated by the recent success of tensor networks to calculate the residual entropy of spin ice and kagome Ising models, we develop a general framework to study frustrated Ising models in terms of infinite tensor networks %, i.e. tensor…
Non-deterministic polynomial-time (NP) problems are ubiquitous in almost every field of study. Recently, all-optical approaches have been explored for solving classic NP problems based on the spin-glass Ising Hamiltonian. However, obtaining…
The last couple of years have seen an ever-increasing interest in using different Ising solvers, like Quantum annealers, Coherent Ising machines, and Oscillator-based Ising machines, for solving tough computational problems in various…
We demonstrate how quantum field theory problems can be embedded on quantum annealers. The general method we use is a discretisation of the field theory problem into a general Ising model, with the continuous field values being encoded into…
Recent work has shown that probabilistic models based on pairwise interactions-in the simplest case, the Ising model-provide surprisingly accurate descriptions of experiments on real biological networks ranging from neurons to genes.…
Compressing resource-intensive large language models by removing whole transformer blocks is a seemingly simple idea, but identifying which blocks to remove constitutes an exponentially difficult combinatorial problem. In this paper, we…
Real-world physical signals are continuous and high-dimensional, yet the statistical-mechanics machinery of associative memory operates on discrete Ising spins. We bridge this divide through a multilayer Ising framework that couples a…
I propose a new method to study computationally difficult problems. I consider a new system, larger than the one I want to simulate. The original system is recovered by imposing constraints on the large system. I simulate the large system…
Finding a ground state of a given Hamiltonian of an Ising model on a graph $G=(V,E)$ is an important but hard problem. The standard approach for this kind of problem is the application of algorithms that rely on single-spin-flip Markov…
The success of a quantum annealing algorithm requires a polynomial scaling of the energy gap. Recently it was shown that a two-dimensional transverse-field Ising model on a square lattice with nearest-neighbor $\pm J$ random coupling has a…
Binary optimization is a central problem in mathematical optimization and its applications are abundant. To solve this problem, we propose a new class of continuous optimization techniques which is based on Mathematical Programming with…