Related papers: An optical Ising spin glass simulator with tuneabl…
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…
Solving intractable mathematical problems in simulators composed of atoms, ions, photons or electrons has recently emerged as a subject of intense interest. Here we extend this concept to phonons that are localised in spectrally pure…
Interest in non-algorithmic, unconventional computing is rising in recent years due to more and more apparent short comings of classic stored-program digital computers, such as energy efficiency, degree of parallelism in computations, clock…
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…
I give a very brief non-technical introduction to the intersection of the fields of spin systems and computational complexity. The focus is on spin glasses and their relationship to NP-complete problems.
We study Ising chains with arbitrary multispin finite-range couplings, providing an explicit solution of the associated inverse Ising problem, i.e. the problem of inferring the values of the coupling constants from the correlation…
Polynomial time reductions between problems have long been used to delineate problem classes. Simulation reductions also exist, where an oracle for simulation from some probability distribution can be employed together with an oracle for…
This paper reports numerical studies of a compressible version of the Ising spin glass in two dimensions. Compressibility is introduced by adding a term that couples the spin-spin interactions and local lattice deformations to the standard…
Spatial photonic Ising machines offer a novel optical platform for optimization and spin-model simulation, but existing diffraction-based schemes rely on auxiliary spins or multiplexing to encode high-rank couplings and external fields,…
We present a parallel machine, based on programmable devices, dedicated to simulate spin glass models with Z2 variables and short range interaction. A working prototype is described for two lattices containing 312x312 spins each with an…
Computing the ground state of Ising spin-glass models with p-spin interactions is, in general, an NP-hard problem. In this work we show that unlike in the case of the standard Ising spin glass with two-spin interactions, computing ground…
It is shown that continuously changing the effective number of interacting particles in p-spin-glass-like model allows to describe the transition from the full replica symmetry breaking glass solution to stable first replica symmetry…
A non-equilibrium open-dissipative neural network, such as a coherent Ising machine based on mutually coupled optical parametric oscillators, has been proposed and demonstrated as a novel computing machine for hard combinatorial…
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…
The Ising machine is an unconventional computing architecture that can be used to solve NP-hard combinatorial optimization problems more efficiently than traditional von Neumann architectures. Fast, compact oscillator networks which provide…
The scaling of fluctuations in the distribution of ground-state energies or costs with the system size N for Ising spin glasses is considered using an extensive set of simulations with the Extremal Optimization heuristic across a range of…
We use finite size scaling to study Ising spin glasses in two spatial dimensions. The issue of universality is addressed by comparing discrete and continuous probability distributions for the quenched random couplings. The sophisticated…
The central object of this PhD thesis is known under different names in the fields of computer science and statistical mechanics. In computer science, it is called the Maximum Cut problem, one of the famous twenty-one Karp's original…
Ising machines (IMs) are specialized devices designed to efficiently solve combinatorial optimization problems (COPs). They consist of artificial spins that evolve towards a low-energy configuration representing a problem's solution. Most…
We describe an efficient approximation algorithm for evaluating the ground-state energy of the classical Ising Hamiltonian with linear terms on an arbitrary planar graph. The running time of the algorithm grows linearly with the number of…