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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…
Many combinatorial optimization problems can be mapped to finding the ground states of the corresponding Ising Hamiltonians. The physical systems that can solve optimization problems in this way, namely Ising machines, have been attracting…
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…
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…
Ising machines, hardware accelerators for combinatorial optimization and probabilistic sampling problems, have gained significant interest recently. A key element is stochasticity, which enables a wide exploration of configurations, thereby…
Combinatorial optimization has wide applications from industry to natural science. Ising machines bring an emerging computing paradigm for efficiently solving a combinatorial optimization problem by searching a ground state of a given Ising…
Hard combinatorial optimization problems, often mapped to Ising models, promise potential solutions with quantum advantage but are constrained by limited qubit counts in near-term devices. We present an innovative quantum-inspired framework…
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…
We explore a case example of networks of classical electronic oscillators evolving towards the solution of complex optimization problems. We show that when driven into subharmonic response, a network of such nonlinear electrical resonators…
Ising machines are hardware solvers which aim to find the absolute or approximate ground states of the Ising model. The Ising model is of fundamental computational interest because it is possible to formulate any problem in the complexity…
A prominent approach to solving combinatorial optimization problems on parallel hardware is Ising machines, i.e., hardware implementations of networks of interacting binary spin variables. Most Ising machines leverage second-order…
Dynamical Ising machines achieve accelerated solving of complex combinatorial optimization problems by remapping the convergence to the ground state of the classical spin networks to the evolution of specially constructed continuous…
Non-universal dynamics is shown to occur in a one-dimensional non-equilibrium system of hard-core particles. The stochastic processes included are pair creation and annihilation (with rates e and e') and symmetric hopping rates which…
The commercial and industrial demand for the solution of hard combinatorial optimization problems push forward the development of efficient solvers. One of them is the Ising machine which can solve combinatorial problems mapped to Ising…
Non-equilibrium dynamics of the Ising model is a classical stochastic process whereas quantum mechanics has no stochastic elements in the classical sense. Nevertheless, it has been known that there exists a close formal relationship between…
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…
The coherent Ising machine (CIM) enables efficient sampling of low-lying energy states of the Ising Hamiltonian with all-to-all connectivity by encoding the spins in the amplitudes of pulsed modes in an optical parametric oscillator (OPO).…
Many combinatorial optimization problems can be reformulated as finding the ground state of the Ising model. Existing Ising solvers are mostly inspired by simulated annealing. Although annealing techniques offer scalability, they lack…
The promise of quantum computing lies in harnessing programmable quantum devices for practical applications such as efficient simulation of quantum materials and condensed matter systems. One important task is the simulation of…
Combinatorial problems such as combinatorial optimization and constraint satisfaction problems arise in decision-making across various fields of science and technology. In real-world applications, when multiple optimal or…