Related papers: A Continuous Energy Ising Machine Leveraging Diffe…
The ground state search of the Ising model can be used to solve many combinatorial optimization problems. Under the current computer architecture, an Ising ground state search algorithm suitable for hardware computing is necessary for…
Periodically driven parametric oscillators offer a convenient way to simulate classical Ising spins. When many parametric oscillators are coupled dissipatively, they can be analogous to networks of Ising spins, forming an effective coherent…
We evaluate the performance of different algorithms in minimizing the Hamiltonian of a spatial-photonic Ising machine (SPIM). We then encode the number-partitioning problem on the SPIM and adiabatically arrive at good solutions for the…
Emerging analog computing substrates, such as oscillator-based Ising machines, offer rapid convergence times for combinatorial optimization but often suffer from limited scalability due to physical implementation constraints. To tackle…
Nonlinear dynamical systems such as coupled oscillators are being actively investigated as Ising machines for solving computationally hard problems in combinatorial optimization. Prior works have established the equivalence between the…
A spatial photonic Ising machine (SPIM) handles large-scale combinatorial optimization problems owing to optical processing with spatial parallelism. However, iterative feedback in the search for optimal solutions limits processing speed…
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…
Networks of optical oscillators simulating coupled Ising spins have been recently proposed as a heuristic platform to solve hard optimization problems. These networks, called coherent Ising machines (CIMs), exploit the fact that the…
The study of spin systems with disorder and frustration is known to be a computationally hard task. Standard heuristics developed for optimizing and sampling from general Ising Hamiltonians tend to produce correlated solutions due to their…
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,…
For arbitrary Ising-like models of any dimension and Hamiltonians with a finite support with all possible multispin interactions and boundary conditions with a shift, the exact value of the free energy in the thermodynamic limit is obtained…
We present an exact spin-elimination technique that reduces the dimensionality of both quadratic and k-local Ising Hamiltonians while preserving their original ground-state configurations. By systematically replacing each removed spin with…
Ising machines show promise as ultrafast hardware for optimizations encoded in Ising Hamiltonians but fall short in terms of success rate and performance scaling. Here, we propose a novel Ising machine that exploits the three-dimensional…
Quantum annealing is a generic solver for optimization problems that uses fictitious quantum fluctuation. The most groundbreaking progress in the research field of quantum annealing is its hardware implementation, i.e., the so-called…
Ising formulations are widely utilized to solve combinatorial optimization problems, and a variety of quantum or semiconductor-based hardware has recently been made available. In combinatorial optimization problems, the existence of local…
We propose a novel type of minor-embedding (ME) in simulated-annealing-based Ising machines. The Ising machines can solve combinatorial optimization problems. Many combinatorial optimization problems are mapped to find the ground…
Conceptual process design is a crucial aspect of chemical engineering that involves process synthesis. Mixed-integer nonlinear programming is a powerful framework for modeling such design problems by combining discrete and continuous…
Resonant energy transport in dense, disordered dipolar spin ensembles relaxes far more slowly than predicted by exchange-only theories. We identify the missing mechanism as an Ising blockade: configuration-dependent diagonal interactions…
The reliable simulation of spin models is of critical importance to tackle complex optimization problems that are intractable on conventional computing machines. The recently introduced hyperspin machine, which is a network of linearly and…
We contribute to the mathematical theory of the design of low temperature Ising machines, a type of experimental probabilistic computing device implementing the Ising model. Encoding the output of a function in the ground state of a…