Related papers: On computational capabilities of Ising machines ba…
The mining in physics and biology for accelerating the hardcore algorithm to solve non-deterministic polynomial (NP) hard problems has inspired a great amount of special-purpose ma-chine models. Ising machine has become an efficient solver…
Ising machines are physical platforms designed to minimize the energy of classical Ising Hamiltonians, yet accessing specific excited states remains an open challenge of both fundamental and practical relevance. In this letter we show that…
We provide an analysis of the classic Kuramoto model of coupled nonlinear oscillators that goes beyond the existing results for all-to-all networks of identical oscillators. Our work is applicable to oscillator networks of arbitrary…
The rich non-linear dynamics of the coupled oscillators (under second harmonic injection) can be leveraged to solve computationally hard problems in combinatorial optimization such as finding the ground state of the Ising Hamiltonian. While…
Quantum annealing is a heuristic algorithm for searching the ground state of an Ising model. Heuristic algorithms aim to obtain near-optimal solutions with a reasonable computation time. Accordingly, many algorithms have so far been…
Ising machines are next-generation computers expected to efficiently sample near-optimal solutions of combinatorial optimization problems. Combinatorial optimization problems are modeled as quadratic unconstrained binary optimization (QUBO)…
Synchronization in networks of coupled oscillators is classically studied via the Kuramoto model, whose intrinsic nonlinearity limits analytical tractability and complicates control design. Complex-valued extensions circumvent this by…
Randomly coupled Ising spins constitute the classical model of collective phenomena in disordered systems, with applications covering ferromagnetism, combinatorial optimization, protein folding, stock market dynamics, and social dynamics.…
The growth of artificial intelligence and IoT has created a significant computational load for solving non-deterministic polynomial-time (NP)-hard problems, which are difficult to solve using conventional computers. The Ising computer,…
Emergence of generalized synchronization patterns in a ring of identical and locally coupled Kuramoto-type rotators are investigated by different methods. These approaches offer a useful visual picture for understanding the complexity 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…
We study the quantum Ising model on (2+1)-dimensional anti-de Sitter space using Matrix Product States (MPS) and Matrix Product Operators (MPOs). We explore the bulk phase diagram of the theory on regular tessellations of hyperbolic space…
Computational workloads are growing exponentially, driving power consumption to unsustainable levels. Efficiently distributing large-scale networks is an NP-Complete problem equivalent to Boolean satisfiability (SAT), making it one of the…
The study of frustrated spin systems often requires time-consuming numerical simulations. As the simplest approach, the classical Ising model is often used to investigate the thermodynamic behavior of such systems. Exploiting the small…
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…
Many spin systems affected by critical slowing down can be efficiently simulated using cluster algorithms. Where such systems have long-range interactions, suitable formulations can additionally bring down the computational effort for each…
The Kuramoto model is a standard model for the dynamics of coupled oscillator networks. In particular, it is used to study long time behavior such as phase-locking where all oscillators rotate at a common frequency with fixed angle…
Oscillator based Ising machines are non-von-Neumann machines ideally suited for solving combinatorial problems otherwise intractable on classic stored-program digital computers due to their run-time complexity. Possible future applications…
Systematic discovery of reduced-order closure models for multi-scale processes remains an important open problem in complex dynamical systems. Even when an effective lower-dimensional representation exists, reduced models are difficult to…
The Kuramoto model provides a concrete mathematical realization of emergent synchrony in a population of phase-coupled oscillators. Since Kuramoto's publication, \textit{Oscillations, Waves, and Turbulence}, researchers have worked to…