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Miniaturized heat engines constitutes a fascinating field of current research. They are being studied theoretically as well as experimentally, with experiments involving colloidal particles and harmonic traps and even bacterial baths acting…
Ising machines are specialized computers for finding the lowest energy states of Ising spin models, onto which many practical combinatorial optimization problems can be mapped. Simulated bifurcation (SB) is a quantum-inspired parallelizable…
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…
Ising machines are dedicated hardware solvers of NP-hard optimization problems. However, they do not always find the most optimal solution. The probability of finding this optimal solution depends on the problem at hand. Using continuation…
In this paper, we report new results on a novel Ising machine technology for solving combinatorial optimization problems using networks of coupled self-sustaining oscillators. Specifically, we present several working hardware prototypes…
Monte Carlo simulations of Ising models coupled to heat baths at two different temperatures are used to study a fluctuation relation for the heat exchanged between the two thermostats in a time $\tau$. Different kinetics (single--spin--flip…
High-performance Ising machines for solving combinatorial optimization problems have been developed with digital processors implementing heuristic algorithms such as simulated bifurcation (SB). Although Ising machines have been designed for…
Ising machines are effective solvers for complex combinatorial optimization problems. The idea is mapping the optimal solution(s) to a combinatorial optimization problem to the minimum energy state(s) of a physical system, which naturally…
The thinning method for numerical generation of the nonhomogeneous Poisson process (NHPP) arrival times has been adapted to accelerate Monte Carlo simulations of the kinetic Ising models (KIMs) with the Glauber spin-flip dynamics. The…
Combinatorial optimization problems can be mapped onto Ising models, and their ground state is generally difficult to find. A lot of heuristics for these problems have been proposed, and one promising approach is to use continuous…
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…
We propose a new sampling method, the thermostat-assisted continuously-tempered Hamiltonian Monte Carlo, for Bayesian learning on large datasets and multimodal distributions. It simulates the Nos\'e-Hoover dynamics of a…
A novel method is introduced in order to treat the dissipative dynamics of quantum systems interacting with a bath of classical degrees of freedom. The method is based upon an extension of the Nos\`e-Hoover chain (constant temperature)…
"Stiff" differential equations are commonplace in engineering and dynamical systems. To solve them we need flexible integrators that can deal with rapidly-changing righthand sides. This tutorial describes the application of "adaptive" […
Computationally hard combinatorial optimization problems are pervasive in science and engineering, yet their NP-hard nature renders them increasingly inefficient to solve on conventional von Neumann architectures as problem size grows.…
Quantum or quantum-inspired Ising machines have recently shown promise in solving combinatorial optimization problems in a short time. Real-world applications, such as time division multiple access (TDMA) scheduling for wireless multi-hop…
Various combinatorial optimization NP-hard problems can be reduced to finding the minimizer of an Ising model, which is a discrete mathematical model. It is an intellectual challenge to develop some mathematical tools or algorithms for…
We present a theoretical investigation of thermal fluctuation statistics in a molecular motor. Energy transfer in the motor is described using a multidimensional discrete master equation with nearest-neighbor hopping. In this theory, energy…
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…
A network of driven nonlinear oscillators without dissipation has recently been proposed for solving combinatorial optimization problems via quantum adiabatic evolution through its bifurcation point. Here we investigate the behavior of the…