Related papers: The algorithm for simulating of phase transition i…
The purpose of this article is to present a detailed numerical study of the second-order phase transition in the 2D Ising model. The importance of correctly presenting elementary theory of phase transitions, computational algorithms and…
The 1+1D Ising model is an ideal benchmark for quantum algorithms, as it is very well understood theoretically. This is true even when expanding the model to include complex coupling constants. In this work, we implement quantum algorithms…
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…
The Ising model is a simple statistical model for ferromagnetism. There are analytic solutions for low dimensions and very efficient Monte Carlo methods, such as cluster algorithms, for simulating this model in special cases. However most…
A linear-time algorithm is presented for the construction of the Gibbs distribution of configurations in the Ising model, on a quantum computer. The algorithm is designed so that each run provides one configuration with a quantum…
We perform a quantum simulation of the Ising model with a transverse field using a collection of three trapped atomic ion spins. By adiabatically manipulating the Hamiltonian, we directly probe the ground state for a wide range of fields…
We present an exact simulation of a one-dimensional transverse Ising spin chain with a quantum computer. We construct an efficient quantum circuit that diagonalizes the Ising Hamiltonian and allows to obtain all eigenstates of the model by…
Presented here is an algorithm for a type-II quantum computer which simulates the Ising model in one and two dimensions. It is equivalent to the Metropolis Monte-Carlo method and takes advantage of quantum superposition for random number…
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…
A computer simulation has to be fast to be helpful, if it is employed to study the behavior of a multicomponent dynamic system. This paper discusses modeling concepts and algorithmic techniques useful for creating such fast simulations.…
A quantum simulator is a well controlled quantum system that can simulate the behavior of another quantum system which may require exponentially large classical computing resources to understand otherwise. In the 1980s, Feynman proposed the…
A new and efficient algorithm is presented for the calculation of the partition function in the $S=\pm 1$ Ising model. As an example, we use the algorithm to obtain the thermal dependence of the magnetic spin susceptibility of an Ising…
A two-replica graphical representation and associated cluster algorithm is described that is applicable to ferromagnetic Ising systems with arbitrary fields. Critical points are associated with the percolation threshold of the graphical…
A promising paradigm of quantum computing for achieving practical quantum advantages is quantum annealing or quantum approximate optimization algorithm, where the classical problems are encoded in Ising interactions. However, it is…
In this paper we continue the description of the possibilities to use numerical simulations for mathematically rigorous computer assisted analysis of integrability of dynamical systems. We sketch some of the algebraic methods of studying…
We control quantum fluctuations to create the ground state magnetic phases of a classical Ising model with a tunable longitudinal magnetic field using a system of 6 to 10 atomic ion spins. Due to the long-range Ising interactions, the…
A new technique is demonstrated for carrying out exact positive-P phase-space simulations of the coherent Ising machine quantum computer. By suitable design of the coupling matrix, general hard optimization problems can be solved. Here,…
Optical Ising machines promise to solve complex optimization problems with an optical hardware acceleration advantage. Here we study the ground state properties of a nonlinear optical Ising machine realized by spatial light modulator,…
Recently experimental techniques, such as magnetic force microscopy (MFM), have enabled the magnetic state of individual sub-micron particles to be resolved. Motivated by these experimental developments, we use Monte Carlo simulations of…
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…