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The strongest evidence for superiority of quantum annealing on spin glass problems has come from comparing simulated quantum annealing using quantum Monte Carlo (QMC) methods to simulated classical annealing [G. Santoro et al., Science 295,…

The Path Integral Monte Carlo simulated Quantum Annealing algorithm is applied to the optimization of a large hard instance of the Random 3-SAT Problem (N=10000). The dynamical behavior of the quantum and the classical annealing are…

Experiments on disordered alloys suggest that spin glasses can be brought into low-energy states faster by annealing quantum fluctuations than by conventional thermal annealing. Due to the importance of spin glasses as a paradigmatic…

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…

Classical and quantum annealing are two heuristic optimization methods that search for an optimal solution by slowly decreasing thermal or quantum fluctuations. Optimizing annealing schedules is important both for performance and fair…

Probing the lowest energy configuration of a complex system by quantum annealing was recently found to be more effective than its classical, thermal counterpart. Comparing classical and quantum Monte Carlo annealing protocols on the random…

Relations of simulated annealing and quantum annealing are studied by a mapping from the transition matrix of classical Markovian dynamics of the Ising model to a quantum Hamiltonian and vice versa. It is shown that these two operators, the…

We review here the recent success in quantum annealing, i.e., optimization of the cost or energy functions of complex systems utilizing quantum fluctuations. The concept is introduced in successive steps through the studies of mapping of…

Recently, Heim, Ronnow, Isakov and Troyer [Science 348 (2015) 215] have reported that Monte Carlo simulations for the Ising spin glass model on the square lattice in the physically relevant continuous-imaginary-time limit do not show…

A novel quantum-classical hybrid scheme is proposed to efficiently solve large-scale combinatorial optimization problems. The key concept is to introduce a Hamiltonian dynamics of the classical flux variables associated with the quantum…

Quantum annealers are commercial devices aiming to solve very hard computational problems named spin glasses. Just like in metallurgic annealing one slowly cools a ferrous metal, quantum annealers seek good solutions by slowly removing the…

We study the role of Hamiltonian complexity in the performance of quantum annealers. We consider two general classes of annealing Hamiltonians: stoquastic ones, which can be simulated efficiently using the quantum Monte Carlo algorithm, and…

We introduce quantum fluctuations into the simulated annealing process of optimization problems, aiming at faster convergence to the optimal state. The idea is tested by the two models, the transverse Ising model and the traveling salesman…

Quantum annealing is analogous to simulated annealing with a tunneling mechanism substituting for thermal activation. Its performance has been tested in numerical simulation with mixed conclusions. There is a class of optimization problems…

We introduce a novel Simulated Quantum Annealing (SQA) algorithm which employs a multispin quantum fluctuation operator. At variance with the usual transverse field, short-range two-spin flip interactions are included in the driver…

Recent demonstrations of D-Wave's annealing-based quantum simulators have established new benchmarks for quantum computational advantage [arXiv:2403.00910]. However, the precise location of the classical-quantum computational frontier…

Quantum annealing provides a powerful platform for simulating magnetic materials and realizing statistical physics models, presenting a compelling alternative to classical Monte Carlo methods. We demonstrate that quantum annealers can…

Quantum annealing is a proposed combinatorial optimization technique meant to exploit quantum mechanical effects such as tunneling and entanglement. Real-world quantum annealing-based solvers require a combination of annealing and classical…

Exploiting quantum properties to outperform classical ways of information-processing is an outstanding goal of modern physics. A promising route is quantum simulation, which aims at implementing relevant and computationally hard problems in…

Here we discuss the annealing behavior of an infinite-range $\pm J$ Ising spin glass in presence of a transverse field using a zero-temperature quantum Monte Carlo. Within the simulation scheme, we demonstrate that quantum annealing not…