Abstract: Quantum computation is based on quantum physics to build quantum devices for performing calculations and processing information. Although large-scale general-purpose quantum computers are still many years away, special-purpose quantum computers, such as quantum annealers, are being built with capabilities that exceed those of classical computers. The quantum annealers are created to realize quantum annealing. This study explores quantum annealing and investigates its statistical properties. As such, we establish a lower bound on the probability of quantum annealing solving optimization problems. Furthermore, we examine physical devices and Monte Carlo simulations to implement quantum annealing and expand our understanding of the quantum annealing process.

Key words and phrases: Annealing, combinatorial optimization, Hamiltonian, Ising model, Markov chain Monte Carlo, quantum computation.