A Hamiltonian is a **mathematical description of the physical system** in terms of its energies. For optimization problems, adiabatic quantum computers / quantum annealers. The system is initialized in the easy-to-produce ground state (the lowest energy state) of a Hamiltonian. Thereafter, the system is adiabatically developed towards the "problem" Hamiltonian, whose ground state then maps the solution of the optimization problem. According to the adiabatic theorem, the system (described by a time-varying Hamiltonian) remains in the ground state as long as development takes place slowly enough. Optimization problems, and thus most problems in machine learning (which include pattern recognition, natural language understanding, forecasting models, clustering, and computer vision) can be expressed as energy value problems. That is, the **quantity to be minimized** (such as the difference from the current to the desired output of the algorithm) is **represented as the energy surface**. The **minimum energy state (equals the optimal solution)**, which the system can always find with adequate problem representation, is thus the output of a calculation process. Classical optimization algorithms may allow us to find the optimal solution; however, the quantum annealing systems combine algorithm and hardware, and by leveraging **quantum tunneling (quantum mechanical effect where particles such as electrons can cross an energy barrier), local minima can be escaped, and the optimum is found.** In addition, the time required for a classical algorithm depends on the floating point operations per second (or “FLOPS”) of the hardware used and the possible parallelization of the algorithm. A quantum annealer may allow finding the solution in milliseconds (given the algorithm is not iterative). On quantum annealers, problems relevant to the industry such as optimization tasks, learning, and stochastic simulations, can be embedded. Even prime factorization is possible