For some computational tasks, quantum computing devices may offer a computational speed up compared to classical devices. For example, quantum computers may achieve a speed up for tasks such as database search, evaluating NAND trees, integer factorization or the simulation of quantum many-body systems.
As another example, adiabatic quantum annealers may achieve a computational speed up compared to classical annealers for some optimization tasks. To perform an optimization task, quantum hardware may be constructed and programmed to encode the solution to a corresponding optimization task into an energy spectrum of a many-body quantum Hamiltonian characterizing the quantum hardware. For example, the solution is encoded in the ground state of the Hamiltonian.