Crushing runtimes in adiabatic quantum computation with Energy Landscape Manipulation (ELM): Application to Quantum Factoring

Understand

We introduce two methods for speeding up adiabatic quantum computations by increasing the energy between the ground and first excited states.

• Our methods are even more general.
• They can be used to shift a Hamiltonian's density of states away from the ground state, so that fewer states occupy the low-lying energies near the minimum, hence allowing for faster adiabatic passages to find the ground state with less risk of getting caught in an undesired low-lying excited state during the passage.
• Even more generally, our methods can be used to transform a discrete optimization problem into a new one whose unique minimum still encodes the desired answer, but with the objective function's values forming a different landscape.