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We introduce two methods for speeding up adiabatic quantum computations byincreasing the energy between the ground and first excited states. Our methodsare even more general. They can be used to shift a Hamiltonian's density ofstates away from the ground state, so that fewer states occupy the low-lyingenergies near the minimum, hence allowing for faster adiabatic passages to findthe ground state with less risk of getting caught in an undesired low-lyingexcited state during the passage. Even more generally, our methods can be usedto transform a discrete optimization problem into a new one whose uniqueminimum still encodes the desired answer, but with the objective function'svalues forming a different landscape. Aspects of the landscape such as theobjective function's range, or the values of certain coefficients, or how manydifferent inputs lead to a given output value, can be decreased *or* increased.One of the many examples for which these methods are useful is in finding theground state of a Hamiltonian using NMR: If it is difficult to find a moleculesuch that the distances between the spins match the interactions in theHamiltonian, the interactions in the Hamiltonian can be changed without at allchanging the ground state. We apply our methods to an AQC algorithm for integerfactorization, and the first method reduces the maximum runtime in our exampleby up to 754%, and the second method reduces the maximum runtime of anotherexample by up to 250%. These two methods may also be combined.

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