OPTIMAL ANNEALING PATHS FOR ADIABATIC QUANTUM COMPUTATION
Shor’s algorithm shows that circuit-model quantum computers can factorize integers in polynomial time – exponentially more efficiently than classical computers. There is currently no analogous algorithm for Adiabatic Quantum Computers(AQCs). We illustrate through a number of factorization problems that a naive AQC implemen- tation fails to reveal an exponential speed up. An exponential speed up does become evident with the optimization of the AQC evolution path utilizing existing optimisa- tion approaches. We reduce the computation time even further by optimization over heuristically-derived parametrised functions. Finally, we improve our own results by exploring two-dimensional paths, and give arguments that using more dimensions in the search space can enhance the computational power to an even greater extent.