Combining a local search and Grover’s algorithm in black-box global optimisation

Grover’s quantum algorithm promises a quadratic acceleration for any problem formulable as a search. For unstructured search problems, its implementation and performance are well understood. The curse of dimensionality and the intractibility of the general global optimisation problem require any identifiable structure or regularity to be incorporated into a solution method. This paper addresses the application of Grover’s algorithm when a local search technique is available, thereby combining the quadratic acceleration with the acceleration seen in the multistart method. MSC2000 Subject Classification: 90C30, 68Q99, 68Q25