Complement Grover's Search Algorithm: An Amplitude Suppression Implementation

Grover's search algorithm was a groundbreaking advancement in quantum algorithms, displaying a quadratic speed-up of querying for items. Since the creation of this algorithm it has been utilized in various ways, including in preparing specific states for the general circuit. However, as the number of desired items increases so does the gate complexity of the sub-process that conducts the query. To counter this complexity, an extension of Grover's search algorithm is derived where the focus of the query is on the undesirable items in order to suppress the amplitude of the queried items. To display the efficacy the algorithm is implemented as a sub-process into QAOA and applied to a traveling salesman problem. For a basis of comparison, the results are compared against QAOA.