Grover Adaptive Search with Problem-Specific State Preparation

Grover's search algorithm is one of the basic building block in the world of quantum algorithms. Successfully applying it to combinatorial optimization problems is a subtle challenge. As a quadratic speedup is not enough to naively search an exponentially large space, the search has to be complemented with a state preparation routine which increases the amplitudes of promising states by exploiting the problem structure. In this paper, we build upon previous work by Baertschi and Eidenbenz to construct heuristic state preparation routines for the Traveling Salesperson Problem (TSP), mimicking the well-known classical Lin-Kernighan heuristic. With our heuristic, we aim to achieve a reasonable approximation ratio with only a polynomial number of Grover iterations. Further, we compare several algorithmic settings relating to termination criteria and the choice of Grover iterations when the number of marked solutions is unknown.