Fixed-point quantum search as implemented in an Ising spin system

The fixed-point quantum search provides a solution to the oscillation problem in a quantum search algorithm through the variation of oracle and inversion phases at each iteration. We simulate the fixed-point algorithm in an Ising spin system with first- and second-nearest neighbor interactions. Since the oracle and the inversion operator acts on O(2), then the oracle qubit is required to be in a superposition of states at the start of the simulation. This provides a way to implement the rotation required in the variation of phases at each iteration.