Optimal fixed-point quantum search in an interacting Ising spin system

Abstract

In Grover’s search algorithm, a priori knowledge of the number of target states is needed to effectively find a solution. This is due to the inherent oscillatory nature of unitary gates in the algorithm. A fixed-point quantum search is introduced in T. J. Yoder, G. H. Low and I. L. Chuang, (Phys. Rev. Lett.)113, 210501 [9] to mitigate this oscillation even without knowing the size of the target space. This is done by modifying the phase inversion and oracle of the original Grover’s algorithm so that the phase can assume intermediate values in $[-\pi ,\pi ]$. Naturally, qubits in a quantum computer are interacting among themselves and this might introduce an error in the phase assignment. In this work, we used the Ising spin chain to simulate the interactions among the qubits and demonstrate how to implement the fixed-point quantum search. By inspecting the state vectors after some finite number of iterations, we found that the error is primarily due to the phase difference of the ideal target state with that of the final state. Further investigation shows that high fidelity between the ideal and real evolution can be achieved by using a low Rabi frequency.