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.

在Grover的搜索算法中，需要有效了解目标状态数量的先验知识。这是由于算法中单一门的固有振荡特性。在TJ Yoder，GH Low和IL Chuang（Phys.Rev.Lett。）113，210501 [9]中引入了定点量子搜索，以减轻这种振荡，即使不知道目标空间的大小。这是通过修改原始Grover算法的相位求逆和oracle来完成的，以便该相位可以假定\（[-\ pi，\ pi] \）中的中间值。自然地，量子计算机中的量子位相互之间相互作用，这可能会在相位分配中引入错误。在这项工作中，我们使用了Ising自旋链来模拟量子位之间的相互作用，并演示了如何实现定点量子搜索。通过在有限次迭代后检查状态向量，我们发现误差主要是由于理想目标状态与最终状态的相位差引起的。进一步的研究表明，通过使用低Rabi频率可以实现理想与真实进化之间的高保真度。