Unstructured searching, which is to find the marked element from a given unstructured data set, is a widely studied problem in computer science. It is well known that Grover algorithm provides a quadratic speedup to solve unstructured search problem compared with the classical algorithm. This algorithm has received a lot of attention due to the strong versatility. In this manuscript, we report experimental results of searching a unique target from 16 elements on five different quantum devices of IBM quantum Experience (IBMQ). We first implement the original Grover algorithm on these devices. However, the experiment probability of success of finding the correct target is almost the same as random choice. We then optimize the quantum circuit size of the search algorithm. The oracle operator and diffusion operator are two of the most costly operators in Grover algorithm. For the 16-element quantum search algorithm, both the oracle operator and diffusion operator consist of a triple controlled Z gate (CCCZ) and some single-qubit gates. So we optimize the implementation of the CCCZ gate according to the qubits layout of different quantum devices. On the ibmq_santiago, the experimental success rate of the 16-element quantum search algorithm is increased to 41.82% by the optimization, which is better than all the published experiments implemented on IBMQ devices. For other IBMQ devices, the experimental success rate of 16-element quantum search also has been significantly improved. We then try to further reduce the size of the quantum circuit by modifying the Grover algorithm, with a tolerable loss of the theoretical success probability. On ibmq_quito, the experimental success rate is further improved from 25.23% to 27.56% after optimization. These experimental results show the importance of circuit optimization and algorithm optimization in the Noisy-Intermediate-Scale Quantum (NISQ) era.

中文翻译：

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IBMQ 上 16 元素量子搜索的优化

非结构化搜索，即从给定的非结构化数据集中找到标记的元素，是计算机科学中广泛研究的问题。众所周知，与经典算法相比，Grover 算法提供了二次加速来解决非结构化搜索问题。该算法由于通用性强而受到广泛关注。在这份手稿中，我们报告了在 IBM 量子体验 (IBMQ) 的五种不同量子设备上从 16 个元素中搜索一个独特目标的实验结果。我们首先在这些设备上实现原始的 Grover 算法。但是，找到正确目标的实验成功概率几乎与随机选择相同。然后我们优化搜索算法的量子电路大小。预言算子和扩散算子是 Grover 算法中成本最高的两个算子。对于 16 元素的量子搜索算法，预言算子和扩散算子都由三重控制的Z门 （CCCZ) 和一些单量子比特门。所以我们优化了CCCZ门根据不同量子器件的量子比特布局。在ibmq_santiago上，16元素量子搜索算法的实验成功率提高到41.82%通过优化，这比在 IBMQ 设备上实现的所有已发布实验都要好。对于其他IBMQ器件，16元量子搜索的实验成功率也有显着提升。然后，我们尝试通过修改 Grover 算法来进一步减小量子电路的大小，理论成功概率的损失是可以容忍的。在 ibmq_quito 上，优化后的实验成功率从 25.23% 进一步提升到 27.56%。这些实验结果表明了电路优化和算法优化在嘈杂中尺度量子 (NISQ) 时代的重要性。