Optimization of 16-Element Quantum Search on IBMQ

Abstract

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 [Formula: see text] gate ([Formula: see text]) and some single-qubit gates. So we optimize the implementation of the [Formula: see text] 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 [Formula: see text] 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.