Abstract
Quantum walk is widely used in search problems, and it has an ideal acceleration effect compared with classical algorithm. Suppose there is a marked vertex w on Johnson graph J(n,k), we hope to find w using quantum walk. We adopt the coined quantum walk model, and we have proved that, for fixed order k, lackadaisical discrete-time quantum walk (DTQW) can find w with success probability 1−o(1), keeping a quadratic speedup. Before this paper, the best result of DTQW is that discrete-time quantum walk finds w with success probability 12−o(1). We improve the success probability to 1−o(1) by adding self-loops with proper weights and choose the appropriate oracle operator. Our result also matches the result of continuous-time quantum walk.
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