AI 中文总结
本文提出懒散量子行走搜索的门级实现框架，验证其搜索性能并分析资源开销，为量子硬件上的懒散量子行走搜索提供实用实现方案及容错资源评估。
AI 中文摘要
懒散量子行走（LQW）通过引入加权自环扩展了离散时间量子行走（DTQW），可通过对行走者的可控局域化提升空间搜索性能。尽管其理论特性和算法优势已被广泛研究，但适用于量子硬件执行的实用门级实现仍未得到充分探索，这一缺口限制了在实际架构约束、噪声过程及资源需求下对懒散量子行走搜索的评估。本研究提出了一种懒散量子行走搜索的门级实现框架，该构造将位置空间和硬币空间编码为量子比特寄存器，通过预言机、硬币和触发器移位操作实现行走动力学。我们通过重现单个及多个标记顶点的预期搜索行为、分析自环权重对成功概率的影响来验证该电路；还利用超导硬件的噪声模型在实际噪声场景下评估该实现，并应用噪声缓解技术提升实测搜索性能。逻辑资源分析显示，对于8×8至64×64的网格，算法寄存器从9量子比特增至15量子比特， transpiled（编译后）门数从3.63×10⁵增至4.38×10⁶，电路深度从2.13×10⁵增至2.56×10⁶。最后，基于微软量子资源估算器的表面码模型进行的容错资源估算，揭示了与魔法态生产相关的显著时空权衡。
英文摘要
Lackadaisical quantum walks (LQW) extend discrete-time quantum walks (DTQW) by introducing weighted self-loops, enabling improved spatial-search performance through controlled localization of the walker. Despite substantial theoretical progress, practical gate-level implementations suitable for quantum hardware remain largely unexplored, limiting evaluation under realistic architectural constraints, noise, and resource requirements. In this work, we present a gate-level implementation framework for lackadaisical quantum walk search. The proposed construction encodes the position and coin spaces into qubit registers, and realizes the walk dynamics through oracle, coin, and flip-flop shift operations. We validate the circuit by reproducing the expected search behavior for single and multiple marked vertices and by analyzing the effect of the self-loop weight on the success probability. We further evaluate the implementation under realistic noisy settings using superconducting hardware's noise models. Logical resource analysis shows that, for grids ranging from $8\times8$ to $64\times64$, the transpiled gate count increases from $3.63\times10^{5}$ to $4.38\times10^{6}$ and the circuit depth from $2.13\times10^{5}$ to $2.56\times10^{6}$. Finally, fault-tolerant resource estimates based on a surface-code model using the Microsoft Quantum Resource Estimator demonstrate the substantial space-time trade-off associated with magic-state production. The results establish a practical circuit-level pathway for implementing the LQW search and provide a basis for evaluating its performance.
Comments27 pages, 15 figures
