There has been increasing interest in developing efficient quantum algorithms for hard classical problems. The Network Signal Coordination (NSC) problem is one such problem known to be NP complete. We implement Grover's search algorithm to solve the NSC problem to provide quadratic speedup. We further extend the algorithm to a Robust NSC formulation and analyse its complexity under both constant and polynomial-precision robustness parameters. The Robust NSC problem determines whether there exists a fraction (alpha) of solutions space that will lead to system delays less than a maximum threshold (K). The key contributions of this work are (1) development of a quantum algorithm for the NSC problem, and (2) a quantum algorithm for the Robust NSC problem whose iteration count is O(1/sqrt(alpha)), independent of the search space size, and (3) an extension to polynomial-precision robustness where alpha = alpha_o/p(N) decays polynomially with network size, retaining a quadratic quantum speedup. We demonstrate its implementation through simulation and on an actual quantum computer.

翻译：近年来，针对困难经典问题开发高效量子算法的研究兴趣日益增长。网络信号协调（NSC）问题正是这样一个已知为NP完全问题的经典难题。我们实现了Grover搜索算法以求解NSC问题，从而提供二次加速。我们进一步将该算法扩展至鲁棒NSC问题形式，并在常数精度与多项式精度鲁棒性参数下分析其复杂度。鲁棒NSC问题旨在判定是否存在解空间的一个比例（α），使得系统延迟小于最大阈值（K）。本工作的主要贡献包括：（1）针对NSC问题开发了一种量子算法；（2）针对鲁棒NSC问题提出了一种量子算法，其迭代次数为O(1/√α)，与搜索空间规模无关；（3）将算法扩展至多项式精度鲁棒性场景，其中α = α₀/p(N) 随网络规模多项式衰减，同时仍保持二次量子加速优势。我们通过仿真及在真实量子计算机上的实验验证了该算法的实现。