Quantum Algorithms for Network Signal Coordination

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.