Quantum Algorithms for Network Signal Coordination

TL;DR

This paper develops quantum algorithms using Grover's search to efficiently solve the NP-complete Network Signal Coordination problem and its robust variant, achieving quadratic speedups demonstrated via simulation and quantum hardware.

Contribution

It introduces quantum algorithms for NSC and Robust NSC problems, extending their robustness and analyzing complexity with polynomial precision, providing practical quantum solutions.

Findings

Quadratic speedup for NSC using Grover's algorithm

Robust NSC algorithm's iteration count is independent of search space size

Successful implementation demonstrated through simulation and on quantum hardware

Abstract

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.