Network Vulnerability Analysis via Quantum Computing

In many complex networking systems, identifying critical nodes whose removal maximally disrupts network connectivity remains an important yet computationally challenging problem for network vulnerability analysis. Finding near-optimal solutions is known to be NP-hard. In this paper, we explore the potential of near-term quantum computing devices to efficiently solve the k-Critical Node Detection (k-CND) problem. We formulate the problem as a quadratic unconstrained binary optimization (QUBO), a mathematical optimization over binary variables amenable to solution on quantum annealers. We present a novel integer linear programming (ILP) formulation and its conversion into QUBOs and provide benchmarking results on D-Wave's quantum annealers. Our theoretical analysis proves that our proposed formulation, ILP2, generates substantially smaller QUBO than the state-of-the-art ILP1 formulation. Experimentally, our efficient QUBO yields a 59.7% decrease in QUBO variables on a graph with 10 vertices and 40 edges, and an 11.7% reduction in qubits on a 15-vertex, 22-edge graph compared to that of QUBO1. We analyze the solution quality and running time across quantum, classical, and hybrid solvers to assess the potential for quantum advantage. Our work showcases the promise and challenges of tackling this important graph problem on near-term quantum hardware.