Quantum Single-Path Transmission Optimization of Complex Networks

How to optimize the single-path transmission is a common issue for resource schedul-ing and network operation in a complex network, where cost and flow must be bal-anced. With the expansion of network scale, traditional optimization methods suffer from rapidly increasing computational complexity in high-dimensional decision space with the nonlinear cost-flow relationship. To solve this problem, this paper proposes a quantum optimization framework for single-path transmission for the first time. In particular, logarithmic-qubit encoding is adopted for path and flow selection, and cost-flow bias coefficients and path flows are embedded into the quadratic uncon-strained binary optimization (QUBO) model, compressing the decision space exponen-tially from O(2^j+k) to O(j(k+i)). The quantum approximate optimization algorithm (QAOA) is then used to obtain the optimal solutions including the selected single path and its discretized optimal flow corresponding to the set bias coefficients. If a precise optimal flow is wanted, the traditional spline interpolation can be applied to refine the discretized flow without introducing much calculation burden. Experimental results on a network with 122 nodes and 131 edges show that the proposed method can achieve high-quality single-path optimization result.