  Gaussian boson sampling (GBS) is not only a feasible protocol for
demonstrating quantum computational advantage, but also mathematically
associated with certain graph-related and quantum chemistry problems. In
particular, it is proposed that the generated samples from the GBS could be
harnessed to enhance the classical stochastic algorithms in searching some
graph features. Here, we use Jiuzhang, a noisy intermediate-scale quantum
computer, to solve graph problems. The samples are generated from a 144-mode
fully-connected photonic processor, with photon-click up to 80 in the quantum
computational advantage regime. We investigate the open question of whether the
GBS enhancement over the classical stochastic algorithms persists -- and how it
scales -- with an increasing system size on noisy quantum devices in the
computationally interesting regime. We experimentally observe the presence of
GBS enhancement with large photon-click number and a robustness of the
enhancement under certain noise. Our work is a step toward testing real-world
problems using the existing noisy intermediate-scale quantum computers, and
hopes to stimulate the development of more efficient classical and
quantum-inspired algorithms.
