Solving Graph Problems Using Gaussian Boson Sampling

Abstract: 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.