Fig. 5: Sparse graph experiments.
From: Efficient classical sampling from Gaussian boson sampling distributions on unweighted graphs
Iterations = 1000, mixing time ≤1000, fugacity λ = c2, annealing parameter γ = 0.95. a Hafnian Random Search on G5 with k = 16, c = 0.6. b Hafnian Simulated Annealing on G5 with k = 16, c = 0.6. In both cases, the four enhanced variants are capable of finding subgraphs with considerable Hafnian values, while the original random search and simulated annealing almost completely fail to find any perfect matching. c Density Random Search on G5 with k = 80, c = 0.8. d Density Simulated Annealing on G5 with k = 80, c = 0.8. Regarding the density values, the three enhanced variants are still 10% higher than the performance of original algorithms with the same stopping time as in dense graphs, demonstrating the convergence of our MCMC-based algorithms on this sparse graph.
