Gaussian Boson Sampling for efficient dense subgraph identification in omic-driven gene networks during anthropogenic methane emission

This work presents a Gaussian Boson Sampling (GBS) method to identify densely connected subgraphs from omics-derived gene networks. The method utilises the intrinsic sampling bias of GBS towards densely connected nodes, providing an efficient strategy for sampling dense subgraphs compared with classical methods. We applied GBS to sheep rumen gene pathway networks under low and high methane yield conditions. The networks were naturally grouped into high, moderate, and low abundance clusters without specifying the number of genes per cluster. These clusters were associated with biochemical functions of facultative anaerobes, which may support methanogenic activity by maintaining reducing conditions favourable for methanogens. Benchmarking against the classical Greedy Peel algorithm showed that GBS consistently identified identical densest subgraphs while requiring 5 to 10 times fewer subgraph evaluations. Moreover, GBS obtained more subgraphs with higher densities than uniform random sampling. These results showed that GBS can substantially reduce the number of subgraph evaluations required to identify biologically meaningful gene clusters. However, the present study was conducted using a classical simulator, and investigations using photonic hardware are needed to evaluate the full potential of GBS. Nevertheless, these findings support the future use of GBS for subgraph search in large multi-omic networks where dense modules exhibit functional significance.