Explicit conserved operators for a class of integrable bosonic networks from the classical Yang-Baxter equation

Let $B$ denote the weighted adjacency matrix of a balanced, symmetric, bipartite graph. We define a class of bosonic networks given by Hamiltonians whose hopping terms are determined by $B$. We show that each quantum Hamiltonian is Yang-Baxter integrable, admitting a set of mutually commuting operators derived through a solution of the classical Yang-Baxter equation. We discuss some applications and consequences of this result.