Hamiltonian: The Bose–Hubbard Model $$H = \sum_{\{i,j\}\in E(G)} A(G)_{ij}a^\dagger_{i}a_{j} + U\sum_{i\in V(G)}n_i(n_i - 1)$$

Problem: Ground state energy

Complexity: QMA–complete

Ref: [CGW14]

Conditionals:

• $U\gt0$
• $G$ is a graph
• $A(G)$ is $G$'s square $0$–$1$ symmetric adjacency matrix
• Fixed particle number

Reductions:

• From the frustration–Free Bose–Hubbard Model