Bose–Hubbard Model

Key: BHM300
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