  A macroscopic energy barrier is a necessary condition for self-correcting
quantum memory. In this paper, we prove tight bounds on the energy barrier
applicable to any quantum code obtained from the hypergraph product of two
classical codes. If the underlying classical codes are low-density parity-check
codes (LDPC), the energy barrier of the quantum code is shown to be the minimum
energy barrier of the underlying classical codes (and their transposes) up to
an additive $O(1)$ constant.
