  This work provides the first explicit and non-random family of $[[N,K,D]]$
LDPC quantum codes which encode $K \in \Theta(N^\frac{4}{5})$ logical qubits
with distance $D \in \Omega(N^\frac{3}{5})$. The family is constructed by
amalgamating classical codes and Ramanujan graphs via an operation called
balanced product.
  Recently, Hastings-Haah-O'Donnell and Panteleev-Kalachev were the first to
show that there exist families of LDPC quantum codes which break the
$\operatorname{polylog}(N)\sqrt{N}$ distance barrier. However, their
constructions are based on probabilistic arguments which only guarantee the
code parameters with high probability whereas our bounds hold unconditionally.
  Further, balanced products allow for non-abelian twisting of the check
matrices, leading to a construction of LDPC quantum codes that can be shown to
have $K\in \Theta(N)$ and that we conjecture to have linear distance $D\in
\Theta(N)$.
