Balanced Product Quantum Codes

This work provides the first explicit and non-random family of [[N, K, D]] LDPC quantum codes which encode K is an element of Theta(N-4/5) logical qubits with distance D is an element of Omega(N-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 polylog(N)root 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 is an element of Theta(N) and that we conjecture to have linear distance D is an element of Theta(N).

Automated summary

This work introduces a novel family of LDPC quantum codes that encode a large number of logical qubits with significant distance. In comparison to previous research, our proposed family offers stronger guarantees and utilizes balanced products for construction.