Balanced Product Quantum Codes

16th Conference on the Theory of Quantum Computation


This work provides the first explicit and non-random family of [[N,K,D]] LDPC quantum codes which encode K∈Θ(N^4/5) logical qubits with distance D∈Ω(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)√N distance barrier. How-ever, 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 quantumcodes that can be shown to have K∈Θ(N) and that we conjecture to have linear distance D∈Θ(N).