Demystifying the Balanced Product Code: A Review

The discovery of the family of balanced product codes was pivotal in the subsequent development of ‘good’ low density quantum error correcting codes that have optimal scaling of the key parameters of distance and storage density. We review this family, giving a completely different presentation to the original, minimising the abstraction and technicalities wherever possible. The target audience is anyone familiar with the stabilizer formalism for error correction wanting to understand how parity-check matrices can be constructed for high storage density quantum codes.