Coupled Layer Construction of Quantum Product Codes

Quantum product codes provide a general framework for constructing quantum codes from pairs of classical codes. This approach has recently yielded the first families of quantum LDPC codes with asymptotically good parameters. However, beyond their algebraic definition, the physical interpretation of how two classical codes are “glued” together to form a quantum code remains less understood. In this talk, we present a coupled-layer construction of quantum product codes, in which multiple copies of one code are connected through the parity checks of the other. This perspective extends naturally to products of arbitrary chain complexes. Moreover, it unifies a variety of coupled-layer constructions of topological phases familiar in condensed matter physics, providing a common framework that connects quantum error correcting codes with anyon condensation.