Quantum Low-Density Parity-Check Codes for Modular Architectures

Abstract

In efforts to scale the size of quantum computers, modularity plays a central role across most quantum computing technologies. In the light of fault tolerance, this necessitates designing quantum error-correcting codes that are compatible with the connectivity arising from the architectural layouts. In this paper, we aim to bridge this gap by giving a novel way to view and construct quantum low-density parity-check (LDPC) codes tailored for modular architectures. We demonstrate that if the intra- and intermodular qubit connectivity can be viewed as corresponding to some classical or quantum LDPC codes then their hypergraph product code fully respects the architectural connectivity constraints. Finally, we show that relaxed connectivity constraints that allow twists of connections between modules pave a way to construct codes with better parameters.