Quantum LDPC Codes for Modular Architectures

TL;DR

This paper introduces a novel approach to designing quantum LDPC codes compatible with modular quantum computer architectures, improving fault tolerance and connectivity constraints.

Contribution

It presents a new method to construct quantum LDPC codes tailored for modular architectures using hypergraph product codes and relaxed connectivity constraints.

Findings

Hypergraph product codes respect architectural connectivity.

Relaxed connectivity allows for codes with better parameters.

The approach bridges quantum error correction with modular quantum computing.

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 LDPC codes tailored for modular architectures. We demonstrate that if the intra- and inter-modular 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.