Explicit Instances of Quantum Tanner Codes

TL;DR

This paper presents explicit constructions of quantum Tanner codes using dihedral groups and classical codes, demonstrating high performance and low overhead in quantum error correction.

Contribution

It introduces new explicit quantum Tanner code constructions with high rates and distances, and analyzes their decoding performance and resource overhead.

Findings

Codes exhibit high encoding rates and relative distances.

Decoding with BP+OSD performs well in noise simulations.

Space-time overhead is comparable to surface codes.

Abstract

We construct several explicit instances of quantum Tanner codes, a class of asymptotically good quantum low-density parity check (qLDPC) codes. The codes are constructed using dihedral groups and random pairs of classical codes and exhibit high encoding rates, relative distances, and pseudo-thresholds. Using the BP+OSD decoder, we demonstrate good performance in the phenomenological and circuit-level noise settings, comparable to the surface code with similar distances. Finally, we conduct an analysis of the space-time overhead incurred by these codes.