Breadth-first graph traversal union-find decoder

TL;DR

This paper introduces simplified variants of the union-find decoder for quantum error correction, capable of handling various error types and adaptable to non-topological codes, with benchmarking results on speed and thresholds.

Contribution

The paper presents new, simplified union-find decoder variants that improve implementation and speed, and extend decoding capabilities to non-topological quantum LDPC codes.

Findings

Decoders can include qubit erasures and Pauli errors directly

Benchmarking shows competitive speed and threshold error rates

Source code is provided for reproducibility

Abstract

Fast decoding algorithms are decisive for real-time quantum error correction and for analyzing properties of error correction codes. Here, we develop variants of the union-find decoder that simplify its implementation and provide potential decoding speed advantages. Furthermore, we show how these methods can be adapted to decode non-topological quantum low-density-parity-check (qLDPC) codes. All the developed decoders can directly include both qubit erasures and Pauli errors in the decoding step, thus addressing the dominant noise mechanisms for photonic quantum computing. We investigate the strengths and weaknesses of the different decoder variants, benchmark their speed and threshold error rates on several codes, and provide the used source code.