Spanning Tree Matching Decoder for Quantum Surface Codes

TL;DR

The paper presents the spanning tree matching decoder for quantum surface codes, offering a faster decoding method with a slight performance trade-off, and introduces an even quicker algorithm for real-time applications.

Contribution

It introduces the STM decoder for surface codes and proposes the RFire decoder for ultra-fast decoding in quantum error correction.

Findings

STM decoder guarantees error correction up to the code's distance.

STM offers faster decoding with slight performance loss compared to MWPM.

RFire decoder provides rapid decoding suitable for time-critical scenarios.

Abstract

We introduce the spanning tree matching (STM) decoder for surface codes, which guarantees the error correction capability up to the code's designed distance by first employing an instance of the minimum spanning tree on a subset of ancilla qubits within the lattice. Then, a perfect matching graph is simply obtained, by selecting the edges more likely to be faulty. A comparative analysis reveals that the STM decoder, at the cost of a slight performance degradation, provides a substantial advantage in decoding time compared to the minimum weight perfect matching (MWPM) decoder. Finally, we propose an even more simplified and faster algorithm, the Rapid-Fire (RFire) decoder, designed for scenarios where decoding speed is a critical requirement.