Local decoder for the toric code via signal exchange

TL;DR

This paper introduces a new local decoder for the toric code that uses binary signal exchange to interpret stabilizer measurements, achieving improved error suppression and scalability for quantum memory.

Contribution

The paper presents the 2D signal-rule local decoder, a novel approach that enhances threshold and finite-size scaling for quantum error correction in the toric code.

Findings

Exponential suppression of logical error rate with system size below threshold.

Achieves a significantly improved threshold compared to hierarchical schemes.

Provides a lightweight, high-performance alternative for 2D local quantum memory.

Abstract

Local decoders provide a promising approach to real-time quantum error-correction by replacing centralized classical decoding, with significant hardware constraints, by a fully distributed architecture based on a simple, local update rule. We propose a new local decoder for Kitaev's toric code: the 2D signal-rule, that interprets odd parity stabilizer measurements as defects, attracted to each other via the exchange of binary signals. We present numerical evidence of exponential suppression of the logical error rate with system size below a threshold, under a phenomenological noise model with data and measurement errors at each iteration. The construction achieves a significantly improved threshold and optimal finite-size scaling relative to hierarchical schemes. It also provides a lightweight alternative to windowed local decoder constructions while maintaining strong performance, thus enabling a streamlined architecture for a two-dimensional local quantum memory.