High-performance local decoders for defect matching in 1D

TL;DR

This paper introduces two novel local decoders for 1D quantum repetition codes that improve error threshold and scalability, enabling more practical real-time quantum error correction with reduced hardware requirements.

Contribution

The paper presents new local decoders with proven thresholds and exponential error suppression, narrowing the gap with global decoders and enabling fully local quantum memory in 1D.

Findings

Proven threshold in the code-capacity model.

Exponential logical error suppression demonstrated.

Reduced implementation complexity with a new shearing rule.

Abstract

Local decoders, also known as cellular-automaton decoders, offer a promising path toward real-time quantum error correction by replacing centralized classical decoding, with inherent hardware constraints, by a natively parallel and streamlined architecture from a simple local transition rule. We propose two new types of local decoders for the quantum repetition code in one dimension. The signal-rule decoders interpret odd parities between neighboring qubits as defects, attracted to each other via the exchange of classical point-like excitations, represented by a few bits of local memory. We prove the existence of a threshold in the code-capacity model and present numerical evidence of exponential logical error suppression under a phenomenological noise model, with data and measurement errors at each error correction cycle. Compared to previously known local decoders that suffer from sub-optimal threshold and scaling, our construction significantly narrows the gap with global decoders for practical system sizes and error rates. Implementation requirements can be further reduced by eliminating the need for local classical memories, with a new rule defined on two rows of qubits. This shearing-rule works well at relevant system sizes making it an appealing short-term solution. When combined with biased-noise qubits, such as cat qubits, these decoders enable a fully local quantum memory in one dimension.