Scalable dissipative quantum error correction for qubit codes

TL;DR

This paper introduces a scalable dissipative quantum error correction protocol for qubit codes that reduces error correction overhead from exponential to polynomial, improving error suppression efficiency.

Contribution

It presents a novel sequential correction mechanism exploiting redundancy in Knill-Laflamme conditions, enabling scalable autonomous QEC for multi-qubit errors.

Findings

Fourfold improvement in exponential suppression factor for repetition codes

Reduces correction operator overhead from exponential to polynomial

Connects autonomous QEC with dissipative protocols for bosonic codes

Abstract

Dissipative quantum error correction (QEC) autonomously protects quantum information using engineered dissipation and offers a promising alternative to error correction via measurement and feedback. However, scalability remains a challenge, as correcting high-weight errors typically requires increasing dissipation rates and exponentially many correction operators. Here, we present a scalable dissipative QEC protocol for discrete-variable codes, correcting multi-qubit errors via a trickle-down mechanism that sequentially reduces errors weight. Our construction exploits redundancy in the Knill-Laflamme conditions to design correction operators that act on multiple error subspaces simultaneously, thereby reducing the overhead from exponential to polynomial in the number of required operators. We illustrate our approach with repetition codes under biased noise, showing a fourfold improvement in the exponential suppression factor at realistic physical error rates. Our approach connects autonomous QEC for discrete-variable codes with demonstrated dissipative protocols for bosonic codes and opens up new avenues for traditional measurement-feedback QEC and fault-tolerant quantum operations.