Fault-tolerant ancilla preparation and noise threshold lower bounds for the 23-qubit Golay code

TL;DR

This paper presents optimized fault-tolerant ancilla preparation circuits for the 23-qubit Golay code, significantly reducing overhead and establishing a noise threshold above 1.32e-3, advancing practical quantum error correction.

Contribution

It introduces simplified, low-error-propagation circuits for Golay code ancilla preparation and proves a noise threshold above 1.32e-3 using malignant set counting under depolarizing noise.

Findings

Reduced overhead by a factor of four with new circuits

Achieved a noise threshold above 1.32 x 10^{-3}

Golay code remains competitive in fault-tolerant schemes

Abstract

In fault-tolerant quantum computing schemes, the overhead is often dominated by the cost of preparing codewords reliably. This cost generally increases quadratically with the block size of the underlying quantum error-correcting code. In consequence, large codes that are otherwise very efficient have found limited fault-tolerance applications. Fault-tolerant preparation circuits therefore are an important target for optimization. We study the Golay code, a 23-qubit quantum error-correcting code that protects the logical qubit to a distance of seven. In simulations, even using a naive ancilla preparation procedure, the Golay code is competitive with other codes both in terms of overhead and the tolerable noise threshold. We provide two simplified circuits for fault-tolerant preparation of Golay code-encoded ancillas. The new circuits minimize error propagation, reducing the overhead by roughly a factor of four compared to standard encoding circuits. By adapting the malignant set counting technique to depolarizing noise, we further prove a threshold above 1.32 x 10^{-3} noise per gate.