Optimization tools for distance-preserving flag fault-tolerant error correction

TL;DR

This paper introduces several optimization techniques for lookup table decoding in flag fault-tolerant quantum error correction, significantly improving performance and pseudothresholds for small-distance CSS codes.

Contribution

The paper develops new optimization tools for lookup table decoding in flag FTQEC, reducing overhead and enhancing error correction performance on CSS codes.

Findings

Over an order of magnitude increase in pseudothreshold for distance-9 hexagonal color code.

Techniques include compact lookup tables, Meet-in-the-Middle, adaptive decoding, and separated X/Z counting.

Numerical simulations demonstrate substantial improvements in error correction thresholds.

Abstract

Lookup table decoding is fast and distance-preserving, making it attractive for near-term quantum computer architectures with small-distance quantum error-correcting codes. In this work, we develop several optimization tools that can potentially reduce the space and time overhead required for flag fault-tolerant quantum error correction (FTQEC) with lookup table decoding on Calderbank-Shor-Steane (CSS) codes. Our techniques include the compact lookup table construction, the Meet-in-the-Middle technique, the adaptive time decoding for flag FTQEC, the classical processing technique for flag information, and the separated $X$ and $Z$ counting technique. We evaluate the performance of our tools using numerical simulation of hexagonal color codes of distances 3, 5, 7, and 9 under circuit-level noise. Combining all tools can result in more than an order of magnitude increase in pseudothreshold for the hexagonal color code of distance 9, from $(1.34 \pm 0.01) \times 10^{-4}$ to $(1.42 \pm 0.12) \times 10^{-3}$.