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arXiv · 2306.12862

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

Balint Pato·Theerapat Tansuwannont·Shilin Huang·Kenneth R. Brown
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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 $(1.42 \pm 0.12) \times 10^{-3}$.

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Balint Pato, Theerapat Tansuwannont, Shilin Huang, Kenneth R. Brown. 2023-06-22. Optimization tools for distance-preserving flag fault-tolerant error correction. https://doi.org/10.1103/prxquantum.5.020336

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