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Lookup table decoding is fast and distance preserving, making it attractivefor near-term quantum computer architectures with small-distance quantum errorcorrecting codes. In this work, we develop several optimization tools which canpotentially reduce the space and time overhead required for flag fault-toleranterror correction (FTEC) with lookup table decoding on Calderbank-Shor-Steane(CSS) codes. Our techniques include the compact lookup table construction, theMeet-in-the-Middle technique, the adaptive time decoding for flag FTEC, theclassical processing technique for flag information, and the separated $X$ and$Z$ counting technique. We evaluate the performance of our tools usingnumerical simulation of hexagonal color codes of distances 3, 5, 7, and 9 undercircuit-level noise. Combining all tools can result in more than an order ofmagnitude increase in pseudothreshold for the hexagonal color code of distance9, from $(1.34 \pm 0.01) \times 10^{-4}$ to $(1.42 \pm 0.12) \times 10^{-3}$.

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