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

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 $(1.42\pm 0.12)\times 10^{-3}$.

33 pages, 18 figures. v2: minor correction. v3: added analysis on memory footprint saving and numerical simulation on the effect of idling noise. v4: minor correction

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Cited by in corpus (3)

• Reducing Quantum Error Correction Overhead with Versatile Flag-Sharing Syndrome Extraction Circuits
• Concatenated Steane code with single-flag syndrome checks
• Improved performance of the Bacon-Shor code with Steane's syndrome extraction method