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

• URL: http://arxiv.org/abs/2306.12862v4
• Date: Wed, 27 Mar 2024 14:07:15 GMT
• Title: Optimization tools for distance-preserving flag fault-tolerant error correction
• Authors: Balint Pato, Theerapat Tansuwannont, Shilin Huang, Kenneth R. Brown,
• Abstract summary: We develop tools that can potentially reduce the space and time overhead required for flag fault-tolerant quantum error correction (FTQEC) Our techniques include the compact lookup table construction, the Meet-in-the-Middle technique, the adaptive time decoding for flag FTQEC, and the separated $X$ and $Z$ counting technique. We evaluate the performance of our tools using numerical simulation of hexagonal color codes of 3, 5, 7, and 9 under circuit-level noise.
• Score: 0.3999851878220878
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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