Optimal Decoder for the Error Correcting Parity Code

• URL: http://arxiv.org/abs/2505.05210v1
• Date: Thu, 08 May 2025 13:03:22 GMT
• Title: Optimal Decoder for the Error Correcting Parity Code
• Authors: Konstantin Tiurev, Christophe Goeller, Leo Stenzel, Paul Schnabl, Anette Messinger, Michael Fellner, Wolfgang Lechner,
• Abstract summary: We present a two-step decoder for the parity code and evaluate its performance in code-capacity and faulty-measurement settings.<n>For noiseless measurements, we find that the decoding problem can be reduced to a series of repetition codes while yielding near-optimal decoding for intermediate code sizes.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We present a two-step decoder for the parity code and evaluate its performance in code-capacity and faulty-measurement settings. For noiseless measurements, we find that the decoding problem can be reduced to a series of repetition codes while yielding near-optimal decoding for intermediate code sizes and achieving optimality in the limit of large codes. In the regime of unreliable measurements, the decoder demonstrates fault-tolerant thresholds above 5% at the cost of decoding a series of independent repetition codes in (1 + 1) dimensions. Such high thresholds, in conjunction with a practical decoder, efficient long-range logical gates, and suitability for planar implementation, position the parity architecture as a promising candidate for demonstrating quantum advantage on qubit platforms with strong noise bias.

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