Quantum Error Correction Analysis

This section evaluates the correcting abilities of decoders and QEC codes, identifying the regimes where QEC provides meaningful error suppression.

1. Decoder Performance Comparison

We evaluate two open-source decoders: BP-OSD and MWPM. The BP-OSD parity-check decoder achieves the best overall performance, outperforming MWPM by 46.66% on average against the SI1000 noise model. However, this accuracy comes at a substantial computational cost (8 hours vs. 0.34 seconds for MWPM).

Figure 1: Trade-off between speed and accuracy across various decoding algorithms.

Takeaway #8: BP-OSD achieves the best general decoding performance and is the most suitable choice for cross-code evaluations, even when dedicated decoders are available.

2. Selective Application of QEC

QEC is not universally beneficial. Once a code’s threshold is crossed, its performance deteriorates rapidly. At a two-qubit error probability of 0.004, all tested codes cross their thresholds, while unprotected qubits still show no observed errors.

Figure 2: Logical error rate vs. physical error probability, showing threshold crossings.

Takeaway #9: QEC should be applied selectively. Once a code's threshold is crossed, the overhead of the correction process itself becomes a net source of faults, making the encoded qubit noisier than the unprotected one.