| # QEC (erasure-aware stabilizer decoding) | |
| Generic, code-agnostic stabilizer-code utilities: Pauli-string commutation | |
| (`pauli_commutes`), syndrome computation from any list of stabilizer | |
| generators (`compute_syndrome`), and an erasure-aware decoder | |
| (`erasure_aware_decode`) that exploits known error *locations* (e.g. a | |
| heralded lost photon in a dual-rail photonic qubit) rather than only the | |
| syndrome. | |
| Erasure-aware decoding rests on a real, foundational result: Grassl, Beth | |
| & Pellizzari, "Codes for the quantum erasure channel," Phys. Rev. A 56, 33 | |
| (1997) — a distance-*d* stabilizer code can correct up to *d*-1 erasures | |
| (known-location errors), versus only floor((*d*-1)/2) arbitrary | |
| (unlocated) errors. `erasure_aware_decode` doesn't hard-code that bound; | |
| it emerges from the brute-force search itself (more heralded qubits than | |
| the code can resolve typically yields zero or multiple syndrome-matching | |
| assignments, so the function returns `None` — never a guess). | |
| ::: dense_evolution.physics.qec | |
| --- | |
| **See also**: promoted from Dense-Evolution-Discovery's Steane [[7,1,3]] | |
| code investigation | |
| ([Block 6](https://tatopenn-cell.github.io/Dense-Evolution-Discovery/steane_qec/) — | |
| heralded-erasure conversion), where a Steane-specific version of this | |
| decoder was first built and validated against STIM's native | |
| `HERALDED_ERASE` noise channel: 0 decoding failures across every | |
| double-erasure shot tested (>60,000 shots total, 40,000 trials × 10 | |
| physical error rates), versus a real ~25% failure rate for a standard | |
| syndrome-only decoder blind to the erasure locations. Also grounded in | |
| Gu, Vaknin, Retzker & Kubica, "Optimizing quantum error correction | |
| protocols with erasure qubits," PRX Quantum 6, 040354 (2025), | |
| arXiv:2408.00829. | |