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 —
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.