{"artifact_id":"L1-921","layer":"L1","title":"Fault-Tolerant Thresholds & Surface-Code Decoding","domain":"Quantum Computing","sub_domain":"Quantum Error Correction","physics_fingerprint":{"title":"Fault-Tolerant Thresholds & Surface-Code Decoding","domain":"Quantum Computing","chapter":"Ch.12 Quantum Technology","sub_domain":"Quantum Error Correction","forward_model":"Logical error rate p_L of a distance-d surface code under a decoder: p_L ≈ A·(p/p_th)^{⌊(d+1)/2⌋}; below threshold p<p_th, p_L falls exponentially with d.","challenge_blurb":"Cross the fault-tolerance threshold — decode the surface code fast enough that adding qubits drives the logical error rate down, not up.","challenge_group":"quantum","challenge_short":"Fault-Tolerant Quantum Computing","grand_challenge":true,"governing_equation":"p_L ≈ A·(p/p_th)^{(d+1)/2};   Λ = p_L(d) / p_L(d+2)"},"observable_profile":{"unit":"logical error rate per cycle (lower better)","floor":0.001,"metric":"logical_error_rate","sota_reference":"Surface-code below-threshold demonstrations (Google Willow) + ML decoders"},"size_tiers":{"code_distance":[3,7,25],"physical_error":[0.001,0.005,0.01]},"hardness_fn":{"type":"grand_challenge","metric":"logical_error_rate","baseline":"Minimum-weight perfect matching","delta_tier":50},"initiator_dataset":[{"name":"Surface-code syndrome-measurement corpus","weight":0.6,"ipfs_cid":null,"license_hash":null},{"name":"Repetition-code error chains","weight":0.4,"ipfs_cid":null,"license_hash":null}],"status":"testnet","staked_pwm":5000.0,"chain_hash":null,"chain_tx_hash":null,"chain_block":null}