frontiers / frontier
The dependency graph over this frontier’s findings. Each edge is a typed link: one finding supporting, contradicting, or refining another. The graph is a reviewable view over accepted finding bundles, not a separate authority layer.
Finding graph
Graph index contract
The graph view makes dependency structure visible while keeping accepted finding bundles as the durable objects.
derived view
Supports, contradicts, refines, and depends-on links help users navigate a frontier's review structure.
record state
The graph points back to finding bundles. It should not replace source spans, provenance, or review history.
review path
Inferred or candidate links should route to review before they affect proof, trails, atlases, or constellations.
impact
A changed source or finding can expose affected proof, dependent findings, and review radius.
Willow's 0.143% logical error rate at distance-7 is well below the 1% surface code threshold, experimentally confirming theoretical prediction. · inferred by reviewer
Willow's exponential error suppression (factor 2.14 per distance +2) confirms the threshold theorem in practice. · inferred by reviewer
Both Willow and Harvard achieve below-threshold on different platforms (superconducting vs. neutral atoms), suggesting threshold regime is platform-independent. · inferred by reviewer
Biased-noise thresholds (28-44%) vastly exceed depolarizing assumptions (1%), challenging universality of the 1% consensus value. · inferred by reviewer
Harvard's 48-qubit LDPC implementation demonstrates LDPC codes achieve exponential suppression in practice, validating theoretical overhead claims. · inferred by reviewer
LDPC overhead advantages (4x reduction) complement lower thresholds in concatenated codes, suggesting hybrid strategies may be optimal. · inferred by reviewer
Concatenated codes now achieve 2.5% thresholds (vs. surface 1%) with 90% overhead reduction, undermining the traditional 'higher threshold but worse overhead' trade-off. · inferred by reviewer
Threshold theorem is the foundational principle; Willow's 2024 demonstration is the first direct experimental proof of this 1997 theory. · inferred by reviewer
Syndrome errors reduce practical thresholds to 0.1-0.5%, suggesting gap between ideal (1%) and real thresholds may be 5-10x. · inferred by reviewer
Hardware-dependent thresholds vary 10-100x; fidelity differences drive code distance requirements, explaining divergence between theory and practice. · inferred by reviewer
IBM's 12 logical qubits on 288 physical qubits (288:12 = 24:1 ratio) exceeds LDPC's 4x advantage claim, approaching practical 50-100:1 overhead targets. · inferred by reviewer
Burst errors and coherence losses remain unquantified in realistic systems; current roadmaps may underestimate required overhead and timelines. · inferred by reviewer
Decoder choice shifts realized threshold by 20-40%, suggesting reported thresholds may overstate achievable performance with practical decoders. · inferred by reviewer
Surface codes' 2D local connectivity advantage may outweigh LDPC overhead savings if routing complexity becomes a hardware bottleneck. · inferred by reviewer