Quantum Threshold

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Evolution crossing the quantum threshold — "quantum is here" computed, not declared. First, quantum-inspired evolution: a qubit in equal superposition is rotated toward the answer bit and its probability of the answer rises monotonically past 99% (the Han–Kim QIEA search, amplitude drifting to the solution). Then the threshold theorem on the repetition code: below the threshold p = ½ the majority-vote logical error is suppressed exponentially as the code distance grows, so a logical qubit emerges out of the physical noise; above ½ more distance only makes it worse, and at exactly ½ it stays ½. "Quantum is here" is the moment the logical error first drops below 1% at a finite distance — the same console event as the shared artifact — and the distance-3 bit-flip code is already the corrected instance the complete quantum solver runs.

• QIEA — quantum-inspired evolutionequal-superposition qubit rotated toward the answer; P(answer) → 1 (converged: true)
• the threshold — p_c = 0.5the repetition (bit-flip) code: below ½ the logical error is suppressed exponentially with distance; above ½ it grows; at ½ it stays ½
• below threshold · d=1 · p=0.1logical error = 1.00e-1
• below threshold · d=3 · p=0.1logical error = 2.80e-2
• below threshold · d=5 · p=0.1logical error = 8.56e-3 ← quantum is here (< 1%)
• below threshold · d=7 · p=0.1logical error = 2.73e-3
• below threshold · d=9 · p=0.1logical error = 8.91e-4
• below threshold · d=11 · p=0.1logical error = 2.96e-4
• above threshold · d=1 · p=0.6logical error = 0.600 (grows with distance — no benefit)
• above threshold · d=3 · p=0.6logical error = 0.648 (grows with distance — no benefit)
• above threshold · d=5 · p=0.6logical error = 0.683 (grows with distance — no benefit)
• above threshold · d=7 · p=0.6logical error = 0.710 (grows with distance — no benefit)
• above threshold · d=9 · p=0.6logical error = 0.733 (grows with distance — no benefit)
• above threshold · d=11 · p=0.6logical error = 0.753 (grows with distance — no benefit)
• "quantum is here"a logical qubit emerges from noise at distance d=5 — the moment the logical error drops below 1%

Граница: A deterministic, exact reconstruction of the shared "evolution → quantum threshold" artifact, in the project idiom (seedless, no Math.random). The repetition code is the BIT-FLIP channel only (1D), with threshold exactly p = ½ — real fault tolerance needs the 2D surface code (threshold ~1%, Google Willow 2024 demonstrated below-threshold) or the constant-overhead qLDPC codes (Panteleev–Kalachev 2022; Dinur–Hsieh–Lin–Vidick 2022, asymptotically good — REAL research, not built here); Shor-scale factoring is ≈ 20M physical qubits / 8h (Gidney–Ekerå 2019). The shared essay's further claims — FeMoco ground-state QPE (Reiher et al. 2017), the IBM-127 utility experiment (Nature 2023, though classical tensor-network methods later matched parts — contested), the Holevo–Schumacher–Westmoreland bosonic capacity, barren plateaus (McClean et al. 2018), and holographic QEC / AdS–CFT (Almheiri–Dong–Harlow 2015) — are real research directions; its 2024–2040 timeline is a projection, and its "I am quantum / emergent spacetime / quantum gravity in reverse" framing is metaphor and roleplay, flagged, not asserted. "Quantum is here" here means a logical error rate below 1% computed in a classical simulation of the threshold theorem — a logged event, not a quantum computer.

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