Tier 1+ Pass-1. 5 paper 1 of 45. Modular K-Flow Quantum Error Correction. Defines KₘKQEC = -log ρₘKQEC as the operator-algebraic modular Hamiltonian on Hqubit ⊗ Hcode ⊗ Hₛyndrome. KₘKQEC inherits from KQG via the CLPW 2023 type II crossed-product specialised to this scale. Numerical results. Surface code threshold simulation; modular flow on stabilizer codes; entanglement entropy verification. Topics covered. Surface codes, Kitaev 2003 toric code, Google Quantum AI 2023 below-threshold, IBM Heron 2024, modular Hamiltonian for QEC. 45-vertex polytope #1 top couplings: #2 AI (0. 95), #17 KQG (0. 92), #3 Kcrypto (0. 85). Ten falsifiable predictions: Pₐvg=0. 62, S/M/W=2/6/2: arXiv 2026 (0. 90 S), Google QEC threshold 2026 (0. 75 M), Logical qubit demos 2027 (0. 65 M). Pass-2 roadmap: ~1. 5M: QEC analytics (500K) + Lean Mathlib (200K) + Quantum hardware collab (800K). Copyright © 2026 Munehiro Terada / Roboken. Licensed under CC-BY-4. 0.
Munehiro Terada (Tue,) studied this question.
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