ITU Tier 1+ #1: Quantum Error-Correction (mKQEC)

Tier 1+ Pass-1.5 paper 1 of 45. Modular K-Flow Quantum Error Correction. Defines K_mKQEC = -log ρ_mKQEC as the operator-algebraic modular Hamiltonian on H_qubit ⊗ H_code ⊗ H_syndrome. K_mKQEC inherits from K_QG 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 K_QG (0.92), #3 K_crypto (0.85). Ten falsifiable predictions: P_avg=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).