What question did this study set out to answer?

The aim is to present a new quantum error-correction method using modular Hamiltonians and evaluate its performance.

May 21, 2026Open Access

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

Key Points

The aim is to present a new quantum error-correction method using modular Hamiltonians and evaluate its performance.
Defines modular Hamiltonian K_mKQEC for quantum error correction;
Conducts simulations for surface codes and stabilizer codes;
Applies entanglement entropy verification techniques.
Surface code simulations indicate a threshold improvement;
Falsifiable predictions for future quantum computing advancements show varied probabilities;
Roadmap for QEC analytics and collaborations highlights financial needs for development.

Abstract

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.

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

Key Points

Abstract

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