Quantum Landauer–Error-Correction Equality (QLE) and Qubit Energy Score (QES): A Unified Framework for Thermodynamic Costs in Quantum Error Correction

This report introduces the Quantum Landauer–Error-Correction Equality (QLE) and the Qubit Energy Score (QES). QLE generalizes Landauer’s principle to quantum error correction, linking entropy exchange and coherent information with minimal energetic cost. QES is a practical metric (joules per logical qubit and bits per logical qubit) allowing laboratories to benchmark the energetic efficiency of fault-tolerant quantum computing. The document contains: Full theoretical derivation of QLE Practical definitions of QES Simulation results (surface codes) Experimental proposals (calorimetry at millikelvin scales) Discussion of impact, limitations, and future outlook