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本报告介绍了量子兰道尔纠错等式（Quantum Landauer–Error-Correction Equality，QLE）与量子比特能量评分（Qubit Energy Score，QES）。QLE将兰道尔原理推广至量子纠错领域，建立了熵交换、相干信息与最小能量代价之间的关联。QES是一项实用度量指标（单位为焦耳每逻辑量子比特、比特每逻辑量子比特），可帮助实验室评估容错量子计算的能量效率。 本报告包含以下内容： 1. QLE的完整理论推导 2. QES的实用定义 3. 基于表面码的仿真结果 4. 实验方案建议（毫开尔文尺度下的量热法） 5. 对研究影响、局限性与未来展望的讨论