用学习方法自动设计量子纠错码的逻辑门，适配硬件噪声。
Learning Logical Operations for Arbitrary Quantum Error Correction Codes
- 基于编码电路，学习实现逻辑操作的物理方案。
- 可生成满足浅深度或横跨性要求的逻辑门，适配不同噪声模型。
- 适合早期容错量子计算中的硬件定制逻辑门设计。
逻辑操作是量子纠错码中实现量子计算的核心。然而，为非加性码（缺乏稳定子描述）寻找其物理实现极具挑战。我们提出一种通用的学习框架，仅需编码电路即可构造满足特定结构属性（如横跨性或浅深度）的逻辑操作物理实现。该方法在标准稳定子码上验证了已知逻辑门的复现。进一步扩展为联合设计流程——变分早期容错量子计算（VarEFTQC），可根据给定噪声模型定制非加性编码，并强制实现期望的逻辑门集，如横跨型IQP类或低深度通用门集。配套软件库实现了完整的学习流程，包括损失函数变体、参数化电路族与优化算法。这些成果使VarEFTQC成为发现适用于早期容错量子计算的硬件适配逻辑门的实用工具。
原文摘要 · Abstract (English)
Logical operations are essential for quantum computation within quantum error-correcting codes. However, discovering their physical realizations is challenging, especially for non-additive codes that lack a stabilizer description. We present a general learning-based framework that, given only an encoding circuit, constructs physical implementations of logical operations while enforcing structural properties such as transversality or shallow depth. Our approach is validated by rediscovering known logical operations of standard stabilizer codes. We then extend it to a co-design procedure, dubbed variational early fault-tolerant quantum computing (VarEFTQC), which tailors non-additive encodings to a given noise model and enforces desired logical gate sets, such as transversal IQP-type families or low-depth universal sets. A software library implements the complete learning pipeline, including loss-function variants, ansatz families, and optimization routines. Together, these results position VarEFTQC as a practical tool for discovering hardware-adapted logical gadgets for early fault-tolerant quantum computing.
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