某些量子物态无法被机器学习识别，因它们具有全局不可区分性。
Unlearnable phases of matter
- 用条件互信息检测局部不可区分态，揭示学习困难本质。
- 在比特翻转噪声下，神经网络无法有效学习拓扑码的物理与纠错分布。
- 该方法可作为探测相变与纠错阈值的新工具，适合量子计算研究者。
我们通过证明非平凡混合态物态在机器学习中存在根本限制，揭示了其计算难解性。聚焦无监督学习分布问题，发现自回归神经网络无法学习由局部不可区分（LI）态表征的分布的全局特性。我们证明条件互信息（CMI）是检测LI的有效指标：对经典分布而言，长程CMI意味着存在空间上的局部不可区分伙伴。通过引入受限统计查询模型，我们证明具有长程CMI的非平凡相（如强到弱自发对称性破缺相）难以学习。我们使用循环、卷积和Transformer神经网络，在比特翻转噪声下验证了拓扑码（toric/surface code）的校验子与物理分布的学习失败。结果表明，学习难度可作为探测混合态相及相变、错误纠正阈值的诊断工具，并建议将CMI以及更一般的“非局域吉布斯性”作为衡量分布学习难易程度的指标。
原文摘要 · Abstract (English)
We identify fundamental limitations in machine learning by demonstrating that non-trivial mixed-state phases of matter are computationally hard to learn. Focusing on unsupervised learning of distributions, we show that autoregressive neural networks fail to learn global properties of distributions characterized by locally indistinguishable (LI) states. We demonstrate that conditional mutual information (CMI) is a useful diagnostic for LI: we show that for classical distributions, long-range CMI of a state implies a spatially LI partner. By introducing a restricted statistical query model, we prove that nontrivial phases with long-range CMI, such as strong-to-weak spontaneous symmetry breaking phases, are hard to learn. We validate our claims by using recurrent, convolutional, and Transformer neural networks to learn the syndrome and physical distributions of toric/surface code under bit flip noise. Our findings suggest hardness of learning as a diagnostic tool for detecting mixed-state phases and transitions and error-correction thresholds, and they suggest CMI and more generally ``non-local Gibbsness'' as metrics for how hard a distribution is to learn.
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