量子神经网络可高效学习量子态所属子空间，具物理意义且难被经典计算模拟。
Fragmentation is Efficiently Learnable by Quantum Neural Networks
- 将量子态分类为低维不连通子空间，构建可学习任务
- 在特定条件下量子计算可高效完成该分类任务
- 经典算法无法通过现有技术实现去量子化，适合量子优势研究
在某些物理量子系统中，指数级大的态空间会分裂为多个低维、动态解耦的子空间。我们提出一种名为片段分类的学习问题：给定一个量子态输入，判断其属于哪个子空间。我们证明，在满足一定条件时，该学习任务可在量子计算机上高效完成。此外，我们通过证明现有去量子化技术对此任务无效，提供了该任务经典困难性的证据。因此，这项工作为物理驱动的量子机器学习任务提供了一个罕见范例——既可在量子计算机上高效执行，又无已知经典去量子化方法。
原文摘要 · Abstract (English)
In certain classes of physical quantum systems, the exponentially large state space "fragments" into many low-dimensional, dynamically disconnected subspaces. We introduce a learning problem known as fragment classification, where given a quantum state input, one is interested in classifying to which subspace the state belongs. We prove that solving this learning problem is efficient on a quantum computer when the fragmentation phenomenon satisfies certain conditions. Furthermore, we give evidence supporting the classical hardness of this task by demonstrating that known dequantization techniques fail for the fragment classification problem. Consequently, this work provides a rare example of a physically motivated quantum machine learning task that is both efficient for quantum computers to perform and admits no known classical dequantization.
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