量子深度集合与序列模型可处理任意输入数量的集合和序列任务。
Quantum Deep Sets and Sequences
- 用量子态平均实现无序集合的不变性映射
- 通过混合态乘积处理有序序列，适配自然语言等任务
- 在合成任务中验证了模型对分类、回归等的通用性
本文提出量子深度集合与序列模型（Quantum Deep Sets and Sequences, QDS），拓展了量子机器学习工具箱，使量子系统能够学习变长输入函数。第一种变体通过元素量子态的平均来映射无序集合，实现排列不变性；第二种变体针对有序集合（如序列），利用最优相干化三随机张量实现混合态乘积，将每个元素映射为密度矩阵并相乘，适用于自然语言处理等场景。最终生成的量子态用于完成分类、回归或密度估计等任务。通过合成问题验证了QDS的有效性与灵活性。
原文摘要 · Abstract (English)
This paper introduces the quantum deep sets model, expanding the quantum machine learning tool-box by enabling the possibility of learning variadic functions using quantum systems. A couple of variants are presented for this model. The first one focuses on mapping sets to quantum systems through state vector averaging: each element of the set is mapped to a quantum state, and the quantum state of the set is the average of the corresponding quantum states of its elements. This approach allows the definition of a permutation-invariant variadic model. The second variant is useful for ordered sets, i.e., sequences, and relies on optimal coherification of tristochastic tensors that implement products of mixed states: each element of the set is mapped to a density matrix, and the quantum state of the set is the product of the corresponding density matrices of its elements. Such variant can be relevant in tasks such as natural language processing. The resulting quantum state in any of the variants is then processed to realise a function that solves a machine learning task such as classification, regression or density estimation. Through synthetic problem examples, the efficacy and versatility of quantum deep sets and sequences (QDSs) is demonstrated.
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