用哈密顿量表示实现高效量子分类，复杂度对数级增长。
An Efficient Quantum Classifier Based on Hamiltonian Representations
- 将输入映射为泡利字符串，通过期望值计算预测结果
- 在文本与图像分类任务中表现优于或相当于经典与量子模型
- 仅需对数级量子比特和门操作，适合大规模应用
量子机器学习旨在将量子计算的优势应用于数据驱动任务。然而，许多研究依赖于小规模数据集或大量特征降维，引发可扩展性担忧。硬件限制和密集向量编码在量子设备上的高成本进一步制约进展。为此，我们提出一种高效方法——哈密顿量分类器，通过将输入映射到有限的泡利字符串集合，并计算其期望值来避免数据编码开销。此外，我们引入两种不同参数与样本复杂度的分类器变体。我们在文本与图像分类任务上评估该方法，对比了经典与量子模型。结果表明，哈密顿量分类器性能相当或更优。特别地，该方法在量子比特和量子门操作上均达到对数级复杂度，适用于大规模真实场景。代码已开源至GitHub。
原文摘要 · Abstract (English)
Quantum machine learning (QML) is a discipline that seeks to transfer the advantages of quantum computing to data-driven tasks. However, many studies rely on toy datasets or heavy feature reduction, raising concerns about their scalability. Progress is further hindered by hardware limitations and the significant costs of encoding dense vector representations on quantum devices. To address these challenges, we propose an efficient approach called Hamiltonian classifier that circumvents the costs associated with data encoding by mapping inputs to a finite set of Pauli strings and computing predictions as their expectation values. In addition, we introduce two classifier variants with different scaling in terms of parameters and sample complexity. We evaluate our approach on text and image classification tasks, against well-established classical and quantum models. The Hamiltonian classifier delivers performance comparable to or better than these methods. Notably, our method achieves logarithmic complexity in both qubits and quantum gates, making it well-suited for large-scale, real-world applications. We make our implementation available on GitHub.
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