用量子干涉实现无需训练的机器学习，可高效提取全局特征。
Bernstein-Vazirani Networks: Quantum Machine Learning by Interference
- 通过量子傅里叶采样在叠加态中实现数据干涉，提取全局特征。
- 在合成与真实数据集上表现优于经典和量子基线模型。
- 无需梯度训练，适合对泛化能力要求高的任务。
我们提出伯恩斯坦-瓦兹里尼网络（BVNs），一种非变分的量子机器学习框架，利用量子干涉进行监督学习，在视觉和表征学习任务中得到验证。标准形式的BVNs遵循量子傅里叶采样原理：将带标签数据置于叠加态，并在傅里叶基下进行干涉，以提取全局信息特征。我们进一步定义广义BVNs，可在问题自适应基下实现干涉，相同测量预算下获得更强表达能力。BVNs通过（过）完备干涉基实现通用函数逼近，且训练过程无需梯度。在合成与真实分类任务及隐式图像表征实验中，表现出强泛化能力，性能可与经典及量子基线媲美。
原文摘要 · Abstract (English)
We introduce Bernstein-Vazirani Networks (BVNs), a non-variational quantum machine learning framework that leverages quantum interference for supervised learning, demonstrated on vision and representation learning tasks. In their standard form, BVNs follow the principle of quantum Fourier sampling: labelled data are placed in superposition and interfered in the Fourier basis to extract globally informative features. We then define generalised BVNs that enable interference in problem-adapted bases, yielding more expressive models under the same measurement budget as in the standard setting. BVNs achieve universal function approximation through (over)complete interference bases, while training of BVNs is gradient-free. Experiments on synthetic and real-world classification tasks, as well as implicit image representation, show strong generalisation capabilities and competitive performance with classical and quantum baselines.
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