可训练与可微分量子生成建模范式
Protocols for Trainable and Differentiable Quantum Generative Modelling
AI总结：
提出基于可微分量子电路的量子生成建模方法，通过相位特征映射和变分电路实现高效采样与可微分训练，支持多维生成与随机微分方程求解。
摘要：
我们提出了一种将概率分布学习为可微分量子电路（DQC）的方法，以实现高效的量子生成建模（QGM）和合成数据生成。与现有QGM方法不同，我们对基于DQC的模型进行训练，其中数据通过相位特征映射编码到潜在空间中，随后接入变分量子电路。然后，我们使用固定的酉变换将训练后的模型映射到位基上，在最简单情况下该变换对应于量子傅里叶变换电路。这允许使用单次读出从参数化分布中进行快速采样。重要的是，简化的潜在空间训练提供了自动可微分的模型，并且我们展示了如何通过量子协议求解静态和时间相关的Fokker-Planck方程，从而获取由随机微分方程（SDE）传播的分布样本。最后，我们的方法为多维生成建模开辟了途径，其中量子比特寄存器通过（固定）纠缠层显式关联。在这种情况下，量子计算机可作为高效采样器提供优势，执行由量子力学基本定律支持的复杂逆变换采样。在技术层面上进展是多方面的，我们引入了相位特征映射，分析了其性质，并开发了包括逐量子比特训练和特征映射稀疏化的频率控制技术。
英文摘要：
We propose an approach for learning probability distributions as differentiable quantum circuits (DQC) that enable efficient quantum generative modelling (QGM) and synthetic data generation. Contrary to existing QGM approaches, we perform training of a DQC-based model, where data is encoded in a latent space with a phase feature map, followed by a variational quantum circuit. We then map the trained model to the bit basis using a fixed unitary transformation, coinciding with a quantum Fourier transform circuit in the simplest case. This allows fast sampling from parametrized distributions using a single-shot readout. Importantly, simplified latent space training provides models that are automatically differentiable, and we show how samples from distributions propagated by stochastic differential equations (SDEs) can be accessed by solving stationary and time-dependent Fokker-Planck equations with a quantum protocol. Finally, our approach opens a route to multidimensional generative modelling with qubit registers explicitly correlated via a (fixed) entangling layer. In this case quantum computers can offer advantage as efficient samplers, which perform complex inverse transform sampling enabled by the fundamental laws of quantum mechanics. On a technical side the advances are multiple, as we introduce the phase feature map, analyze its properties, and develop frequency-taming techniques that include qubit-wise training and feature map sparsification.
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