As the quantum computing community gravitates towards understanding the practical benefits of quantum computers, having a clear definition and evaluation scheme for assessing practical quantum advantage in the context of specific applications is paramount. Generative modeling, for example, is a widely accepted natural use case for quantum computers, and yet has lacked a concrete approach for quantifying success of quantum models over classical ones. In this work, we construct a simple and unambiguous approach to probe practical quantum advantage for generative modeling by measuring the algorithm's generalization performance. Using the sample-based approach proposed here, any generative model, from state-of-the-art classical generative models such as GANs to quantum models such as Quantum Circuit Born Machines, can be evaluated on the same ground on a concrete well-defined framework. In contrast to other sample-based metrics for probing practical generalization, we leverage constrained optimization problems (e.g., cardinality-constrained problems) and use these discrete datasets to define specific metrics capable of unambiguously measuring the quality of the samples and the model's generalization capabilities for generating data beyond the training set but still within the valid solution space. Additionally, our metrics can diagnose trainability issues such as mode collapse and overfitting, as we illustrate when comparing GANs to quantum-inspired models built out of tensor networks. Our simulation results show that our quantum-inspired models have up to a $68 \times$ enhancement in generating unseen unique and valid samples compared to GANs, and a ratio of 61:2 for generating samples with better quality than those observed in the training set. We foresee these metrics as valuable tools for rigorously defining practical quantum advantage in the domain of generative modeling.

翻译：随着量子计算领域逐渐聚焦于理解量子计算机的实际效益，针对特定应用场景建立清晰的实用量子优势定义与评估体系至关重要。生成建模作为公认的量子计算机天然应用场景之一，至今仍缺乏量化评估量子模型相较经典模型成功程度的具体方法。本研究构建了一种简明无歧义的方案，通过测量算法的泛化性能来探查生成建模中的实用量子优势。采用本文提出的基于样本的方法，任何生成模型——从最先进的经典生成模型（如GAN）到量子模型（如量子电路陪集机）——均可在统一的具体化框架下进行公平评估。与其他基于样本的实用泛化度量指标不同，我们利用约束优化问题（如基数约束问题），通过离散数据集定义能明确衡量样本质量与模型泛化能力的专用指标——即模型能否生成超出训练集但仍处于有效解空间的数据。此外，我们的指标可诊断模式坍塌、过拟合等可训练性问题，这在对比GAN与基于张量网络的量子启发模型时得到验证。仿真结果显示，相较于GAN，我们的量子启发模型在生成未见过的唯一有效样本时性能提升达68倍，且生成优于训练集样本质量的样本比例达到61:2。我们预计这些指标将成为严格定义生成建模领域实用量子优势的重要工具。