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arXiv 2201.08770cs.LGquant-ph
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生成模型中实用量子优势的泛化度量

Generalization Metrics for Practical Quantum Advantage in Generative Models

University of Oxford(牛津大学);Zapata Computing Canada Inc.(加拿大扎帕塔计算公司)

Kaitlin Gili, Marta Mauri, Alejandro Perdomo-Ortiz

AI总结:

本研究提出基于泛化性能的采样度量,用于无歧义评估生成模型的实用量子优势,实验显示量子启发模型在生成新颖有效样本上较GAN有68倍提升。

摘要:

随着量子计算社区日益关注理解量子计算机的实际益处,在特定应用背景下评估实用量子优势时,拥有清晰的定义和评估方案至关重要。例如,生成建模被广泛认为是量子计算机的自然用例,但一直缺乏一种具体的方法来量化量子模型相对于经典模型的成功程度。在本工作中,我们构建了一种简单且无歧义的方法来探测生成建模中的实用量子优势,通过衡量算法的泛化性能。利用本文提出的基于采样的方法,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Born机),都可以在相同的具体明确定义框架下进行评估。与其他用于探测实际泛化能力的基于采样的度量不同,我们利用约束优化问题(例如基数约束问题),并使用这些离散数据集来定义特定度量,能够无歧义地衡量样本质量以及模型在生成超出训练集但仍位于有效解空间内的数据时的泛化能力。此外,我们的度量能够诊断可训练性问题,如模式崩溃和过拟合,正如我们在比较GAN与基于张量网络构建的量子启发模型时所展示的。我们的模拟结果表明,与GAN相比,我们的量子启发模型在生成未见过的独特且有效样本方面有高达68倍的增强,并且在生成质量优于训练集中观察到的样本的比例为61:2。我们预见这些度量将成为在生成建模领域严格定义实用量子优势的有价值工具。

英文摘要:

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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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