标题： 从噪声量子数据中学习密度泛函 显示英文标题

标题： Learning Density Functionals from Noisy Quantum Data

摘要： 噪声中等规模量子（NISQ）设备在量子模拟中的有用应用的探索受到其固有噪声以及实现高精度相关高成本的阻碍。一种有希望的方法是在这些挑战下使用量子设备为经典机器学习（ML）模型生成训练数据。在本研究中，我们探讨了使用量子算法生成的噪声数据在训练ML模型以学习费米-哈伯德模型的密度泛函中的应用。我们对各种ML模型进行了基准测试，证明神经网络ML模型可以从受NISQ算法典型噪声影响的小数据集中成功推广。学习过程可以有效过滤无偏采样噪声，从而得到一个优于任何单独训练数据点的训练模型。相反，当在具有变分量子本征值求解器典型的表现力和优化误差的数据上进行训练时，模型会复制训练数据中的偏差。训练后的模型可以应用于类似Kohn-Sham的密度优化方案中的新问题实例，受益于自动微分，并在大多数问题实例上实现了合理准确的解决方案。我们的研究结果表明了一条利用NISQ设备在实际量子模拟中发挥作用的有前景的路径，突显了量子计算和ML技术成功整合所需的潜在优势和需要解决的挑战。 显示英文摘要

摘要： The search for useful applications of noisy intermediate-scale quantum (NISQ) devices in quantum simulation has been hindered by their intrinsic noise and the high costs associated with achieving high accuracy. A promising approach to finding utility despite these challenges involves using quantum devices to generate training data for classical machine learning (ML) models. In this study, we explore the use of noisy data generated by quantum algorithms in training an ML model to learn a density functional for the Fermi-Hubbard model. We benchmark various ML models against exact solutions, demonstrating that a neural-network ML model can successfully generalize from small datasets subject to noise typical of NISQ algorithms. The learning procedure can effectively filter out unbiased sampling noise, resulting in a trained model that outperforms any individual training data point. Conversely, when trained on data with expressibility and optimization error typical of the variational quantum eigensolver, the model replicates the biases present in the training data. The trained models can be applied to solving new problem instances in a Kohn-Sham-like density optimization scheme, benefiting from automatic differentiability and achieving reasonably accurate solutions on most problem instances. Our findings suggest a promising pathway for leveraging NISQ devices in practical quantum simulations, highlighting both the potential benefits and the challenges that need to be addressed for successful integration of quantum computing and ML techniques.