The variational quantum eigensolver (VQE) is a hybrid algorithm that has the potential to provide a quantum advantage in practical chemistry problems that are currently intractable on classical computers. VQE trains parameterized quantum circuits using a classical optimizer to approximate the eigenvalues and eigenstates of a given Hamiltonian. However, VQE faces challenges in task-specific design and machine-specific architecture, particularly when running on noisy quantum devices. This can have a negative impact on its trainability, accuracy, and efficiency, resulting in noisy quantum data. We propose variational denoising, an unsupervised learning method that employs a parameterized quantum neural network to improve the solution of VQE by learning from noisy VQE outputs. Our approach can significantly decrease energy estimation errors and increase fidelities with ground states compared to noisy input data for the $\text{H}_2$, LiH, and $\text{BeH}_2$ molecular Hamiltonians, and the transverse field Ising model. Surprisingly, it only requires noisy data for training. Variational denoising can be integrated into quantum hardware, increasing its versatility as an end-to-end quantum processing for quantum data.

翻译：变分量子本征求解器（VQE）是一种混合算法，有望在经典计算机当前难以处理的实用化学问题中提供量子优势。VQE利用经典优化器训练参数化量子电路，以逼近给定哈密顿量的本征值和本征态。然而，VQE在任务特定设计和机器特定架构方面面临挑战，尤其是在噪声量子设备上运行时，这会对其可训练性、准确性和效率产生负面影响，导致输出噪声量子数据。我们提出变分去噪——一种无监督学习方法，通过参数化量子神经网络从噪声VQE输出中学习来改进VQE的解。对于H₂、LiH、BeH₂分子哈密顿量以及横向场伊辛模型，与噪声输入数据相比，我们的方法可显著降低能量估计误差并提高基态保真度。令人惊讶的是，该方法仅需噪声数据即可训练。变分去噪可集成至量子硬件中，增强其作为量子数据端到端量子处理器的多功能性。