Near-term quantum computers provide a promising platform for finding ground states of quantum systems, which is an essential task in physics, chemistry, and materials science. Near-term approaches, however, are constrained by the effects of noise as well as the limited resources of near-term quantum hardware. We introduce "neural error mitigation," which uses neural networks to improve estimates of ground states and ground-state observables obtained using near-term quantum simulations. To demonstrate our method's broad applicability, we employ neural error mitigation to find the ground states of the H$_2$ and LiH molecular Hamiltonians, as well as the lattice Schwinger model, prepared via the variational quantum eigensolver (VQE). Our results show that neural error mitigation improves numerical and experimental VQE computations to yield low energy errors, high fidelities, and accurate estimations of more-complex observables like order parameters and entanglement entropy, without requiring additional quantum resources. Furthermore, neural error mitigation is agnostic with respect to the quantum state preparation algorithm used, the quantum hardware it is implemented on, and the particular noise channel affecting the experiment, contributing to its versatility as a tool for quantum simulation.

翻译：近期量子计算机为寻找量子系统的基态提供了有前景的平台，这是物理学、化学和材料科学中的关键任务。然而，近期量子方法受到噪声效应以及近期量子硬件有限资源的限制。我们提出"神经误差缓解"，该方法利用神经网络改进通过近期量子模拟获得的基态和基态可观测量估计。为展示该方法广泛适用性，我们采用神经误差缓解寻找通过变分量子本征求解器（VQE）制备的H$_2$和LiH分子哈密顿量以及格点施温格模型的基态。结果表明，神经误差缓解能改进数值和实验VQE计算，实现低能量误差、高保真度，并对序参量和纠缠熵等更复杂可观测量进行准确估计，且无需额外量子资源。此外，神经误差缓解对所用量子态制备算法、其实现的量子硬件以及影响实验的特定噪声通道均具有无关性，这有助于其作为量子模拟工具的通用性。