  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.
