Variational Denoising for Variational Quantum Eigensolver
This addresses the challenge of improving VQE performance on noisy quantum devices for practical chemistry problems, representing an incremental advancement in quantum computing methods.
The paper tackled the problem of noisy quantum data in variational quantum eigensolver (VQE) algorithms by proposing variational denoising, an unsupervised learning method using a parameterized quantum neural network, which significantly decreased energy estimation errors and increased fidelities with ground states for molecular Hamiltonians and the transverse field Ising model.
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.