We introduce a general framework called neural network (NN) encoded
variational quantum algorithms (VQAs), or NN-VQA for short, to address the
challenges of implementing VQAs on noisy intermediate-scale quantum (NISQ)
computers. Specifically, NN-VQA feeds input (such as parameters of a
Hamiltonian) from a given problem to a neural network and uses its outputs to
parameterize an ansatz circuit for the standard VQA. Combining the strengths of
NN and parameterized quantum circuits, NN-VQA can dramatically accelerate the
training process of VQAs and handle a broad family of related problems with
varying input parameters with the pre-trained NN. To concretely illustrate the
merits of NN-VQA, we present results on NN-variational quantum eigensolver
(VQE) for solving the ground state of parameterized XXZ spin models. Our
results demonstrate that NN-VQE is able to estimate the ground-state energies
of parameterized Hamiltonians with high precision without fine-tuning, and
significantly reduce the overall training cost to estimate ground-state
properties across the phases of XXZ Hamiltonian. We also employ an
active-learning strategy to further increase the training efficiency while
maintaining prediction accuracy. These encouraging results demonstrate that
NN-VQAs offer a new hybrid quantum-classical paradigm to utilize NISQ resources
for solving more realistic and challenging computational problems.Comment: 4.4 pages, 5 figures, with supplemental material