  Neural networks have been used as variational wave functions for quantum
many-particle problems. It has been shown that the correct sign structure is
crucial to obtain the high accurate ground state energies. In this work, we
propose a hybrid wave function combining the convolutional neural network (CNN)
and projected entangled pair states (PEPS), in which the sign structures are
determined by the PEPS, and the amplitudes of the wave functions are provided
by CNN. We benchmark the ansatz on the highly frustrated spin-1/2 $J_1$-$J_2$
model. We show that the achieved ground energies are competitive to
state-of-the-art results.
