  Efficient numerical methods are promising tools for delivering unique
insights into the fascinating properties of physics, such as the highly
frustrated quantum many-body systems. However, the computational complexity of
obtaining the wave functions for accurately describing the quantum states
increases exponentially with respect to particle number. Here we present a
novel convolutional neural network (CNN) for simulating the two-dimensional
highly frustrated spin-$1/2$ $J_1-J_2$ Heisenberg model, meanwhile the
simulation is performed at an extreme scale system with low cost and high
scalability. By ingenious employment of transfer learning and CNN's
translational invariance, we successfully investigate the quantum system with
the lattice size up to $24\times24$, within 30 million cores of the new
generation of sunway supercomputer. The final achievement demonstrates the
effectiveness of CNN-based representation of quantum-state and brings the
state-of-the-art record up to a brand-new level from both aspects of remarkable
accuracy and unprecedented scales.
