Solving quantum many-body problems is one of the most fascinating research fields in condensed matter physics. An efficient numerical method is crucial to understand the mechanism of novel physics, such as the high Tc superconductivity, as one has to find the optimal solution in the exponentially large Hilbert space. The development of Artificial Intelligence (AI) provides a unique opportunity to solve the quantum many-body problems, but there is still a large gap from the goal. In this work, we present a novel computational framework, and adapt it to the Sunway supercomputer. With highly efficient scalability up to 40 million heterogeneous cores, we can drastically increase the number of variational parameters, which greatly improves the accuracy of the solutions. The investigations of the spin-1/2 J1-J2 model and the t-J model achieve unprecedented accuracy and time-to-solution far beyond the previous state of the art.

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$24\times 24$, 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.