Bridging the Gap between Deep Learning and Frustrated Quantum Spin System for Extreme-Scale Simulations on New Generation of Sunway Supercomputer

$2^{1296}$ Exponentially Complex Quantum Many-Body Simulation via Scalable Deep Learning Method

“…Comparing the energies in this work to the results obtained by the PP+RBM method on the "Fugaku" supercomputer [33]. When 𝐿=10 the energy in this work is -0.497468, which is 3.2 × 10 −4 higher than the -0.497629 reported in [33], and 5.8×10 −4 lower than the -0.49717 reported in [24]. For 𝐿=18, the ground state energy obtained in this work is -0.496500, which is 4.5 × 10 −4 lower than -0.496275 reported in [33].…”

“…The frustrated-free Heisenberg model has been solved by RBM to a rather high precision [8]. For the 𝐽 1-𝐽 2 model, three kinds of methods are used: 1, a single CNN [27]; 2, a deep CNN [11,24,26,43]; 3, a Gutzwiller projected wave-function and a RBM [16,33]. Because of the high computational complexity of Gutzwiller projected wave-function, the investigated lattice size is limited to 𝐿=18 [33].…”

“…The method of a deep CNN with has lower computational complexity, however the energy's precision depends on the representation ability of the deep CNN [11,26,43]. With a proper deep CNN structure, and increasing the parameter number to the magnitude of 10 5 , the energy's precision reaches state-of-the-art [24]. In this work, the parameter number is further increased to the magnitude of 4 × 10 5 , and the investigated lattice size is increased to 𝐿=36.…”

“…In the year of 2021, on the "Fugaku" supercomputer, the pair product states with a RBM has achieved high accuracy on the lattice as large as 18×18 [33]. In the year of 2022, by increasing the deep CNN's parameter number to 106529, the energy's precision is highly improved and the lattice size is increased to 24 × 24 [24]. In this work, the deep CNN's parameter number is further increased to 421953, and the square lattice size is increased to…”

Deep learning representations for quantum many-body systems on heterogeneous hardware

“…In 2021, on the Fugaku supercomputer, the pair product states with a RBM has achieved high accuracy on the lattice as large as 18 × 18 [25]. In 2022, by increasing the deep CNN parameter number to 106 529, the energy precision is greatly improved and the lattice size is increased to 24 × 24 [26]. Since that various quantum states can be represented by CNN based wavefunctions [27], the quantum state representation is named the convolutional neural quantum state (CNQS).…”