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

Abstract

For decades, people are developing efficient numerical methods for solving the challenging quantum many-body problem, whose Hilbert space grows exponentially with the size of the problem. However, this journey is far from over, as previous methods all have serious limitations. The recently developed deep learning methods provide a very promising new route to solve the long-standing quantum many-body problems. We report that a deep learning based simulation protocol can achieve the solution with state-of-the-art precision in the Hilbert space as large as 2 1296 for spin system and 3 144 for fermion system , using a HPC-AI hybrid framework on the new Sunway supercomputer. With highly scalability up to 40 million heterogeneous cores, our applications have measured 94% weak scaling efficiency and 72% strong scaling efficiency. The accomplishment of this work opens the door to simulate spin models and Fermion models on unprecedented lattice size with extreme high precision.

Ground state search by local and sequential updates of neural network quantum states

“…1(a) for a depiction of an RBM. Together with RBMs [2,[20][21][22][23][24][25][26][27][28][29][30][31][32][33][34], other network structures such as a feed-forward [34][35][36][37][38], recurrent [39,40] and convolutional neural networks [41][42][43][44][45][46][47][48][49][50][51][52] have also been intensively studied. The significant interest in the field is attributed to the fact that these networks could offer possibility to fight against the curse of dimensionality in many-body quantum systems.…”

“…Different strategies have been studied in order to improve the accuracy and speed of convergence of neural network quantum states algorithms, such as transfer learning [20], pruning [24], importance sampling [44], and massive parallelization [52]. Between these different techniques, it has been consistently shown that stochastic reconfiguration [56], effectively a Hessian based optimization routine motivated by imaginary time evolution, can provide significantly better performance.…”