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Supplementing Recurrent Neural Network Wave Functions with Symmetry and Annealing to Improve Accuracy
Mohamed Hibat Allah · Juan Carrasquilla · Roger Melko

Recurrent neural networks (RNNs) are a class of neural networks that have emerged from the paradigm of artificial intelligence and has enabled lots of interesting advances in the field of natural language processing. Interestingly, these architectures were shown to be powerful ansatze to approximate the ground state of quantum systems [1]. Here, we build over the results of Ref. [1] and construct a more powerful RNN wave function ansatz in two dimensions. We use symmetry and annealing to obtain accurate estimates of ground state energies of the two-dimensional (2D) Heisenberg model, on the square lattice and on the triangular lattice. We show that our method is superior to Density Matrix Renormalisation Group (DMRG) for system sizes larger than or equal to 12x12 on the triangular lattice.

[1] M. Hibat-Allah, M. Ganahl, L. E. Hayward, R. G. Melko, and J. Carrasquilla, "Recurrent neural network wave functions," Physical Review Research, Jun 2020.

Author Information

Mohamed Hibat Allah (Vector Institute / University of Waterloo)
Juan Carrasquilla (Vector Institute)

Juan Carrasquilla is a full-time researcher at the Vector Institute for Artificial Intelligence in Toronto, Canada, where he works on the intersection of condensed matter physics, quantum computing, and machine learning - such as combining quantum Monte Carlo simulations and machine learning techniques to analyze the collective behaviour of quantum many-body systems. He completed his PhD in Physics at the International School for Advanced Studies in Italy and has since held positions as a Postdoctoral Fellow at Georgetown University and the Perimeter Institute, as a Visiting Research Scholar at Penn State University, and was a Research Scientist at D-Wave Systems Inc. in Burnaby, British Columbia.

Roger Melko (University of Waterloo / Perimeter Institute)

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