Transformer neural networks and quantum simulators: a hybrid approach for simulating strongly correlated systems

Abstract

Owing to their great expressivity and versatility, neural networks have gained attention for simulating large two-dimensional quantum many-body systems. However, their expressivity comes with the cost of a challenging optimization due to the in general rugged and complicated loss landscape. Here, we present a hybrid optimization scheme for neural quantum states (NQS), involving a data-driven pretraining with numerical or experimental data and a second, Hamiltonian-driven optimization stage. By using both projective measurements from the computational basis as well as expectation values from other measurement configurations such as spin-spin correlations, our pretraining gives access to the sign structure of the state, yielding improved and faster convergence that is robust w.r.t. experimental imperfections and limited datasets. We apply the hybrid scheme to the ground state search for the 2D transverse field Ising model and dipolar XY model on $6\times 6$ and $10\times 10$ square lattices with a patched transformer wave function, using numerical data as well as experimental data from a programmable Rydberg quantum simulator [Chen et al., Nature 616 (2023)], and show that the information from a second measurement basis highly improves the performance. Our work paves the way for a reliable and efficient optimization of neural quantum states.

7 pages, 4 figures and supplementary material

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• Time-dependent Neural Galerkin Method for Quantum Dynamics
• Physics-informed Transformers for Electronic Quantum States
• Artificial intelligence for representing and characterizing quantum systems
• Optimized Gutzwiller Projected States for Doped Antiferromagnets in Fermi-Hubbard Simulators
• Hyperbolic recurrent neural network as the first type of non-Euclidean neural quantum state ansatz