Correlations Behavior in a Simulated 2D Array of Rydberg Atoms

Fabien Lefebvre, University of Ottawa

Our interest lies in using the RNN to simulate two-dimensional (2D) arrays of Rydberg atoms. A Hamiltonian-driven approach is then used to train the RNN and find the ground state energy of the system. During this Hamiltonian-driven training to find the ground state energy, sudden jumps are observed in the convergence process of the system’s expected energy. During this talk, I will give insights into the nature of these jumps and discuss how we can use this knowledge to improve the training process of the RNN. I will first discuss the behavior of different spin correlations during the training process, and that the build-up of long-range spin correlations causes the late jumps. I will confirm these findings with single-shot Fourier transforms of the 2D array, which gives information about the long-range order in the array. This allows us to observe the change in long-range order around the jumps at different points in the phase diagram. I will further discuss a modified architecture for the RNN by having a 2-qubit input. This modified RNN architecture promises the encoding of spin correlations in the RNN, which can eliminate the jumps in the training process and thus suggest a faster convergence to the ground state energy.