Reconstructing quantum molecular rotor ground states

Abstract

Nanomolecular assemblies of C 60 can be synthesized to enclose dipolar molecules. The low-temperature states of such endofullerenes are described by quantum mechanical rotors, which are candidates for quantum information devices with higher-dimensional local Hilbert spaces. The experimental exploration of endofullerene arrays comes at a time when machine learning techniques are rapidly being adopted to characterize, verify, and reconstruct quantum states from measurement data. In this paper, we develop a strategy for reconstructing the ground state of chains of dipolar rotors using restricted Boltzmann machines (RBMs) adapted to train on data from higher-dimensional Hilbert spaces. We demonstrate accurate generation of energy expectation values from an RBM trained on data in the free-rotor eigenstate basis and explore the learning resources required for various chain lengths and dipolar interaction strengths. Finally, we show evidence for fundamental limitations in the accuracy achievable by RBMs due to the difficulty in imposing symmetries in the sampling procedure. We discuss possible avenues to overcome this limitation in the future, including the further development of autoregressive models such as recurrent neural networks for the purposes of quantum state reconstruction.

Stochastic series expansion quantum Monte Carlo for Rydberg arrays

“…Our SSE algorithm will be useful in directly characterizing equilibrium groundstate properties on Rydberg arrays of the exact size and lattice geometry of current experiments [8,9,46,47]. In addition, QMC simulations such as this will be crucial for providing data for pretraining generative machine learning models, which are poised to become important tools in state reconstruction and tomography [48][49][50][51]. To this point, it is foreseeable that our SSE algorithm will be required to access system sizes beyond current experiments to facilitate the aforementioned numerical studies.…”

Azimuthal Dipolar Rotor Arrays on Surfaces

“…[ 3 , 4 ] Besides the investigation and construction of individual, molecular functional units, the coupling of ensembles of rotors in 2D and 3D arrays is intriguing from a fundamental and an application oriented point of view. [ 5 , 6 , 7 ]…”