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Abstract Trapped-ion quantum simulators have demonstrated a long history of studying the physics of interacting spin-lattice systems using globally addressed entangling operations. Yet despite the multitude of studies so far, most have been limited to studying variants of the same spin interaction model, namely an Ising model with power-law decay in the couplings. Here, we demonstrate that much broader classes of effective spin–spin interactions are achievable using exclusively global driving fields. Specifically, we find that these new categories of interaction graphs become achievable with perfect or near-perfect theoretical fidelity by tailoring the coupling of the driving fields to each vibrational mode of the ion crystal. Given the relation between the ion crystal vibrational modes and the accessible interaction graphs, we show how the accessible interaction graph set can be further expanded by shaping the trapping potential to include specific anharmonic terms. Finally, we derive a rigorous test to determine whether a desired interaction graph is accessible using only globally driven fields. These tools broaden the reach of trapped-ion quantum simulators so that they may more easily address open questions in materials science and quantum chemistry. 

The exponential scaling of the quantum degrees of freedom with the size of the system is one of the biggest challenges in computational chemistry and particularly in quantum dynamics. We present a tensor network approach for the time-evolution of the nuclear degrees of freedom of multiconfigurational chemical systems at a reduced storage and computational complexity. We also present quantum algorithms for the resultant dynamics. To preserve the compression advantage achieved via tensor network decompositions, we present an adaptive algorithm for the regularization of nonphysical bond dimensions, preventing the potentially exponential growth of these with time. While applicable to any quantum dynamical problem, our method is particularly valuable for dynamical simulations of nuclear chemical systems. Our algorithm is demonstrated using ab initio potentials obtained for a symmetric hydrogen-bonded system, namely, the protonated 2,2′-bipyridine, and compared to exact diagonalization numerical results.