Simulating quantum chemical dynamics on ion-trap quantum computers

The quantum mechanical treatment of both electrons and nuclei is critical for a wide range of chemical, biological, and atmospheric problems. Such studies, however, are deeply limited by the steep algebraic scaling of electron correlation methods, coupled with the exponential scaling in studying quantum nuclear dynamics. Recently, with the experimental and algorithmic developments in quantum computing, considerable progress has been made in the study of electronic structure on quantum hardware. We, here, provide a theoretical framework, along with experimental verification, that allows for the simulation of quantum nuclear dynamics on ion-trap quantum devices.

We consider a short strong hydrogen-bonded system to illustrate a map between the quantum nuclear Hamiltonian and a generalized Ising Hamiltonian that describes the dynamics of the ion trap. We use the Born-Oppenheimer potential surface and kinetic energy of the quantum nuclei to compute the Ising Hamiltonian parameters such that the spin-lattice dynamics exactly reproduces the dynamics of the shared proton. Additionally, we use Sandia National Lab’s (QSCOUT) ion-trap device to emulate the trajectory of the shared proton. This then allows us to extract the vibrational frequencies for the shared proton motion from the spin-lattice dynamics with spectroscopic accuracies of the order of 3.3cm-1. Thus, our approach offers a new paradigm for studying the quantum chemical dynamics and vibrational spectra of molecules on quantum hardware.