Simulating quantum chemical dynamics on ion-trap quantum computers.*

The accurate computational determination of chemical, materials, biological, and atmospheric properties has a critical impact on a wide range of health and environmental problems. However, such studies are deeply limited by the steep algebraic scaling of electron correlation methods, and the exponential scaling in studying quantum nuclear dynamics. We, here, present an algorithm for simulating quantum nuclear dynamics on a quantum device using the parameters of a generalized Ising Hamiltonian that can be realized on a spin-lattice quantum computer. Our method radically differs from the commonly used gate-based circuit implementation facilitated by spin-statistics based transformations for electronic structure problems in quantum chemistry. Here, the Born-Oppenheimer potential energy and the kinetic energy that constitute the quantum nuclear Hamiltonian are directly used to compute the on-site and inter-site parameters of the Ising Hamiltonian. This method, well in line with Feynman's vision of simulating a quantum system using another controllable quantum system, is demonstrated by mapping the proton-transfer dynamics in a short-strong hydrogen bonded system onto an ion-trap quantum computer.