Mapping quantum chemical dynamics problems onto spin-lattice simulators
Abstract
The accurate computational determination of chemical, materials, biological,
and atmospheric properties has critical impact on a wide range of health and
environmental problems, but is deeply limited by the computational scaling of
quantum-mechanical methods. The complexity of quantum-chemical studies arises
from the steep algebraic scaling of electron correlation methods, and the
exponential scaling in studying nuclear dynamics and molecular flexibility. To
date, efforts to apply quantum hardware to such quantum chemistry problems have
focused primarily on electron correlation. Here, we provide a framework which
allows for the solution of quantum chemical nuclear dynamics by mapping these
to quantum spin-lattice simulators. Using the example case of a short-strong
hydrogen bonded system, we construct the Hamiltonian for the nuclear degrees of
freedom on a single Born-Oppenheimer surface and show how it can be transformed
to a generalized Ising model Hamiltonian. We then demonstrate a method to
determine the local fields and spin-spin couplings needed to identically match
the molecular and spin-lattice Hamiltonians. We describe a protocol to
determine the on-site and inter-site coupling parameters of this Ising
Hamiltonian from the Born-Oppenheimer potential and nuclear kinetic energy
operator. Our approach represents a paradigm shift in the methods used to study
quantum nuclear dynamics, opening the possibility to solve both electronic
structure and nuclear dynamics problems using quantum computing systems.