Mapping quantum chemical dynamics problems onto spin-lattice simulators

TL;DR

This paper introduces a novel framework for simulating quantum chemical nuclear dynamics by mapping them onto quantum spin-lattice models, enabling the use of quantum hardware for complex molecular simulations.

Contribution

It presents a method to transform nuclear Hamiltonians into generalized Ising models, facilitating quantum simulation of nuclear dynamics beyond electron correlation.

Findings

Mapped nuclear Hamiltonian to Ising model for hydrogen-bonded systems

Demonstrated parameter determination from potential and kinetic energy data

Proposed a paradigm shift in quantum nuclear dynamics simulation

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.