Quantum Algorithms for the Study of Electronic Structure and Molecular Dynamics: Novel Computational Protocols

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. In this article we provide an overview of the challenges involved in performing accurate post-Hartree-Fock electronic structure and quantum nuclear dynamics calculations on quantum hardware. For electronic structure, we present a procedure to drastically reduce the depth of quantum circuits and improve the accuracy of results in computing post-Hartree-Fock electronic structure energies for large molecular systems. The method is based on molecular fragmentation where a molecular system is divided into overlapping fragments through a graph theoretic procedure. This allows us to create a set of projection operators that decompose the unitary evolution of the full system into separate sets of unitary processes, some of which can be treated on quantum hardware and others on classical hardware. Thus, we develop a procedure for electronic structure that can be asynchronously spawned on to a potentially large ensemble of classical and quantum hardware systems. We also discuss a framework which allows for the solution of quantum chemical nuclear dynamics by mapping these to quantum spin-lattice simulators. This mapping procedure allows us to determine the local fields and spin-spin couplings needed to identically match the molecular and spin-lattice Hamiltonians and hence the resultant dynamics.