Sparse-Hamiltonian approach to the time evolution of molecules on quantum computers

TL;DR

This paper introduces a hybrid quantum-classical method for molecular electronic structure calculations by mapping molecules onto sparse Hubbard-like Hamiltonians, demonstrated with a hydrogen ring example.

Contribution

It proposes a novel approach using sparse Hamiltonian mapping and Green's-function techniques for quantum chemistry on quantum computers.

Findings

Demonstrated time evolution on a four-site hydrogen ring

Mapped molecular problems onto sparse Hubbard-like Hamiltonians

Showcased potential for efficient quantum simulations of molecules

Abstract

Quantum chemistry has been viewed as one of the potential early applications of quantum computing. Two techniques have been proposed for electronic structure calculations: (i) the variational quantum eigensolver and (ii) the phase-estimation algorithm. In both cases, the complexity of the problem increases for basis sets where either the Hamiltonian is not sparse, or it is sparse, but many orbitals are required to accurately describe the molecule of interest. In this work, we explore the possibility of mapping the molecular problem onto a sparse Hubbard-like Hamiltonian, which allows a Green's-function-based approach to electronic structure via a hybrid quantum-classical algorithm. We illustrate the time-evolution aspect of this methodology with a simple four-site hydrogen ring.