System-bath model for quantum chemistry

TL;DR

This paper introduces a novel system-bath Hamiltonian mapping for quantum chemistry that simplifies molecular excitation calculations by focusing on a small active space and modeling remaining excitations with oscillators, inspired by RPA.

Contribution

It presents a new approximate mapping of molecular Hamiltonians to a system-bath model using a minimal active space and bosonic excitations, facilitating quantum computations.

Findings

High accuracy in vertical excitation energy calculations

Reduction of molecular Hamiltonian to a two-qubit system

Potential for near-term quantum computer applications

Abstract

We propose an approximate mapping of a molecular Hamiltonian to a Hamiltonian of qubits, which allows for high accuracy quantum chemistry calculations of vertical excitation energies of some molecules. The mapping is based on separating of a very small active space of only two orbitals and on modeling the electronic excitations in the remaining orbitals by a set of qubits or, equivalently, by a set of oscillators. This approach is inspired by the Random Phase Approximation (RPA), in which the excitations of electron gas are described by bosonic degrees of freedom. As a result, the Hamiltonian of the molecule is reduced to that of a system-bath model. The "system" part of the Hamiltonian describes the two molecular orbitals -- the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) -- which are populated by two electrons. Two qubits are sufficient to encode the Hamiltonian of such a system. The "bath" consists of oscillators or, equivalently, of two level systems with each of them corresponding to an electron excitation from a doubly occupied orbital below the Fermi level to an empty orbital above the Fermi level. We hope that this mapping can inspire new approaches and algorithms aimed at calculating excitation energies of molecules on near term quantum computers.