Simulation of Electronic Structure Hamiltonians Using Quantum Computers

TL;DR

This paper details how quantum computers can simulate molecular electronic structure Hamiltonians efficiently, using quantum phase estimation and pre-computed integrals, exemplified with hydrogen molecule.

Contribution

It introduces a method to construct quantum circuits from molecular integrals for simulating quantum chemistry on quantum computers, extending previous results and discussing state preparation.

Findings

Quantum circuits can be explicitly constructed from molecular integrals.

The method enables energy estimation of molecules using quantum phase estimation.

A complete example with hydrogen molecule demonstrates practical implementation.

Abstract

Over the last century, a large number of physical and mathematical developments paired with rapidly advancing technology have allowed the field of quantum chemistry to advance dramatically. However, the lack of computationally efficient methods for the exact simulation of quantum systems on classical computers presents a limitation of current computational approaches. We report, in detail, how a set of pre-computed molecular integrals can be used to explicitly create a quantum circuit, i.e. a sequence of elementary quantum operations, that, when run on a quantum computer, to obtain the energy of a molecular system with fixed nuclear geometry using the quantum phase estimation algorithm. We extend several known results related to this idea and discuss the adiabatic state preparation procedure for preparing the input states used in the algorithm. With current and near future quantum devices in mind, we provide a complete example using the hydrogen molecule, of how a chemical Hamiltonian can be simulated using a quantum computer.