Towards Perturbation Theory Methods on a Quantum Computer

TL;DR

This paper introduces a quantum circuit method for applying perturbation theory to estimate energy and eigenstates corrections, demonstrating advantages over classical methods and applying it to the extended Hubbard model.

Contribution

It presents a novel quantum circuit approach for perturbation theory that does not require training, derived directly from the unperturbed Hamiltonian, and shows potential for complex system analysis.

Findings

Quantum circuit estimates second order energy correction more accurately than classical methods.

Application to the extended Hubbard model demonstrates practical utility.

No training or optimization needed in the quantum circuit approach.

Abstract

Perturbation theory (PT) might be one of the most powerful and fruitful tools for both physicists and chemists, which evoked an explosion of applications with the blooming of atomic and subatomic physics. Even though PT is well-used today, techniques for PT are significantly lacking in quantum computing. Here we present a quantum circuit estimating both the energy and eigenstates corrections with PT methods, which we claim is far superior to the classical version when estimating the second order energy correction. Our approach is further demonstrated with an application on the extended Hubbard model, where numerical simulation based on qiskit is also presented. Unlike the popular quantum variational circuit, there is no training or optimizing process in our circuit, and all parameters are derived from the unperturbed Hamiltonian. Our work offers a new approach to studying complex systems with quantum devices, which might shed light on the quantum implementation of the more intricate methods based on PT.