Constructing Local Bases for a Deep Variational Quantum Eigensolver for Molecular Systems

TL;DR

This paper evaluates the deep variational quantum eigensolver's effectiveness for molecular systems, demonstrating its potential to achieve chemical accuracy with reduced qubit requirements through various basis construction methods.

Contribution

It explores the application of deep VQE to quantum chemistry, compares subspaceforming methods, and proposes techniques to lower qubit counts for molecular ground state calculations.

Findings

Deep VQE achieves below 1% error in electron-correlation energy.

Basis creation method significantly impacts accuracy and qubit reduction.

Deep VQE is effective for complex molecules like retinal.

Abstract

Current quantum computers are limited in the number of qubits and coherence time, constraining the algorithms executable with sufficient fidelity. The variational quantum eigensolver (VQE) is an algorithm to find an approximate ground state of a quantum system and is expected to work on even such a device. The deep VQE [K. Fujii, et al., arXiv:2007.10917] is an extension of the original VQE algorithm, which takes a divide-and-conquer approach to relax the hardware requirement. While the deep VQE is successfully applied for spin models and periodic material, its validity on a molecule, where the Hamiltonian is highly nonlocal in the qubit basis, is still unexplored. Here, we discuss the performance of the deep VQE algorithm applied to quantum chemistry problems. Specifically, we examine different subspaceforming methods and compare their accuracy and complexity on a 10 H-atom treelike molecule as well as a 13 H-atom version. Additionally, we examine the performance on the natural occurring molecule retinal. This work also proposes multiple methods to lower the number of qubits required to calculate the ground state of a molecule. We find that the deep VQE can simulate the electron-correlation energy of the ground state to an error of below 1%, thus helping us to reach chemical accuracy in some cases. The accuracy differences and qubits' reduction highlights the basis creation method's impact on the deep VQE.