Qubit-excitation-based adaptive variational quantum eigensolver

TL;DR

This paper introduces a novel qubit-excitation-based adaptive VQE method that constructs efficient, shallow quantum circuits for molecular simulations, outperforming previous fermionic and qubit-based approaches in efficiency and convergence.

Contribution

The paper proposes the QEB-ADAPT-VQE, a new adaptive ansatz construction method using qubit excitations, which is more efficient and converges faster than existing approaches.

Findings

QEB-ADAPT-VQE outperforms qubit-ADAPT-VQE in efficiency and convergence.

Qubit excitation evolutions require fewer gates than fermionic ones.

Numerical benchmarks show effective molecular simulation results.

Abstract

Molecular simulations with the variational quantum eigensolver (VQE) are a promising application for emerging noisy intermediate-scale quantum computers. Constructing accurate molecular ans\"atze that are easy to optimize and implemented by shallow quantum circuits is crucial for the successful implementation of such simulations. Ans\"atze are, generally, constructed as series of fermionic-excitation evolutions. Instead, we demonstrate the usefulness of constructing ans\"atze with "qubit-excitation evolutions", which, contrary to fermionic excitation evolutions, obey "qubit commutation relations". We show that qubit excitation evolutions, despite the lack of some of the physical features of fermionic excitation evolutions, accurately construct ans\"atze, while requiring asymptotically fewer gates. Utilizing qubit excitation evolutions, we introduce the qubit-excitation-based adaptive (QEB-ADAPT)-VQE protocol. The QEB-ADAPT-VQE is a modification of the ADAPT-VQE that performs molecular simulations using a problem-tailored ansatz, grown iteratively by appending evolutions of qubit excitation operators. By performing classical numerical simulations for small molecules, we benchmark the QEB-ADAPT-VQE, and compare it against the original fermionic-ADAPT-VQE and the qubit-ADAPT-VQE. In terms of circuit efficiency and convergence speed, we demonstrate that the QEB-ADAPT-VQE outperforms the qubit-ADAPT-VQE, which to our knowledge was the previous most circuit-efficient scalable VQE protocol for molecular simulations.