Molecular excited state calculations with the QEB-ADAPT-VQE

TL;DR

This paper introduces the e-QEB-ADAPT-VQE protocol, a quantum algorithm for efficiently calculating molecular excited state energies with fewer quantum gates, suitable for noisy intermediate-scale quantum computers.

Contribution

The paper presents a new adaptive VQE protocol that constructs problem-specific ansätze for excited states, reducing quantum circuit complexity compared to standard methods.

Findings

e-QEB-ADAPT-VQE achieves high accuracy in excited state energy calculations.

The protocol requires at least ten times fewer CNOT gates than traditional UCC-based ansätze.

Classical simulations validate the efficiency and accuracy of the method on LiH and BeH2 molecules.

Abstract

Calculations of molecular spectral properties, like photodissociation rates and absorption bands, rely on knowledge of the excited state energies of the molecule of interest. Protocols based on the variational quantum eigensolver (VQE) are promising candidates to calculate such energies on emerging noisy intermediate scale quantum (NISQ) computers. The successful implementation of these protocols on NISQ computers, relies on ans\"atze that can accurately approximate the molecular states and that can be implemented by shallow quantum circuits. In this paper, we introduce the excited qubit-excitation-based adaptive (e-QEB-ADAPT)-VQE protocol to calculate molecular excited state energies. The e-QEB-ADAPT-VQE constructs efficient problem-tailored ans\"atze by iteratively appending evolutions of qubit excitation operators. The e-QEB-ADAPT-VQE is an adaptation of the QEB-ADAPT-VQE protocol, which is designed to be independent on the choice of an initial reference state. We perform classical numerical simulations for LiH and BeH$_2$ to benchmark the performance of the e-QEB-ADAPT-VQE. We demonstrate that the e-QEB-ADAPT-VQE can construct highly accurate ans\"atze that require at least an order of magnitude fewer $CNOT$s than standard fixed UCC ans\"atze, such as the UCCSD and the GUCCSD.