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The Journal of Physical Chemistry Letters

Toward Accurate Calculation of Excitation Energies on Quantum Computers with ΔADAPT-VQE: A Case Study of BODIPY Derivatives

Anton Nykänen, Leander Thiessen, Elsi-Mari Borrelli, Vijay B. Krishna, Stefan Knecht, Fabijan Pavošević

Published Jul 2, 2024• 9 citations
Publisher

Abstract

Quantum chemistry simulations offer a cost-effective way to computationally design BODIPY photosensitizers. However, accurate predictions of excitation energies pose a challenge for time-dependent density functional theory and equation-of-motion coupled-cluster singles and doubles methods. By contrast, reliable predictions can be achieved by multireference quantum chemistry methods; unfortunately, their computational cost increases exponentially with the number of electrons. Alternatively, quantum computing holds potential for an exact simulation of the photophysical properties in a computationally more efficient way. Herein, we introduce the state-specific ΔUCCSD-VQE (unitary coupled-cluster singles and doubles-variational quantum eigensolver) and ΔADAPT-VQE methods in which the electronically excited state is calculated via a non-Aufbau configuration. We show for six BODIPY derivatives that the proposed methods predict accurate excitation energies that are in good agreement with those from experiments. Due to its performance and simplicity, we believe that ΔADAPT will become a useful approach for the simulation of BODIPY photosensitizers on near-term quantum devices.

DOI
10.1021/acs.jpclett.4c01301

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ΔΔΔADAPT-VQE: Toward Accurate Calculation of Excitation Energies on Quantum Computers for BODIPY Molecules With Application in Photodynamic Therapy
Quantum chemistry simulations offer a cost-effective way for computational design of BODIPY photosensitizers with potential use in photodynamic therapy (PDT). However, accurate predictions of photophysical properties, such as excitation energies, pose a challenge for the popular time-dependent density functional theory (TDDFT) and equation-of-motion coupled cluster with singles and doubles (EOM-CCSD) methods. By contrast, reliable descriptions can be achieved by multi-reference quantum chemistry methods, though unfortunately, their computational cost grows exponentially with the number of correlated electrons. Alternatively, quantum computing holds a great potential for exact simulation of photophysical properties in a computationally more efficient way. To this end, we introduce the state-specific ΔΔΔUCCSD-VQE (unitary coupled cluster with singles and doubles variational quantum eigensolver) and ΔΔΔADAPT-VQE methods in which the electronically excited state is calculated via a non-Aufbau electronic configuration. The accuracy and capability of the developed methods are assessed against experimentally determined excitation energies for six BODIPY-derivatives. We show that the proposed methods predict accurate vertical excitation energies that are not only in good agreement with experimental reference data but also outperform popular quantum chemistry methods, such as TDDFT and EOM-CCSD. Spurred by its impressive performance and simplicity, we are confident that ΔΔΔADAPT will emerge as the method of choice for guiding the rational design of photosensitizers for PDT and photocatalysis in the era of near-term quantum computing.
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. 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 also improves on previous ADAPT-VQE protocol in that it is designed to be independent on the choice of initial reference state. We perform classical numerical simulations for LiH and BeH2{\mathrm{BeH}}_{2}BeH2​ 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 gates than standard fixed unitary coupled-cluster ans\"atze, such as the UCCSD and the GUCCSD. We also show that the e-QEB-ADAPT-VQE is more successful in constructing ans\"atze for excited molecular states than other ADAPT-VQE protocols.
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Quantum chemistry calculations of large, strongly correlated systems are typically limited by the computation cost that scales exponentially with the size of the system. Quantum algorithms, designed specifically for quantum computers, can alleviate this, but the resources required are still too large for today's quantum devices. Here we present a quantum algorithm that combines a localization of multireference wave functions of chemical systems with quantum phase estimation (QPE) and variational unitary coupled cluster singles and doubles (UCCSD) to compute their ground state energy. Our algorithm, termed "local active space unitary coupled cluster" (LAS-UCC), scales linearly with system size for certain geometries, providing a polynomial reduction in the total number of gates compared with QPE, while providing accuracy above that of the variational quantum eigensolver using the UCCSD ansatz and also above that of the classical local active space self-consistent field. The accuracy of LAS-UCC is demonstrated by dissociating (H2_22​)2_22​ into two H2_22​ molecules and by breaking the two double bonds in trans-butadiene and resources estimates are provided for linear chains of up to 20 H2_22​ molecules.