A state-averaged orbital-optimized hybrid quantum–classical algorithm for a democratic description of ground and excited states

Saad Yalouz*, Bruno Senjean, Jakob Günther, Francesco Buda, Thomas E. O'Brien, Lucas Visscher

*Corresponding author for this work

Research output: Contribution to JournalArticleAcademicpeer-review


In the noisy intermediate-scale quantum (NISQ) era, solving the electronic structure problem from chemistry is considered as the ‘killer application’ for near-term quantum devices. In spite of the success of variational hybrid quantum/classical algorithms in providing accurate energy profiles for small molecules, careful considerations are still required for the description of complicated features of potential energy surfaces. Because the current quantum resources are very limited, it is common to focus on a restricted part of the Hilbert space (determined by the set of active orbitals). While physically motivated, this approximation can severely impact the description of these complicated features. A perfect example is that of conical intersections (i.e. a singular point of degeneracy between electronic states), which are of primary importance to understand many prominent reactions. Designing active spaces so that the improved accuracy from a quantum computer is not rendered useless is key to finding useful applications of these promising devices within the field of chemistry. To answer this issue, we introduce a NISQ-friendly method called ‘state-averaged orbital-optimized variational quantum eigensolver’ which combines two algorithms: (1) a state-averaged orbital-optimizer, and (2) a state-averaged VQE. To demonstrate the success of the method, we classically simulate it on a minimal Schiff base model (namely the formaldimine molecule CH2NH) relevant also for the photoisomerization in rhodopsin—a crucial step in the process of vision mediated by the presence of a conical intersection. We show that merging both algorithms fulfil the necessary condition to describe the molecule’s conical intersection, i.e. the ability to treat degenerate (or quasi-degenerate) states on the same footing.

Original languageEnglish
Article number024004
Pages (from-to)1-20
Number of pages20
JournalQuantum Science and Technology
Issue number2
Early online date13 Jan 2021
Publication statusPublished - Apr 2021


SY and BS sincerely thank Benjamin Lasorne and Emmanuel Fromager for fruitful discussions. SY and BS acknowledge support from the Netherlands Organization for Scientific Research (NWO/OCW). BS acknowledges support from Shell Global Solutions BV.

FundersFunder number
Shell Global Solutions BV
Ministerie van Onderwijs, Cultuur en Wetenschap
Nederlandse Organisatie voor Wetenschappelijk Onderzoek


    • Conical intersection
    • Quantum chemistry
    • Quantum computing


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