https://doi.org/10.1140/epjp/s13360-025-06858-0
Regular Article
Quantum annealing eigensolver as a NISQ era tool for probing strong correlation effects in quantum chemistry
1
Centre for Quantum Engineering, Research and Education, TCG CREST, 700091, Kolkata, India
2
Department of Physics, IIT Tirupati, 517619, Chindepalle, Andhra Pradesh, India
3
Graduate School of Science and Technology, Keio University, 7-1 Shinkawasaki, Saiwai-ku, 212-0032, Kawasaki, Kanagawa, Japan
4
Quantum Computing Center, Keio University, 3-14-1 Hiyoshi,
Kohoku-ku, 223-8522, Yokohama, Kanagawa, Japan
5
Keio University Sustainable Quantum Artificial Intelligence Center (KSQAIC), Keio University, 2-15-45 Mita, 108-8345, Minato-ku, Tokyo, Japan
6
Qilimanjaro Quantum Tech, Carrer de Veneçuela 74, 08019, Barcelona, Spain
7
Departament de Física Quàntica i Astrofísica, Facultat de Física, Universitat de Barcelona, 08028, Barcelona, Spain
8
Institut de Ciències del Cosmos, Universitat de Barcelona, ICCUB, Martí i Franquès 1, 08028, Barcelona, Spain
9
Universitat Politècnica de Catalunya, Carrer de Jordi Girona, 3, 08034, Barcelona, Spain
10
Barcelona Supercomputing Center, Pl. Eusebi Güell 1, 08032, Barcelona, Spain
11
Academy of Scientific and Innovative Research (AcSIR), 201002, Ghaziabad, India
Received:
9
June
2025
Accepted:
15
September
2025
Published online:
29
September
2025
The quantum–classical hybrid variational quantum eigensolver (VQE) algorithm is arguably the most popular noisy intermediate-scale quantum (NISQ) era approach to quantum chemistry. We consider the underexplored quantum annealing eigensolver (QAE) algorithm as a worthy alternative. We use a combination of numerical calculations for a system where strong correlation effects dominate, and conclusions drawn from our preliminary scaling analysis for QAE and VQE to make the case for QAE as a NISQ era contender to VQE for quantum chemistry. For the former, we pick the representative example of computing avoided crossings in the H
molecule in a rectangular geometry and demonstrate that we obtain results to within about 1.2% of the full configuration interaction value on the D-Wave Advantage system 4.1 hardware. We carry out analyses on the effect of the number of shots, anneal time, and the choice of Lagrange multiplier on our obtained results. Following our numerical results, we carry out a detailed yet preliminary analysis of the scaling behaviours of both the QAE and the VQE algorithms. We analyse the non-recurring and recurring costs involved in both the algorithms and arrive at their net scaling behaviours.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
