From Geminals to 2D-Block Pair Unitary Coupled Cluster: Going Quantum

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Abstract

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Like many traditional electronic structure methods, the recently proposed antisymmetrized product of 2D-block geminals (AP2D-BG) approach [1,2] faces exponential computational scaling with respect to the dimension of the one-electron, “spin-orbital”, Hilbert space, limiting its applicability on classical hardware. Adapting the method to quantum computers could eliminate these constraints without increasing computational overhead. However, the fundamental differences between classical and quantum architectures prevent a direct transfer. To address this, the method has been reformulated within a unitary coupled-cluster (UCC) framework. The new approach called the “2D-Block pair Unitary Coupled Cluster” (2DBpUCC) method, leverages localized orbital pairs and unitary transformations to reduce the complexity of quantum circuits while preserving accuracy. Compared with previously proposed UCC methods, it offers several advantages to harness the power of near-term quantum devices. In particular, we will show that Trotterization can be completely avoided [3].

[1] P. Cassam-Chena¨ı, Thomas Perez, Davide Accomasso, J. Chem. Phys 158, 074106 (2023).

[2] P. Cassam-Chena¨ı, L. Jourdan, J. Chem. Phys 163, 174111 (2025).

[3] L. Jourdan and P. Cassam-Chena¨ı, A Remarkable Application of Zassenhaus Formula to Quantum Physics and Chemistry, https://hal.science/hal-05220683, arXiv:2510.24364

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About the Speaker

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Patrick Cassam-Chenaï, Ph.D. is a Research Director at CNRS and Deputy Director of the Quantazur Institute at Université Côte d'Azur. A former student of the École Normale Supérieure, he holds a Ph.D. in Quantum Physics from the University of Paris (1992) and received the CNRS Bronze Medal in 1996. His research focuses on quantum chemistry methods and quantum computing applications, including the development of 2D-block geminal methods for NISQ devices. He serves on the editorial board of the Journal of Mathematical Chemistry, has supervised over 45 researchers at various levels, and contributes to the CONVIV, TONTO, and BDF quantum chemistry codes.