A Remarkable Application of Zassenhaus Formula to Strongly Correlated Electron Systems

Louis Jourdan; Patrick Cassam-Chenaï

doi:10.22331/q-2026-04-08-2057

A Remarkable Application of Zassenhaus Formula to Strongly Correlated Electron Systems

Université Côte d'Azur, CNRS, LJAD, UMR 7351, 28 avenue Valrose, 06108 Nice, France

Published:	2026-04-08, volume 10, page 2057
Editor:	Changpeng Shao
Eprint:	arXiv:2510.24364v4
Doi:	https://doi.org/10.22331/q-2026-04-08-2057
Citation:	Quantum 10, 2057 (2026).

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Abstract

We show that the Zassenhaus decomposition for the exponential of the sum of two non-commuting operators, simplifies drastically when these operators satisfy a simple condition, called the no-mixed adjoint property. An important application to a Unitary Coupled Cluster method for strongly correlated electron systems is presented. This ansatz requires no Trotterization and is exact on a quantum computer with a finite number of Givens gate equals to the number of free parameters. The formulas obtained in this work also shed light on why and when optimization after Trotterization gives exact solutions in disentangled forms of unitary coupled cluster.

Featured image: Givens gate circuits for LiH in a minimal basis set

Popular summary

We show that the Trotter-Suzuki approximation can be completely avoided thanks to the Zassenhaus formula in the 2D-Block pair Unitary Coupled Cluster” (2D-BpUCC) ansatz for Quantum Chemistry, so that the latter can be exactly prepared on a quantum computer.

The underlying mathematical property of this result has broad potential applications across a diverse spectrum of quantum algorithms, extending well beyond quantum chemistry.

► BibTeX data

@article{Jourdan2026remarkable,
  doi = {10.22331/q-2026-04-08-2057},
  url = {https://doi.org/10.22331/q-2026-04-08-2057},
  title = {A {R}emarkable {A}pplication of {Z}assenhaus {F}ormula to {S}trongly {C}orrelated {E}lectron {S}ystems},
  author = {Jourdan, Louis and Cassam-Chena{\"{i}}, Patrick},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {10},
  pages = {2057},
  month = apr,
  year = {2026}
}

► References

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