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QI: Fachverband Quanteninformation

QI 36: Poster – Quantum Information (joint session QI/Q)

QI 36.52: Poster

Donnerstag, 13. März 2025, 17:00–19:00, Tent

Cluster-additivity of perturbative discrete product of unitaries and applications to the variational quantum eigensolver — •Max Hörmann, Harald Leiser, Sumeet Sumeet, and Kai Phillip Schmidt — Chair for Theoretical Physics V, FAU Erlangen-Nürnberg, Germany

We explore the cluster-additivity properties of a perturbatively defined unitary transformation U= U₁ · … · U_n, where each successive order in perturbation theory introduces an additional unitary operator U_n [1]. We establish connections to continuous unitary transformations and compare this approach with globally defined transformations, such as the projective cluster-additive transformation [2]. Furthermore, we emphasize the striking parallels between this transformation and ansätze commonly employed in the variational quantum eigensolver algorithm. Building on this, we propose a variational extension of the transformation, expanding its applicability beyond the perturbative framework. Finally, we assess whether this transformation can effectively construct good initial guesses for larger systems by leveraging information from smaller subsystems.

[1] N. Datta, J. Fröhlich, L. Rey-Bellet and R. Fernández, Low-temperature phase diagrams of quantum lattice systems. II. Convergent perturbation expansions and stability in systems with infinite degeneracy, Helv. Phys. Acta 69(5-6), 752 (1996).

[2] M. Hörmann and K. P. Schmidt, Projective cluster-additive transformation for quantum lattice models, SciPost Phys. 15, 097 (2023).

Keywords: Cluster additivity; Continuous unitary transformations; Variational quantum eigensolver; Scalability; Perturbation theory