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QI: Fachverband Quanteninformation

QI 5: Quantum Computing and Algorithms II

QI 5.4: Vortrag

Dienstag, 10. März 2026, 10:15–10:30, BEY/0137

Quantum algorithm for one quasi-particle excitations in the thermodynamic limit via cluster-additive block-diagonalization — •Sumeet Sumeet, Max Hörmann, and Kai Phillip Schmidt — Department of Physics, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), 91058 Erlangen, Germany

We present a hybrid quantum-classical algorithm for computing one quasi-particle excitation energies in the thermodynamic limit by combining the variational quantum eigensolver (VQE) with numerical linked-cluster expansions (NLCEs) [1], extending our NLCE+VQE approach for ground states [2] to excitations. We minimize variance (or trace) cost functions with VQE to block-diagonalize the Hamiltonian, then extend to the thermodynamic limit with NLCE. The central challenge is ensuring cluster additivity for degenerate subspaces, essential for NLCE convergence. We address this by integrating the projective cluster-additive transformation (PCAT) with VQE: PCAT constructs the cluster-additive unitary from a polynomial number of measurements on the quantum device. Benchmarking on the transverse-field Ising model demonstrates NLCE convergence with circuit depth scaling linearly with system size. We analyze cost function robustness for models with broken symmetry. The PCAT post-processing framework applies to any quantum eigenstate preparation method, demonstrated via VQE and adiabatic sweeps on real quantum hardware. [1] Sumeet, M. Hörmann, and K. P. Schmidt, arXiv:2511.06623 (2025).
[2] Sumeet, M. Hörmann, and K. P. Schmidt, Phys. Rev. B 110, 155128 (2024).

Keywords: Variational Quantum Eigensolver (VQE); Numerical Linked Cluster Expansions (NLCE); Quasi-particle excitations; Quantum algorithms; Block-diagonalization