Bonn 2025 – scientific programme

Parts | Days | Selection | Search | Updates | Downloads | Help

QI: Fachverband Quanteninformation

QI 16: Quantum Computing Theory III

QI 16.5: Talk

Tuesday, March 11, 2025, 15:00–15:15, HS IV

Hybrid Quantum-Classical Method for Excited-State Calculations — •Sumeet Sumeet, Max Hörmann, and Kai Phillip Schmidt — Chair for Theoretical Physics V, FAU Erlangen-Nürnberg, Germany

We present a comprehensive hybrid quantum-classical framework for calculating excited-state energies in the thermodynamic limit, integrating the variational quantum eigensolver (VQE) with numerical linked-cluster expansions (NLCE), a method we call NLCE+VQE [1]. This methodology introduces a cost function designed to minimize the off-diagonal elements of the Hamiltonian, decoupling subspaces of the Hamiltonian via a single unitary transformation, T, derived from the periodic-Hamiltonian variational ansatz.

The transformation T′ is subsequently reformulated into a manifestly local unitary operator, T, through a projective cluster-additive transformation[2], ensuring the preservation of cluster additivity. This localized quasi-particle representation is systematically extended to the entire lattice using NLCE.

We validate the proposed approach by benchmarking its performance against traditional NLCEs with exact diagonalization (ED) for several non-integrable one-dimensional spin models and the transverse-field Ising model (TFIM) on the square lattice. The results demonstrate the efficacy of the method in capturing excited-state physics.

[1] Sumeet, M. Hörmann, and K. P. Schmidt, Phys. Rev. B 110, 155128 (2024).

[2] M. Hörmann, K. P. Schmidt, SciPost Phys. 15, 097 (2023).

Keywords: Variational quantum eigensolver; Effective Hamiltonian; Numerical Linked cluster expansions; Excitations; Transverse field Ising model