Berlin 2024 – scientific programme

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QI: Fachverband Quanteninformation

QI 27: Quantum Simulation II

QI 27.7: Talk

Thursday, March 21, 2024, 16:45–17:00, HFT-FT 101

Hybrid quantum-classical algorithm for ground state and excitations of the transverse-field Ising model in the thermodynamic limit — •Sumeet Sumeet, Max Hörmann, and Kai P. Schmidt — Department of Physics, Staudtstraße 7, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), 91058 Erlangen, Germany

We describe a hybrid quantum-classical approach to treat quantum many-body systems in the thermodynamic limit by combining numerical linked-cluster expansions (NLCE) with the variational quantum eigensolver (VQE). Here, the VQE algorithm is used as a cluster solver within the NLCE. We test our hybrid quantum-classical algorithm (NLCE+VQE) for the ferromagnetic transverse-field Ising model (TFIM) on the one-dimensional chain and the two-dimensional square lattice [1]. The calculation of ground-state energies on each open cluster demands a modified Hamiltonian variational ansatz for the VQE. One major finding is convergence of NLCE+VQE to the conventional NLCE result in the thermodynamic limit when at least N/2 layers are used in the VQE ansatz for each cluster with N sites. We further extend this approach for calculation of excited states for the TFIM. We further extend NLCE+VQE to determine the one quasi-particle dispersion and energy gap of the TFIM in the polarized phase. To this end we determine we developed a new variational cost function based on the projective cluster-additive transformation [2].
[1] Sumeet, M. Hörmann, K.P. Schmidt, arXiv:2310.07600
[2] M. Hörmann and K.P. Schmidt. SciPost Phys., 15:097, 2023.

Keywords: Variational quantum eigensolver; Numerical linked cluster expansions; Transverse field Ising model; Ground state and excited states; Hamiltonian variational ansatz