Optimizing VQE Ansatz for Studying Tight-Binding Models with \textit{sd}-Interaction and On-Site Coulomb Repulsion
Oleg Udalov
TL;DR
The paper addresses finding the ground state of a tight-binding lattice with on-site Coulomb repulsion $U_c$ and sd-interaction $J$ using VQE. It evaluates multiple ansatze, including cluster, generic, and YAB variants, and introduces a simplified, low-CX-depth approach based on repeating single-transition blocks to suit NISQ devices; it also analyzes the effect of initial guesses and classical optimizers. Key findings show that a single-transition-based ansatz repeated several times can achieve comparable accuracy to the full cluster ansatz while dramatically reducing two-qubit gate counts, and that noise primarily degrades energy estimates but often preserves high wavefunction fidelity. The results provide practical recommendations for hardware-aware VQE implementations on lattice models with interactions, illustrating how to balance circuit depth, optimization performance, and robustness to noise.
Abstract
The VQE algorithm is applied to the problem of finding the ground state of a lattice model with on-site Coulomb repulsion, nearest-neighbor hopping, and on-site sd-interaction. We compare the performance of several ansatze, including cluster and generic forms. Several modifications of the standard cluster ansatz implementation are proposed, which significantly reduce the number of two-qubit gates. Different classical optimizers are employed within the VQE algorithm. The performance of the algorithms is evaluated using both noiseless and noisy simulations.