  We present a novel quantum algorithm for approximating the ground-state in
quantum many-body systems, particularly suited for Noisy Intermediate-Scale
Quantum (NISQ) devices. Our approach integrates Variational Quantum
Eigensolvers (VQE) with Quantum Gaussian Filters (QGF), utilizing an iterative
methodology that discretizes the application of the QGF operator into small,
optimized steps through VQE. Demonstrated on the Transverse Field Ising models,
our method shows improved convergence speed and accuracy, particularly under
noisy conditions, compared to conventional VQE methods. This advancement
highlights the potential of our algorithm in effectively addressing complex
quantum simulations, marking a significant stride in quantum computing
applications within the NISQ era.
