Quantum annealing (QA) is a method that introduces quantum fluctuations into the simulated annealing (SA) process to achieve faster convergence to the optimal state. The transverse Ising model is used to test this approach, where the transverse field acts similarly to temperature in SA. The goal is to find the ground state of the Hamiltonian with high accuracy. Numerical solutions of the time-dependent Schrödinger equation for small systems show that QA achieves higher probabilities of reaching the ground state compared to SA under the same conditions. The transverse field controls state transitions, similar to temperature in SA. The study compares QA and SA for various models, including ferromagnetic, frustrated, and random interaction systems. The results indicate that QA generally performs better in reaching the ground state. The single-spin case is analyzed, showing that QA can reach the ground state under specific schedules, though not always perfectly. The study concludes that QA can outperform SA in certain scenarios, though further research is needed for practical applications. The results highlight the potential of quantum effects in optimization problems.Quantum annealing (QA) is a method that introduces quantum fluctuations into the simulated annealing (SA) process to achieve faster convergence to the optimal state. The transverse Ising model is used to test this approach, where the transverse field acts similarly to temperature in SA. The goal is to find the ground state of the Hamiltonian with high accuracy. Numerical solutions of the time-dependent Schrödinger equation for small systems show that QA achieves higher probabilities of reaching the ground state compared to SA under the same conditions. The transverse field controls state transitions, similar to temperature in SA. The study compares QA and SA for various models, including ferromagnetic, frustrated, and random interaction systems. The results indicate that QA generally performs better in reaching the ground state. The single-spin case is analyzed, showing that QA can reach the ground state under specific schedules, though not always perfectly. The study concludes that QA can outperform SA in certain scenarios, though further research is needed for practical applications. The results highlight the potential of quantum effects in optimization problems.