Using a Feedback-Based Quantum Algorithm to Analyze the Critical Properties of the ANNNI Model Without Classical Optimization

Abstract: We investigate the critical properties of the Anisotropic Next-Nearest-Neighbor Ising (ANNNI) model using a feedback-based quantum algorithm (FQA). We demonstrate how this algorithm enables the computation of both ground and excited states without relying on classical optimization methods. By exploiting symmetries in the algorithm initialization, we show how targeted initial states can increase convergence and facilitate the study of excited states. Using this approach, we study the quantum phase transitions with the Finite Size Scaling method, analyze correlation functions through spin correlations in the ground state, and examine magnetic structure by calculating structure factors via the Discrete Fourier Transform. Our findings highlight FQA's potential as a versatile tool for studying not only the ANNNI model but also other quantum systems, providing insights into quantum phase transitions and the magnetic properties of complex spin models.