Chiara Capecci - Università di Trento

Non-stabilizerness in Quantum Optimization: From QAOA to Non-Stoquastic Annealing

Quantum optimization algorithms are promising candidates for solving hard classical optimization problems on quantum devices. However, the role played by genuinely quantum resources in their performance is still not fully understood. Here, we investigate the emergence and behavior of quantum resources in both variational and adiabatic optimization protocols. We first analyze the Quantum Approximate Optimization Algorithm (QAOA) applied to spin-glass models, including the Sherrington--Kirkpatrick model and long-range Ising systems. We show that the QAOA dynamics is characterized by a non-monotonic growth of non-stabilizerness, leading to the formation of a transient 'magic barrier'. Remarkably, non-stabilizerness curves corresponding to different circuit depths and system sizes collapse under a suitable rescaling. A similar barrier is observed in standard quantum annealing protocols, suggesting that this phenomenon is a generic feature of quantum optimization dynamics. We then extend the analysis to non-stoquastic quantum annealing, where catalyst Hamiltonians modify the annealing path and can improve algorithmic performance. Focusing on paradigmatic models such as the ferromagnetic p-spin model and local Ising systems, we find that regions associated with improved annealing performance are accompanied by enhanced non-stabilizerness and entanglement generation. These results indicate a close connection between the buildup of quantum resources and the behavior of quantum optimization protocols across different paradigms.