Dynamic Circuit QAOA Ansatz for Solving MaxCut

^{Quantum computers offer an alternative approach to solving large-scale combinatorial optimization problems. The Quantum Approximate Optimization Algorithm (QAOA) is a widely used method for these challenges, but it is known to encounter trainability issues due to the existence of barren plateaus. Recently, it has been shown that certain dynamic circuits, specifically circuits with mid-circuit measurements (MCMs), have the potential to circumvent these barren plateaus. Here, we introduce a dynamic circuit ansatz for QAOA, incorporating MCMs, which we term DC‑QAOA. We assess the performance of this non‑unitary formulation in the optimization process by applying it to max‑cut instances. In the shallow‑circuit regime (few layers), we investigate how the dynamic, non‑unitary nature of DC‑QAOA affects convergence speed and the probability of obtaining high‑quality solutions. In the deep‑circuit regime (many layers), we explore its potential for mitigating barren plateaus, a known shortcoming of QAOA in which trainability significantly degrades for deep circuits. To reduce training overhead, we analyze the properties of optimized parameters, particularly the feasibility of reusing parameters obtained from small instances when scaling to larger graphs. Finally, we compare DC‑QAOA with the standard, unitary QAOA, reporting results from both classical simulations and quantum hardware experiments.}