Learning parameterized quantum circuits with quantum gradient

Parameterized quantum circuits (PQCs) are crucial for quantum machine learning and circuit synthesis, enabling the practical implementation of complex quantum tasks. However, PQC learning has been largely confined to classical optimization methods, which suffer from issues like gradient vanishing. In this work, we introduce a nested optimization model, a hybrid approach that leverages quantum gradients to improve PQC learning for arbitrary polynomial-type cost functions. The proposed approach decomposes the learning problem into multiple subproblems, each aimed at learning the state identified by the quantum gradient using current circuit synthesis methods. Leveraging quantum gradients, our method detects unfavorable local stationary points via an adaptive indicator and resolves them with a guided state. Meanwhile, its warm-started, layer-wise expansion reduces susceptibility to barren-plateau. Numerically, we demonstrate the feasibility of the approach on two tasks: the Max-Cut problem and polynomial optimization. Furthermore, we benchmark against standard fixed and adaptive baselines under matched settings on unfavorable local stationary points prone instances together with reduced BP sensitivity. From the perspective of quantum algorithms, our model improves quantum optimization for polynomial-type cost functions, addressing the challenge of exponential sample complexity growth.