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.By leveraging quantum gradients, the optimization procedure is free of a specific type of gradient vanishing, such as unfavorable local stationary points and barren plateaus.Specifically, with the guidance of quantum gradient, unfavorable local stationary points can be overcome by increasing the depth of the ansatz, while barren plateaus can be mitigated by constraining the optimization region.Numerically, we demonstrate the feasibility of the approach on two tasks: the Max-Cut problem and polynomial optimization. Additionally, we analyze the overheads introduced by this approach, which are primarily polynomial in the number of qubits in the system and can be controlled by adjusting the learning rate.The method can generate circuits while avoiding gradient vanishing, thus effectively optimizing the cost function.From the perspective of quantum algorithms, our model improves quantum optimization for polynomial-type cost functions, addressing the challenge of exponential sample complexity growth.