Learning Parameterized Quantum Circuits with Quantum Gradient

Abstract: 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 that leverages quantum gradient to enhance PQC learning for polynomial-type cost functions. Our approach utilizes quantum algorithms to identify and overcome a type of gradient vanishing-a persistent challenge in PQC learning-by effectively navigating the optimization landscape. We also mitigate potential barren plateaus of our model and manage the learning cost via restricting the optimization region. Numerically, we demonstrate the feasibility of the approach on two tasks: the Max-Cut problem and polynomial optimization. The method excels in generating circuits without gradient vanishing and effectively optimizes 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.