Computing the gradients with respect to all parameters of a quantum neural network using a single circuit

Finding gradients is a crucial step in training machine learning models. For quantum neural networks, computing gradients using the parameter-shift rule requires evaluating the cost function twice for each adjustable parameter in the network. When the total number of parameters is large, the quantum circuit must be repeatedly adjusted and executed, leading to significant computational overhead. In this work, we propose a novel approach that computes all gradients using only a single circuit, significantly reducing both the circuit depth and the number of classical registers required. We experimentally validate our approach on both quantum simulators and IBM's real quantum hardware, demonstrating that our method significantly reduces circuit compilation time compared to the conventional approach, resulting in a substantial speedup in total runtime.