Quantum circuit simulation has taken a significant step forward with the introduction of a backpropagation algorithm that leverages Pauli propagation. This method enables the efficient evaluation of parameter gradients, boasting a computational complexity on par with standard sparse Pauli simulation techniques. The resulting gradients exhibit accuracy comparable to observable expectation values, making this approach particularly useful for optimizing quantum circuits. By harnessing the reversibility of quantum circuits, the algorithm achieves this feat without incurring substantial computational overhead. The development of such techniques is crucial for advancing quantum computing capabilities, which in turn, challenges traditional cryptography and computation assumptions1. This breakthrough matters to practitioners because it paves the way for more sophisticated quantum circuit optimization, ultimately driving progress in the field of quantum computing.