Practical block encodings of matrix polynomials that can also be trivially controlled
This work introduces block encoding techniques for matrix polynomials that are easily controlled in quantum circuits. The method uses a Fast One-Qubit Controlled Select Linear Combination of Unitaries (FOQCS-LCU) framework to reduce circuit depth scaling linearly with polynomial degree, independent of system size. It shows that controlling the entire encoding requires negligible overhead, significantly simplifying complex quantum operations.