Fig. 22

a is a general method for calculating aP using the quantum circuit. b is the quantum circuit using windowed arithmetic to calculate aP, where m is the size of the window and \(T_i\) is \(2^m\) pre-calculated values. Here is just a simple schematic diagram of the window technique to show its principle. We omit the process of point operation and recovery of auxiliary qubits. For more specific circuits see Fig. 33