On finding optimal quantum query algorithms using numerical optimization

In this work we examine how numerical optimization can be used to create optimal quantum query algorithms [1]. For this purpose we created a program in Mathematica 5.2 which constructs a general quantum query algorithm and then finds optimal values of parameters using numerical optimization. We applied our program to all 3 and 4 argument Boolean functions. To decrease the amount of computation (there are 2 N N -argument functions, see Table 1) we introduced the notion of symmetric functions.