An open problem in the area of combinatorial representation theory is to find a satisfactory combinatorial formula for the Kronecker (or inner tensor) product of two Schur functions. I will show some different types of formulas for Kronecker products arising in a problem related to calculating the interference of quantum bits. The subproblem is the calculation of the Kronecker product by the Schur function indexed by the partition (d,d) which corresponds through the Frobenius map to an S_{2d} representation with a Catalan number dimension. I will examine some different techniques that we have used to calculate Kronecker products and indicate some results and conjectures that seem very promising. This talk will include joint work with various researchers including (but perhaps not limited to) A. Bergeron-Brlek, A. Brown, A. Garsia, N. Wallach, S. van Willigenburg, and G. Xin.