Mappings between Arithmetic Expressions and Quantum Logic Trees

There are two fundamental paradigms for processing digital objects using algorithms: numeric processing , which uses arithmetic functions, and the symbolic approach, which uses logic. Although arithmetic functions are very powerful, they are usually difficult for humans to interpret and control. In many cases, the opposite is true of the logic approach. If we could bridge the gap between these two paradigms, we could benefit from both. This work attempts to establish such a bridge. On the numerical side, we restrict ourselves to positive interaction functions, and on the logic side, we exploit the laws of Boolean algebra resulting from commuting quantum logic. Our method computes minterm coefficients from the coefficients of a positive interaction function. We have developed several algorithms for converting real-valued minterm coefficients into binary ones. These binary minterm coefficients express a logic expression, which we present as a compact logic tree.