Analysis of Variable Reordering on the QMDD Representation of Quantum Circuits

In previous research, a novel structure was discussed for representing the matrices that can be built from an n-variable r-valued reversible/quantum circuit. This structure, called a QMDD, takes on a form similar to that of a reduced-ordered-binary-decision-diagram (ROBDD). It is known that the order of variables used for developing an ROBDD from a binary logic circuit is relevant to the size and structure of that ROBDD. This paper determines what effect, if any, variable order has on the QMDD structure and proposes a simple heuristic for choosing a ´good´ variable order.