QMDD: a decision diagram structure for reversible and quantum circuits. In this paper, we present a novel structure, QuantumMultiple- valued Decision Diagrams (QMDD), specifically designed to represent and manipulate the matrices encountered in the specification of reversible and quantum gates and circuits, both binary and multiple-valued. QMDD use many common decision diagram techniques, ideas introduced in QuIDDPro and novel techniques introduced here. Building the QMDD for the matrices for individual gates and the subsequent construction of the QMDD for the matrix describing a circuit are discussed. A prototype C implementation is described and experimental results are given that show the new structure is a promising and compact representation for reversible and quantum logic circuits.