An extended XQDD representation for multiple-valued quantum logic

X-decomposition Quantum Decision Diagram (XQDD) can represent a quantum operation and perform matrix operations. It can be used to verify quantum and reversible circuits even if the reversible circuits have different number of garbage qubits. It is efficient in terms of space and time. In this paper, we extend the original XQDD to multiple-valued quantum logic. The extended XQDD can represent a multiple-valued quantum operation and perform matrix operations. It can be used to check the equivalence of two multiple-valued quantum or reversible circuits which are synthesized by different approaches. In this paper, we show that the space in multiple-valued XQDD is less than other representations and it is much better than multiple-valued QuIDD and very close to QMDD in terms of time.