  Single qubit rotation gate and the controlled-NOT (CNOT) gate constitute a
complete set of gates for universal quantum computation. In general the CNOT
gate are only for two nearby qubits. For two qubits which are remote from each
other, we need a series of swap gates to transfer these two qubits to the
nearest neighboring sites, and then after the CNOT gate we should transfer them
to their original sites again. However, a series of swap gates are resource for
quantum information processing. One economy way which does not consume so much
resource is to implement CNOT gate remotely. The remote CNOT gate is to
implement the CNOT gate for two remotely separated qubits with the help of one
additional maximally entangled state. The original remote CNOT gate is for two
qubits, here we will present the d-dimensional remote CNOT gate. The role of
quantum teleportation is identified in the process of the remote CNOT gate.
