  Quantum algorithms can be realized in the form of a quantum circuit. To map
quantum circuit for specific quantum algorithm to quantum hardware, qubit
mapping is an imperative technique based on the qubit topology. Due to the
neighbourhood constraint of qubit topology, the implementation of quantum
algorithm rightly, is essential for moving information around in a quantum
computer. Swapping of qubits using SWAP gate moves the quantum state between
two qubits and solves the neighbourhood constraint of qubit topology. Though,
one needs to decompose the SWAP gate into three CNOT gates to implement SWAP
gate efficiently, but unwillingly quantum cost with respect to gate count and
depth increases. In this paper, a new formalism of moving quantum states
without using SWAP operation is introduced for the first time to the best of
our knowledge. Moving quantum states through qubits have been attained with the
adoption of temporary intermediate qudit states. This introduction of
intermediate qudit states has exhibited a three times reduction in quantum cost
with respect to gate count and approximately two times reduction in respect to
circuit depth compared to the state-of-the-art approach of SWAP gate insertion.
Further, the proposed approach is generalized to any dimensional quantum
system.
