Moving Quantum States without SWAP via Intermediate Higher Dimensional Qudits

Abstract

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.