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In order to achieve speedup over conventional classical computing for findingsolution of computationally hard problems, quantum computing was introduced.Quantum algorithms can be simulated in a pseudo quantum environment, butimplementation involves realization of quantum circuits through physicalsynthesis of quantum gates. This requires decomposition of complex quantumgates into a cascade of simple one qubit and two qubit gates. Themethodological framework for physical synthesis imposes a constraint regardingplacement of operands (qubits) and operators. If physical qubits can be placedon a grid, where each node of the grid represents a qubit then quantum gatescan only be operated on adjacent qubits, otherwise SWAP gates must be insertedto convert non-Linear Nearest Neighbor architecture to Linear Nearest Neighborarchitecture. Insertion of SWAP gates should be made optimal to reducecumulative cost of physical implementation. A schedule layout generation isrequired for placement and routing apriori to actual implementation. In thispaper, two algorithms are proposed to optimize the number of SWAP gates in anyarbitrary quantum circuit. The first algorithm is intended to start withgeneration of an interaction graph followed by finding the longest pathstarting from the node with maximum degree. The second algorithm optimizes thenumber of SWAP gates between any pair of non-neighbouring qubits. Our proposedapproach has a significant reduction in number of SWAP gates in 1D and 2D NTCarchitecture.

2D Qubit Placement of Quantum Circuits using LONGPATH