Line ordering of reversible circuits for linear nearest neighbor realization

Real quantum computing technologies have different restrictions and constraints which need to be considered during circuit synthesis. In certain technologies, only physically adjacent qubits can interact, which restricts their realizations to only linear nearest neighbor (LNN) architecture. In this work, we formulate the line ordering problem in LNN architecture as task assignment problem to find a mapping (permutation) between task graph and processor graph with minimum cost. We propose two different approaches, a greedy heuristic and a meta-heuristic algorithm based on Harmony Search to solve the task assignment problem. Experimental results show that our algorithms were able to reduce the quantum cost of benchmark circuits by approximately 30 % on average. Moreover, the proposed algorithms were compared to one recently proposed ordering algorithm and were found to further improve the cost by approximately 16 %.