A Novel Heuristic Method for Linear Nearest Neighbour Realization of Reversible Circuits

Abstract

With the advancement of technological footprints, high-end computation techniques, like quantum computation, have made significant progress in the design industry. Although quantum computation has proved itself as the next-generation computing paradigm, it is facing several design challenges, and one such design issue is in the form of the Nearest Neighbour (NN)t. This much-talked NN property demands the qubits in operating quantum gates to be adjacent, and a circuit should satisfy this NN property to be eligible for implementation. Considering the importance of NN enforcement in implementing circuits, we introduce a synthesis approach for the efficient transformation of reversible circuits to equivalent LNN representations. Our main focus in this work is to minimize the use of SWAP gates in designing NN-satisfied MCT-based reversible circuits. Towards transforming input circuits to LNN architecture, we have exploited a template matching scheme followed by two-qubit reordering policies, global and local, to improve the NN designs and reduce SWAP utilization. In finding the global solution, here we have used a dynamic programming algorithm where the initial order of qubit lines gets changed, while a heuristic-based SWAP placement function is used for finding a local qubit order sequence. The proposed synthesis workflow has been tested over an extensive set of benchmark functions, and comparison with the reported design approaches showed a substantial reduction in cost parameters.