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Synthesis of quaternary quantum circuits using optimized gate realizations Thapliyal, Himanshu


Quaternary encoded binary circuits are more compact than their binary counterpart. Although quaternary reversible circuits are realizable, design of such circuits is still in its infancy. This work proposes a new, enhanced method of quaternary Galois field sum of products (QGFSOP) synthesis for quaternary quantum circuits. To achieve improved performance results, the algorithm makes use of 11 newly defined quaternary Galois field (QGF) expansions (for a total of 21 QGF expansions). This algorithm achieves QGFSOP minimization with the assistance of a pseudo-Kronecker Galois field decision diagram (QGFDD). This is a novel approach for QGFSOP synthesis. QGFSOP expressions are translated into quaternary quantum circuits by using newly developed quaternary quantum gate realizations optimized for quantum cost. Performance evaluation against existing works in the literature determined that are proposed method achieves an average QGFSOP expression product term savings of 32.66%. Toffoli gate realizations from the proposed gate library were found to achieve a minimum quantum cost savings of 39%. Other composite gate realizations either outperformed or matched existing realizations in terms of quantum cost.

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