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Lecture notes in computer science

Improved Decomposition of Multiple-Control Ternary Toffoli Gates Using Muthukrishnan-Stroud Quantum Gates

P. Mercy Nesa Rani, Abhoy Kole, Kamalika Datta, Indranil Sengupta

Published Jan 1, 2017• 5 citations
Publisher
DOI
10.1007/978-3-319-59936-6_16

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We present realization of ternary Toffoli gate and modified Fredkin gate for quantum computing on top of ion trap realizable Muthukrishnan-Stroud primitive gates. Our design methodology is based on first realizing the quantum circuits using generalized ternary gates and Feynman gates and then replacing them with their equivalent realization using Muthukrishnan-Stroud gates. Our realization of ternary Toffoli gate is more efficient than the previously published result and modified Fredkin gate is realized for the first time in literature using Muthukrishnan-Stroud gates.
The designs using ternary logic exploit its logarithmic reduction in the number of qudits compared with the binary circuits. In this paper, we propose quantum ternary multiplication gate. We term it as QTMG. Then we present the symbol and the realization of QTMG. Researchers will be able to use this gate as well as its symbol and realizations in their future studies. We also present a new realization of ternary Toffoli gate in specific state. Moreover, in this paper, we propose 1-qutrit multiplier circuit. The symbol and the realization of the proposed 1-qutrit multiplier circuit are also provided. Afterward, we proposed ternary partial products generation circuit (TPPG) and summation network circuit in order to design quantum ternary 2-qutrit multiplier circuit. Overall, the proposed design of QTMG in this paper is suggested for the first time. In addition, the proposed realization of ternary Toffoli gate, TPPG, summation network and 2-qutrit multiplier circuits are compared with the existing designs and the improvements are reported. The proposed gate and circuits are realized using macro-level ternary gates which are built on the top of the ion-trap realizable 1-qutrit gates and 2-qutrit Muthukrishnan–Stroud gates.