School of Computer Science and Engineering, University of Electronics Science and Technology of China; Department of Electrical Engineering, University of California at Los Angeles, USA

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Abstract—This paper investigates a universal approach of synthesizing arbitrary ternary logic circuits in quantum computation based on the truth table technology. It takes into account of the relationship of classical logic and quantum logic circuits. By adding inputs with constant value and garbage outputs, the classical non-reversible logic can be transformed into reversible logic. Combined with group theory, it provides an algorithm using the ternary Swap gate, ternary NOT gate and ternary Toffoli gate library. Simultaneously, the main result shows that the numbers of qutrits we use are minimal compared to other methods. We also illustrate with two examples to test our approach.

Index Terms—ternary quantum computation, reversible logic, circuit synthesis, group theory

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Cite: Xiaoyu Li, Guowu Yang, and Desheng Zheng, " Logic Synthesis of Ternary Quantum Circuits with Minimal Qutrits," Journal of Computers vol. 8, no. 8, pp. 1941-1946, 2013.