Realizing Ternary Quantum Switching Networks without Ancilla Bits

Details Realizing Ternary Quantum Switching Networks without Ancilla Bits Realizing Ternary Quantum Switching Networks without Ancilla Bits

2005-09-27

arxiv.org/abs/quant-ph/0509192v1

Physics

Quantum Physics

10 pages, Latex. in press, J. Phys. A: Math. Gen. (2005)

Scientific paper

10.1088/0305-4470/38/44/006

This paper investigates the synthesis of quantum networks built to realize ternary switching circuits in the absence of ancilla bits. The results we established are twofold. The first shows that ternary Swap, ternary Not and ternary Toffoli gates are universal for the realization of arbitrary $n\times n$ ternary quantum switching networks without ancilla bits. The second result proves that all $n\times n$ quantum ternary networks can be generated by Not, Controlled-Not, Multiply-Two, and Toffoli gates. Our approach is constructive. key words: ternary quantum logic synthesis, quantum circuit optimization, group theory.

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