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Exact synthesis of 3-qubit quantum circuits from non-binary quantum gates using multiple-valued logic and group theory

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4 Author(s)
Guowu Yang ; Dept. of Electr. & Comput. Eng., Portland State Univ., OR, USA ; Hung, W.N.N. ; Xiaoyu Song ; Perkowski, M.

We propose an approach to optimally synthesize quantum circuits from non-permutative quantum gates such as controlled-square-root-of-not (i.e., controlled-V). Our approach reduces the synthesis problem to multiple-valued optimization and uses group theory. We devise a novel technique that transforms the quantum logic synthesis problem from a multi-valued constrained optimization problem to a group permutation problem. The transformation enables us to utilize group theory to exploit the properties of the synthesis problem. Assuming a cost of one for each two-qubit gate, we find all reversible circuits with quantum costs of 4, 5, 6, etc, and give another algorithm to realize these reversible circuits with quantum gates.

Published in:

Design, Automation and Test in Europe, 2005. Proceedings

Date of Conference:

7-11 March 2005