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

By: Xiaoyu Song; Hung, W.N.N.; Guowu Yang; Perkowski, M.;

2005 / IEEE / 0-7695-2288-2

Description

This item was taken from the IEEE Conference ' Exact synthesis of 3-qubit quantum circuits from non-binary quantum gates using multiple-valued logic and group theory ' 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.