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arXiv · 0710.4694

Exact Synthesis of 3-Qubit Quantum Circuits from Non-Binary Quantum Gates Using Multiple-Valued Logic and Group Theory

Guowu Yang·William N. N. Hung·Xiaoyu Song·Marek Perkowski
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Abstract

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 found all reversible circuits with quantum costs of 4, 5, 6, etc, and give another algorithm to realize these reversible circuits with quantum gates.

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Guowu Yang, William N. N. Hung, Xiaoyu Song, Marek Perkowski. 2007-10-25. Exact Synthesis of 3-Qubit Quantum Circuits from Non-Binary Quantum Gates Using Multiple-Valued Logic and Group Theory. https://arxiv.org/abs/0710.4694

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