Clifford+V synthesis for multi-qubit unitary gates

• URL: http://arxiv.org/abs/2510.08312v1
• Date: Thu, 09 Oct 2025 14:57:55 GMT
• Title: Clifford+V synthesis for multi-qubit unitary gates
• Authors: Soichiro Yamazaki, Seiseki Akibue,
• Abstract summary: We develop a general framework for synthesizing target gates by using a finite set of basic gates.<n>We introduce a suboptimal but short run-time algorithm for synthesizing multi-qubit controlled gates.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: We developed a general framework for synthesizing target gates by using a finite set of basic gates, which is a crucial step in quantum compilation. When approximating a gate in SU($n$), a naive brute-force search requires a computational complexity of $O(1/\varepsilon^{(n^2 - 1)})$ to achieve an approximation with error $\varepsilon$. In contrast, by using our method, the complexity can be reduced to $O(-n^2 \log\varepsilon/\varepsilon^{((n^2 - 1)/2)})$. This method requires almost no assumptions and can be applied to a variety of gate sets, including Clifford+$T$ and Clifford+$V$. Further, we introduce a suboptimal but short run-time algorithm for synthesizing multi-qubit controlled gates. This approach highlights the role of subgroup structures in reducing synthesis complexity and opens a new direction of study on the compilation of multi-qubit gates. The framework is broadly applicable to different universal gate sets, and our analysis suggests that it can serve as a foundation for resource-efficient quantum compilation in near-term architectures.

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