Optimized quantum folding Barrett reduction for quantum modular multipliers

Jian Zhang, Seong-Min Cho, Changyeol Lee, Seung-Hyun Seo · 2025 · Scientific Reports

| 编号 QM010 | 主题 模运算与乘法 | 链接 DOI 10.1038/s41598-025-04987-1 |

摘要

摘要保留原文（英文）

摘要取自出版方页面元数据（OpenAlex inverted index 重建），未作翻译，以保证与原文一致。

Due to the reversibility constraints of quantum circuits, the development of modular operations in quantum modular multiplication has been significantly limited. In this work, we propose an optimized modular operation scheme based on Barrett reduction and implement quantum circuits for three versions of Barrett reduction, including our optimized approach. The proposed quantum modular operation circuit can be integrated with quantum-quantum and quantum-classical multiplication circuits. Additionally, we analyze the quantum resource requirements of the proposed circuit and compare the results across the three versions. Our optimized folding Barrett reduction scheme demonstrates superior performance. Furthermore, general quantum modular reduction relies on recursive subtractors and controlled adders to avoid division operation, resulting in a T-depth of approximately $O(2^n)$, where n is the bit length of the modulus. In contrast, our approach achieves a T-depth of only $O(n^2)$ by utilizing the Barrett reduction.

摘录说明

元数据中的两处 $O(2^n)$ / $O(n^2)$ 以公式占位符存放，此处按上下文还原为上标形式，未改变任何数值。

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