Optimal Toffoli-Depth Quantum Adder

Siyi Wang, Suman Deb, Ankit Mondal, Anupam Chattopadhyay · 2024 · arXiv

| 编号 QA015 | 主题 加法与减法 | 链接 arXiv:2405.02523 |

摘要

摘要保留原文（英文）

摘要取自 arXiv / 出版方元数据，未作翻译，以保证与原文一致。

Efficient quantum arithmetic circuits are commonly found in numerous quantum algorithms of practical significance. Till date, the logarithmic-depth quantum adders includes a constant coefficient $k\ge 2$ while achieving the Toffoli-Depth of $k\log n+O(1)$. In this work, 160 alternative compositions of the carry-propagation structure are comprehensively explored to determine the optimal depth structure for a quantum adder. By extensively studying these structures, it is shown that an exact Toffoli-Depth of $\log n+O(1)$ is achievable. This presents a reduction of Toffoli-Depth by almost 50% compared to the best known quantum adder circuits presented till date. We demonstrate a further possible design by incorporating a different expansion of propagate and generate forms, as well as an extension of the modular framework. Our paper elaborates on these designs, supported by detailed theoretical analyses and simulation-based studies, firmly substantiating our claims of optimality. The results also mirror similar improvements, recently reported in classical adder circuit complexity.

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