Quantum adders: on the structural link between the ripple-carry and carry-lookahead techniques

Maxime Remaud · 2025 · arXiv

| 编号 QA010 | 主题 加法与减法 | 链接 arXiv:2510.00840 |

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。

This paper is motivated by two key observations. First, Toffoli ladders can be implemented in three distinct ways: with linear or polylogarithmic depth using no ancilla, or with logarithmic depth using ancilla qubits. Second, two fundamental structural approaches to designing addition algorithms can be identified in several well-known quantum adders. At their core is the Toffoli ladder, and both provide a clear and simple connection between ripple-carry and carry-lookahead adder designs. Combining these two structures with the three Toffoli ladder implementations yields six quantum adders: four are well-known and two novel. Notably, one of the novel designs is a carry-lookahead adder that outperforms previous approaches.

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