A linear-size quantum circuit for addition with no ancillary qubits

Yasuhiro Takahashi, Noboru Kunihiro · 2005 · Quantum Inf. Comput. 5(6-2):440-448

| 编号 QA005 | 主题 加法与减法 | 链接 出版页（研究底稿未定位到 arXiv 记录） |

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。 We construct a quantum circuit for addition of two $n$-bit binary numbers that uses no ancillary qubits. The circuit is based on the ripple-carry approach. The depth and size of the circuit are $O(n)$. This is an affirmative answer to the question of Kutin \cite{Kutin} as to whether a linear-depth quantum circuit for addition can be constructed without ancillary qubits using the ripple-carry approach. We also construct quantum circuits for addition modulo $2^n$, subtraction, and comparison that use no ancillary qubits by modifying the circuit for addition.

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