A Classical-Quantum Adder with Constant Workspace and Linear Gates

Craig Gidney · 2025 · arXiv

| 编号 QA034 | 主题 加法与减法 | 链接 arXiv:2507.23079 |

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。

In 2004, Cuccaro et al found a quantum-quantum adder with $O(n)$ gate cost and $O(1)$ ancilla qubits. Since then, it’s been an open question whether classical-quantum adders can achieve the same asymptotic complexity. These costs are particularly relevant to modular arithmetic circuits, which often offset by the classically known modulus.

In this paper, I construct an adder that uses 3 clean ancillae and $4n\pm O(1)$ Toffoli gates to add a classical offset into a quantum register. I also present an adder with a Toffoli cost of $3n\pm O(1)$ that uses 2 clean ancillae and $n-2$ dirty ancillae. I further show that applying the presented adders conditioned on a control qubit requires no additional workspace or Toffolis.

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