Work

Ancilla-free optimal quantum adder

Year: 2026

Type: preprint

Abstract: We construct an exact $n$-bit quantum adder with $O(n)$ gates and $O(\log n)$ depth that requires no ancillary qubits. The circuit uses only $X$, CNOT, and Toffoli gates under all-to-all connectivity and is classically reversible. Our construction accelerates the controlled ladder underlying addition. Grouping the data into blocks and use existing control qubits as conditional workspace gives a recursive construction with $O(n\log\log n)$ gates and $O(\log n)$ depth. We then coordinate inter-block propagation via two short-path forest operations to cut the per-block workspace requirement, yielding a nonrecursive implementation with $O(n)$ gates. Both the gate count and circuit depth are asymptotically optimal.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.34446

Authors: Nie, Junhong, Tang, Jialiang, Sun, Xiaoming, Zi, Wei

Institutions: Shandong University, Chinese Academy of Sciences, Institute of Computing Technology, Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area, University of Chinese Academy of Sciences

Language: English

Topic: Quantum Computing Algorithms and Architecture

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funder: National Natural Science Foundation of China

OpenAlex ID: W7223805656

Cites: 1

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Related to: 10