Quantum computers are believed to solve a class of computational problems that are based on modular arithmetic faster than classical computers. Among the arithmetic building blocks, comparison of integer pairs is a primitive. Here we report its demonstration in the Reimei quantum computer at RIKEN, whose trapped-ion architecture provides all-to-all qubit connectivity together with high gate fidelities. We observe high success probabilities for bit widths n = 3, 5, 7, and 9: Under a conventional output-only success criterion we obtain 95% at n=9; under a stricter criterion additionally requiring the ancilla to be correct, the success is 69% at n=9. These results demonstrate reliable quantum comparison at scales far beyond those previously achieved experimentally, not only for comparators but also in the broader context of quantum arithmetic circuits.
@article{arxiv.2512.17779,
title = {Demonstration of a quantum comparator on an ion-trap quantum device},
author = {Tatsuhiko N. Ikeda and Riku Nakama and Shunsuke Saeki and Hiroki Kuwata and Shuhei M. Yoshida and Akira Shimizu and Sho Sugiura},
journal= {arXiv preprint arXiv:2512.17779},
year = {2025}
}