{
  "abstract": "Quantum comparators decide the order of two operands. They rely on reversible logic acting on basis-encoded integers, so their width grows with the precision. We introduce the Quantum Phase-based Comparator (QPC), which compares two values carried in relative phases instead. The circuit places the two phases, entered with opposite signs, between a pair of Hadamard gates, and a fixed offset centers the interference, so that the probability of measuring zero falls below one half exactly when the first phase is the smaller. We give two implementations. With hard-coded values, the two values are written into the parameters of two phase gates, and the comparison costs one qubit and five gates. With the register-driven cascade, the values are drawn from two $t$-qubit registers through binary-weighted controlled-phase gates, at a cost of one qubit beyond the registers and depth linear in $t$; since the cascade induces each phase linearly from the register content, one circuit handles a superposition of operand pairs. The readout yields a biased coin rather than a definite bit, and we quantify the shots that a decision takes at a given phase separation. Scaling both phases by an integer widens the decision margin at no cost in width or depth, and an adaptive doubling schedule turns this amplification into a shot count logarithmic in the inverse separation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.25262",
  "author_total": 2,
  "authors": [
    {
      "name": "Alessandro Berti"
    },
    {
      "name": "Alessandro Poggiali"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6tszp8xn7b65n.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.25262",
  "fulltext_url": null,
  "id": "6tszp8xn7b65n",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.25262",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "quant-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.25262",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6tszp8xn7b65n.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:39Z",
      "native_id": "2609.25262",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.25262"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "A Quantum Phase-based Comparator",
  "title_text": "A Quantum Phase-based Comparator",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:39Z",
  "url": "https://research.draconitic.com/paper/6tszp8xn7b65n",
  "venue": "arXiv",
  "versions": []
}