{
  "abstract": "Predicting how molecular weight distribution and monomer sequence evolve during polymerization is central to polymer science, yet classical approaches face a trade-off between molecular resolution and computational cost: for copolymers, the number of distinguishable species grows exponentially with chain length. Quantum computing offers a potential alternative, provided the non-unitary rate matrices governing the kinetics can be embedded into unitary quantum circuits, a task known as block encoding. Here we construct explicit block-encoding circuits for two kinetic models of living polymerization: Model A, single-monomer polymerization, whose lower-bidiagonal rate matrix is encoded via a sparse-oracle construction and a two-term linear combination of unitaries (LCU) decomposition; and Model B, two-monomer copolymerization, where a bijective labeling of polymer species by an integer index (the m-index) yields a structured sparse matrix encoded via either a five-term LCU or a sparse-oracle construction. Numerical simulations with the sparse-oracle encodings reproduce the classical time evolution for reactivity ratios drawn from reported olefin copolymerization systems spanning near-random ($r_1 r_2 \\simeq 1$) and blocky ($r_1 r_2 > 1$) microstructures, and the LCU encodings are verified by explicit reconstruction of the encoded matrix block. Resource estimation shows that both implementations require only $O(\\log N)$ qubits in the matrix dimension $N$ (an exponential memory saving over the classical state space), with gate counts growing gradually, reaching $10^4$ to $10^5$ gates at $10^3$ system qubits. These results establish a concrete quantum circuit foundation for simulating polymerization kinetics on fault-tolerant quantum hardware, and a first step toward exploiting exponential state-space compression for high-dimensional polymer reaction networks.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.08432",
  "author_total": 4,
  "authors": [
    {
      "name": "Yuhei Ikeda"
    },
    {
      "name": "Hokuto Iwakiri"
    },
    {
      "name": "Soichiro Nishio"
    },
    {
      "name": "Kentaro Matsumoto"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/12mzt0cb69g7s.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.08432",
  "fulltext_url": null,
  "id": "12mzt0cb69g7s",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.08432",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "physics.chem-ph"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7212038622",
  "pdf_url": "https://arxiv.org/pdf/2609.08432",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/12mzt0cb69g7s.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:49Z",
      "native_id": "2609.08432",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.08432"
    }
  ],
  "subjects": [
    {
      "field": "chemistry",
      "origin": "arxiv:physics.chem-ph",
      "subfield": "physical"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Explicit block encodings of rate matrices for simulating polymerization kinetics on quantum computers",
  "title_text": "Explicit block encodings of rate matrices for simulating polymerization kinetics on quantum computers",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:49Z",
  "url": "https://research.draconitic.com/paper/12mzt0cb69g7s",
  "venue": "arXiv",
  "versions": []
}