{
  "abstract": "The choice of mixer is a central design decision in the Quantum Approximate Optimization Algorithm (QAOA), yet different structural limitations of a mixer need not be captured by a single metric. We identify two complementary structural bottlenecks for shallow QAOA: configuration-space transport, which limits how strongly probability can concentrate on high-quality solutions, and finite-depth causal reach, which limits which parts of a problem instance can influence a local objective term. In Part I, we derive first-order mixer-dependent objective bounds in complementary small-$β$ and small-$γ$ regimes. For connected regular mixer graphs, the two leading-order expressions are exactly equivalent through a graph-Laplacian identity and reduce to the same cost-weighted Dirichlet energy. We then derive a non-perturbative upper envelope from the layer-wise $\\ell_1$ spreading of the mixer unitary, yielding a cost-distribution-dependent necessary spreading condition for attaining a target approximation ratio. In Part II, we study the locality bottleneck for MaxCut by augmenting the transverse-field mixer with problem-graph-aligned two-local interactions. The resulting $k$-hop construction has causal radius at most $(k+1)p$ at depth $p$; for the $k=1$ architectures studied numerically, this gives radius $2p$. Across cycles, circular ladders, and high-girth regular bipartite graphs, $X{+}XX$ and $X{+}YY$ improve the best-found approximation ratios over the standard $X$ mixer at equal depth, while $X{+}YY$ at depth $p$ comes within about one approximation-ratio point of plain $X$ at depth $2p$ in the reach-matched cases examined. The unequal performance of the equal-reach $XX$ and $YY$ augmentations shows that satisfying a structural capability does not by itself guarantee performance. Together, the results provide complementary structural insights for mixer design.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.40424",
  "author_total": 2,
  "authors": [
    {
      "name": "Jasjyot Singh Gulati"
    },
    {
      "name": "Tharrmashastha SAPV"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/34hmg2v898b5v.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.40424",
  "fulltext_url": null,
  "id": "34hmg2v898b5v",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.40424",
  "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",
      "quant-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.40424",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/34hmg2v898b5v.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:28Z",
      "native_id": "2610.40424",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.40424"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Structural Bottlenecks in QAOA Mixer Design: Transport and Causal Reach",
  "title_text": "Structural Bottlenecks in QAOA Mixer Design: Transport and Causal Reach",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:47Z",
  "url": "https://research.draconitic.com/paper/34hmg2v898b5v",
  "venue": "arXiv",
  "versions": []
}