{
  "abstract": "We study a Continuous-Variable Quantum Approximate Optimization Algorithm (CV-QAOA) for high-dimensional continuous optimization. Our formulation extends an earlier CV-QAOA proposal with a variationally optimized initial state and recovers the convergence guarantees of Quantum Hamiltonian Descent (QHD) in the high-depth limit. We prove rigorous performance guarantees of CV-QAOA on several families of cost functions. First, we show $d$-step CV-QAOA minimizes any $d$-dimensional strictly convex quadratic function with $2d$ quantum queries to the cost function. We then analyze a family of nonconvex \"Rotated Double Well\" (RDW) functions with $2^d$ local minima introduced by arXiv:2311.00811. While prior work showed QHD reaches its global minimum with $\\tilde O(d^3)$ queries, we prove that 1-step CV-QAOA solves RDW with just two quantum queries. Although general-purpose classical solvers need superpolynomial time for RDW and structure-awareness can reduce the cost to polynomial time, we show that the 1-step CV-QAOA protocol can be efficiently dequantized, and that a gradient-aligned line search succeeds with $O(d)$ queries, nearly matching the information-theoretic $Ω(d/\\log d)$ query lower bound. To move beyond the dequantizable regime, we introduce a ``Rotated Square Well'' (RSW) problem, whose globally flat landscape suppresses useful local gradient information. For this family, we show that an adiabatic evolution simulated by CV-QAOA can reach the global minimum using $d^{o(1)}$ queries. On the other hand, any classical algorithm that learn the hidden rotation in RSW provably requires $Ω(d^2/\\log d)$ queries, a bound we nearly match with an explicit $Θ(d^2\\log d)$-query classical algorithm.Numerical simulations on deflected corrugated spring and Easom functions illustrate the promising performance of CV-QAOA on more general problems.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.06815",
  "author_total": 3,
  "authors": [
    {
      "name": "Sriram Bharadwaj"
    },
    {
      "name": "Di Luo"
    },
    {
      "name": "Leo Zhou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5we5ar7n3k20z.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.06815",
  "fulltext_url": null,
  "id": "5we5ar7n3k20z",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.06815",
  "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",
      "cs.DS"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7220649021",
  "pdf_url": "https://arxiv.org/pdf/2610.06815",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5we5ar7n3k20z.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:05Z",
      "native_id": "2610.06815",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.06815"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "CV-QAOA: Efficient Low-Depth Quantum Optimization of Continuous Variables",
  "title_text": "CV-QAOA: Efficient Low-Depth Quantum Optimization of Continuous Variables",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:05Z",
  "url": "https://research.draconitic.com/paper/5we5ar7n3k20z",
  "venue": "arXiv",
  "versions": []
}