{
  "abstract": "Variational Quantum Algorithms (VQAs) rely heavily on classical optimization routines to navigate high-dimensional, noisy parameter landscapes. However, the evaluation of analytical gradients via the parameter-shift rule requires $\\mathcal{O}(p)$ circuit executions, rendering this approach computationally prohibitive for deep circuits. While simultaneous perturbation methods provide an $\\mathcal{O}(1)$ alternative, their gradient estimates suffer from severe $\\mathcal{O}(p)$ spatial variance, which impedes convergence. To resolve this tension, we introduce the Cached Recycled Variance-Reduced Gradient (CRVG) by leveraging variance reduction techniques. We formulate two variants: a 3-Circuit (1-Sided) Non-Recursive CRVG and a Recursive CRVG. By introducing a center-point caching mechanism, the 3-Circuit CRVG mathematically recycles quantum measurements to reduce the inner-loop circuit complexity by 25\\% across both variants. We establish a theoretical separation between the two routing paths to achieve an $ε^2$-stationary point: the non-recursive variant reaches a sample complexity of $\\mathcal{O}(\\max\\{p/ε^2, p^{2/3}/ε^{10/3}\\})$, while the recursive variant achieves an improved complexity of $\\mathcal{O}(\\max\\{p/ε^2, \\sqrt{p}/ε^3\\})$. Empirically, extensive evaluations on MaxCut and Maximum Independent Set (MIS) benchmarks validate these findings. While standard simultaneous perturbation remains a robust baseline across varying depths, CRVG demonstrates targeted advantages in specific amortizable regimes, such as the non-recursive variant on EfficientSU2 circuits and both variants on depth-three QAOA, yielding superior energy minimums and tighter output variances. Ultimately, CRVG establishes a principled bias-throughput trade-off for scaling near-term quantum optimization.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.38800",
  "author_total": 3,
  "authors": [
    {
      "name": "Lam M. Nguyen"
    },
    {
      "name": "Sumanta Mukherjee"
    },
    {
      "name": "Dzung T. Phan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cnpdc7mrbzx1q.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.38800",
  "fulltext_url": null,
  "id": "cnpdc7mrbzx1q",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.38800",
  "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",
      "math.OC"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7215106276",
  "pdf_url": "https://arxiv.org/pdf/2609.38800",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cnpdc7mrbzx1q.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:49Z",
      "native_id": "2609.38800",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.38800"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Breaking the Shot-Noise Barrier: Cached Recycled Variance-Reduced Gradients for Quantum Optimization",
  "title_text": "Breaking the Shot-Noise Barrier: Cached Recycled Variance-Reduced Gradients for Quantum Optimization",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:49Z",
  "url": "https://research.draconitic.com/paper/cnpdc7mrbzx1q",
  "venue": "arXiv",
  "versions": []
}