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  "path": "/abs/2605.02845v1",
  "publishedAt": "2026-05-05T00:00:00.000Z",
  "site": "https://arxiv.org",
  "tags": [
    "Alex B. Grilo",
    "Marios Rozos"
  ],
  "textContent": "**Authors:** Alex B. Grilo, Marios Rozos\n\nDespite having an unnatural definition, $\\mathsf{StoqMA}$ plays a central role in Hamiltonian complexity, e.g., in the classification theorem of the complexity of Hamiltonians by Cubitt and Montanaro (SICOMP 2016). Moreover, it lies between the two randomized extensions of $\\mathsf{NP}$, $\\mathsf{MA}$ and $\\mathsf{AM}$. Therefore, understanding the exact power of $\\mathsf{StoqMA}$ (and hopefully collapsing it with more natural complexity classes) is of great interest for different reasons. In this work, we take a step further in understanding this complexity class by showing that the Stoquastic Sparse Hamiltonians problem ($\\mathsf{StoqSH}$) is in $\\mathsf{StoqMA}$. Since Stoquastic Local Hamiltonians are $\\mathsf{StoqMA}$-hard, this implies that $\\mathsf{StoqSH}$ is $\\mathsf{StoqMA}$-complete. We complement this result by showing that the separable version of $\\mathsf{StoqSH}$ is $\\mathsf{StoqMA}(2)$-complete, where $\\mathsf{StoqMA}(2)$ is the version of $\\mathsf{StoqMA}$ that receives two unentangled proofs.",
  "title": "The Complexity of Stoquastic Sparse Hamiltonians"
}