← 研踪 PaperTrailarXiv:2611.08180 · v1
Quantum Advantage with Sign-Free Proofs: An Oracle Separation between $\mathsf{StoqMA}$ and $\mathsf{MA}$
首次提交 2026-11-05 23:34
版本更新 2026-11-05 23:34
雷达观测 2026-11-06 12:09
摘要
Several landmark oracle results (FOCS 2000, FOCS 2025, STOC 2026) establish strict separations along the chain $\mathsf{MA} \subseteq \mathsf{QCMA} \subseteq \mathsf{QMA}$, showing that quantum verification and quantum witnesses can each provide additional power over classical proof systems. These separations, however, use substantial coherent quantum computation, often through the quantum Fourier transform. We prove that a minimal quantum resource already suffices to outperform every classical verifier. Namely, we show the separation $$\mathsf{MA} \subsetneq \mathsf{StoqMA}$$ relative to a classical oracle. The class $\mathsf{StoqMA}$, introduced by Bravyi, Bessen, and Terhal (arXiv 2006), restricts the verifier to classical reversible computation, followed by a single Hadamard-basis measurement. Its power is closely tied to the complexity of stoquastic Hamiltonians, a sign-problem-free and seemingly more tractable class of quantum Hamiltonians. Our separating problem is to determine whether a sparse high-girth graph, given via an adjacency-list oracle, has a large or small Perron--Frobenius eigenvalue. This amounts to a ground-energy estimation task for a related stoquastic Hamiltonian. Our construction builds on a line of work on graph exploration problems with exponential quantum speedups, from welded trees (STOC 2003) to recent constructions (STOC 2021, arXiv 2026).
作者备注：21 pages, 3 figures
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v1 · 2026-11-05 23:34 · 最新观测版本
Quantum Advantage with Sign-Free Proofs: An Oracle Separation between $\mathsf{StoqMA}$ and $\mathsf{MA}$
Several landmark oracle results (FOCS 2000, FOCS 2025, STOC 2026) establish strict separations along the chain $\mathsf{MA} \subseteq \mathsf{QCMA} \subseteq \mathsf{QMA}$, showing that quantum verification and quantum witnesses can each provide additional power over classical proof systems. These separations, however, use substantial coherent quantum computation, often through the quantum Fourier transform. We prove that a minimal quantum resource already suffices to outperform every classical verifier. Namely, we show the separation $$\mathsf{MA} \subsetneq \mathsf{StoqMA}$$ relative to a classical oracle. The class $\mathsf{StoqMA}$, introduced by Bravyi, Bessen, and Terhal (arXiv 2006), restricts the verifier to classical reversible computation, followed by a single Hadamard-basis measurement. Its power is closely tied to the complexity of stoquastic Hamiltonians, a sign-problem-free and seemingly more tractable class of quantum Hamiltonians. Our separating problem is to determine whether a sparse high-girth graph, given via an adjacency-list oracle, has a large or small Perron--Frobenius eigenvalue. This amounts to a ground-energy estimation task for a related stoquastic Hamiltonian. Our construction builds on a line of work on graph exploration problems with exponential quantum speedups, from welded trees (STOC 2003) to recent constructions (STOC 2021, arXiv 2026).
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