Dynamical spectral functions from bitstring-sampled quantum subspaces: entanglement, not one-body magic, tracks the sampling cost

• URL: http://arxiv.org/abs/2608.16436v2
• Date: Sat, 22 Aug 2026 18:12:46 GMT
• Title: Dynamical spectral functions from bitstring-sampled quantum subspaces: entanglement, not one-body magic, tracks the sampling cost
• Abstract summary: We use a bitstring-sampling primitive to reconstruct quantum subspaces.<n>The reconstruction matches exact diagonalization on Hubbard chains and, for $A()$, across nineteen molecules.<n>We prove moment exactness and a sampling bound in $|mathcalS|$, independent of Hilbert-space dimension.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Sample-based quantum diagonalization (SQD) and quantum-selected configuration interaction (QSCI) are the electronic-structure methods with most hardware traction, yet their canonical target -- the ground-state energy -- is where classical methods have caught up. We move the target to dynamics and the resource question. From one bitstring-sampling primitive -- computational-basis measurements of a shallow real-time circuit, with no Hadamard or controlled unitaries -- we reconstruct, from sampled subspaces, the single-particle spectral functions $A(ω)$ and $A(k,ω)$ and the neutral-sector dynamical structure factors $S(q,ω)$ and $S^{zz}(q,ω)$, each built classically in the Lehmann representation from its own subspace. The reconstruction matches exact diagonalization on Hubbard chains and, for $A(ω)$, across nineteen molecules (FCI-verified to $<10^{-5}$ Ha), and runs on the IBM Heron processor. Second, we ask which resource controls the cost -- the determinant support $|\mathcal{S}|$ the sampler must populate. On number-conserving states the fermionic AntiFlatness collapses to one 1-RDM invariant, $\mathcal{F}_1 = 4\,\mathrm{tr}[γ(1-γ)] = 2N_u$. An orbital-rotation (Gaussian) invariant while $|\mathcal{S}|$ is basis dependent, $\mathcal{F}_1$ is provably decoupled from the cost; the cost is instead lower-bounded and tracked by the entanglement -- the minimal bond dimension $χ$ (Spearman $ρ= 0.90$). One-body magic is thus a faithful multireference diagnostic but an unreliable cost predictor; any genuine advantage lives in the non-Gaussianity of the higher-body cumulants. We prove moment exactness and a sampling bound polynomial in $|\mathcal{S}|$, independent of Hilbert-space dimension. Self-consistent configuration recovery improves the subspace under device noise, while a learned generative model does not beat that classical baseline.

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