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

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 $A(\omega)$ and $A(k,\omega)$ and the neutral-sector dynamical structure factors $S(q,\omega)$ and $S^{zz}(q,\omega)$, each built classically in the Lehmann representation from its own subspace. The reconstruction matches exact diagonalization on Hubbard chains and, for $A(\omega)$, 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, $\mathcal{F}_1 = 4\,\mathrm{tr}[\gamma(1-\gamma)] = 2N_u$. 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 $\chi$ (Spearman $\rho = 0.90$). 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.

39 pages, 20 figures. Code and full reproduction repository: this https URL

Quantum Physics (quant-ph); Strongly Correlated Electrons (cond-mat.str-el)

arXiv:2608.16436 [quant-ph]

(or arXiv:2608.16436v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2608.16436 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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