A Kernel-Based Density of States Estimator for Quantum Computing

Abstract:The density of states (DoS) encodes the thermodynamic and spectral properties of quantum many-body systems, yet its reconstruction becomes intractable for Hilbert spaces too large to diagonalize. Classically, the kernel polynomial method (KPM) addresses this by combining stochastic trace estimation with a smoothing kernel. Here we show that the Rodeo algorithm---one of the simplest eigenvalue-location protocols for near-term quantum hardware---provides a direct quantum analogue of this approach. Averaging the Rodeo response over Haar-random input states yields the DoS convolved with a spectral kernel fixed entirely by the distribution of evolution times: the random states play the role of stochastic trace estimation, and the temporal sampling distribution that of the damping kernel. The construction requires only the standard single-ancilla circuit, and quantum typicality suppresses the statistical error as the Hilbert-space dimension grows. We derive the estimator and its uncertainties, establish an explicit dictionary between signal-processing window functions and quantum reconstruction kernels, and validate the method on the one-dimensional transverse-field Ising and spin-1 models.

Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech)

arXiv:2607.24972 [quant-ph]

(or arXiv:2607.24972v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2607.24972 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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