A Kernel-Based Density of States Estimator for Quantum Computing

• URL: http://arxiv.org/abs/2607.24972v1
• Date: Mon, 27 Jul 2026 18:26:20 GMT
• Title: A Kernel-Based Density of States Estimator for Quantum Computing
• Abstract summary: We show that the simplest eigenvalue protocols for near-term quantum hardware can be used for reconstruction of density of states.<n>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.<n>We derive the estimator and its uncertainties, establish an explicit dictionary of window functions and quantum reconstruction kernels, and validate the method on the one-field Ising and spin-1 models.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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