Q-SPARSE: Quantum Subspace Projection for Near-Field Angle-Range Spectrum Estimation
Abstract
Near-field wavefront curvature enables joint angle-range localization, but exploiting it entails repeated covariance-eigenspace tests over a two-dimensional spherical manifold. We propose a quantum subspace-projection algorithm (Q-SPARSE) for super-resolution estimation of parameters in the near field, employing spectral signature similar to MUSIC. Q-SPARSE prepares each spherical steering hypothesis as a quantum state, applies quantum phase estimation (QPE) to covariance-generated evolution, and converts the resolved spectral mass into a localization spectrum. The proposed method does not need the full classical preparation of the eigenstates, which is a major bottleneck of the QPE algorithm, the main subroutine in quantum variants of MUSIC algorithms. Under an ideal signal-noise partition, its score equals the classical signal-subspace overlap exactly and thus preserves the maximizer of normalized near-field MUSIC. For a finite q number of qubit phase registers, we derive the score from the complete QPE kernel, and propose a nearest-bin selection scheme with soft-thresholding based on Marchenko-Pastur-calibrated logistic weighting decision criteria. Numerical results on IBM's QISKIT software platform are demonstrated for near-field array processing.
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BibTeX
@misc{laskar2026qsparse,
title = {{Q-SPARSE: Quantum Subspace Projection for Near-Field Angle-Range Spectrum Estimation}},
author = {Mostafizur Rahaman Laskar and Sajad Daei and Gabor Fodor and Mikael Skoglund},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.38500},
eprint = {2609.38500},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.38500},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Q-SPARSE: Quantum Subspace Projection for Near-Field Angle-Range Spectrum Estimation
AU - Mostafizur Rahaman Laskar
AU - Sajad Daei
AU - Gabor Fodor
AU - Mikael Skoglund
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.38500
UR - https://arxiv.org/abs/2609.38500
AB - Near-field wavefront curvature enables joint angle-range localization, but exploiting it entails repeated covariance-eigenspace tests over a two-dimensional spherical manifold. We propose a quantum subspace-projection algorithm (Q-SPARSE) for super-resolution estimation of parameters in the near field, employing spectral signature similar to MUSIC. Q-SPARSE prepares each spherical steering hypothesis as a quantum state, applies quantum phase estimation (QPE) to covariance-generated evolution, and converts the resolved spectral mass into a localization spectrum. The proposed method does not need the full classical preparation of the eigenstates, which is a major bottleneck of the QPE algorithm, the main subroutine in quantum variants of MUSIC algorithms. Under an ideal signal-noise partition, its score equals the classical signal-subspace overlap exactly and thus preserves the maximizer of normalized near-field MUSIC. For a finite q number of qubit phase registers, we derive the score from the complete QPE kernel, and propose a nearest-bin selection scheme with soft-thresholding based on Marchenko-Pastur-calibrated logistic weighting decision criteria. Numerical results on IBM's QISKIT software platform are demonstrated for near-field array processing.
ER -