Robustness of Quantum Signal Processing and Resource-aware Polynomial Design
Abstract
Quantum signal processing (QSP) realizes operator functions through polynomial transformations of a finite degree. In addition to function approximation errors, realistic implementations incur algorithmic errors also when encoding the input operator and in synthesizing gates into a discrete fault-tolerant gate set. We provide an end-to-end analysis of these errors and show that the input error propagation is governed by the operator-Lipschitz constant L⋆ of the implemented function. We then derive an efficient classical algorithm to compute tight lower and upper bounds on L⋆, and we show that these bounds induce in turn lower and upper bounds on the total quantum-resource cost (for instance, T-gate count) needed for QSP implementations compatible with a target total error. We further devise a procedure to search for a polynomial with minimum cost based solely on its coefficients, yielding a resource-aware polynomial-design procedure for QSP. We illustrate the resulting method for ground state energy estimation via eigenvalue thresholding for the H6 molecular Hamiltonian. In the tested hardware profiles, the resource-aware family improves the total-error budget and reduces the modeled T-gate count by 51.9%--56.7% relative to the standard analytical polynomial obtained from an error-function approximation.
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BibTeX
@misc{maciel2026robustness,
title = {{Robustness of Quantum Signal Processing and Resource-aware Polynomial Design}},
author = {Thiago O. Maciel and Giancarlo Camilo and Allan Tosta and Daniel Stilck-França and Leandro Aolita and Thais de Lima Silva},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.03885},
eprint = {2610.03885},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.03885},
}
RIS
TY - UNPB
TI - Robustness of Quantum Signal Processing and Resource-aware Polynomial Design
AU - Thiago O. Maciel
AU - Giancarlo Camilo
AU - Allan Tosta
AU - Daniel Stilck-França
AU - Leandro Aolita
AU - Thais de Lima Silva
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2610.03885
UR - https://arxiv.org/abs/2610.03885
AB - Quantum signal processing (QSP) realizes operator functions through polynomial transformations of a finite degree. In addition to function approximation errors, realistic implementations incur algorithmic errors also when encoding the input operator and in synthesizing gates into a discrete fault-tolerant gate set. We provide an end-to-end analysis of these errors and show that the input error propagation is governed by the operator-Lipschitz constant L_⋆ of the implemented function. We then derive an efficient classical algorithm to compute tight lower and upper bounds on L_⋆, and we show that these bounds induce in turn lower and upper bounds on the total quantum-resource cost (for instance, T-gate count) needed for QSP implementations compatible with a target total error. We further devise a procedure to search for a polynomial with minimum cost based solely on its coefficients, yielding a resource-aware polynomial-design procedure for QSP. We illustrate the resulting method for ground state energy estimation via eigenvalue thresholding for the H_6 molecular Hamiltonian. In the tested hardware profiles, the resource-aware family improves the total-error budget and reduces the modeled T-gate count by 51.9%--56.7% relative to the standard analytical polynomial obtained from an error-function approximation.
ER -