Quantum signal processing angles admit closed-form expressions via orthogonal polynomial theory, allowing O(log(1/ε)) gate block-encodings of smooth functions through Hermite expansions and full characterization of SU(1,1)-QSP polynomials by roots.
On multivariate polynomials achievable with quantum signal processing.Quantum, 9:1641
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Quantum algorithms for element-wise polynomial matrix transforms achieve exponential space reduction in polynomial degree with corrections to prior constructions.
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Analytical Angle-Finding and Series Expansions for Quantum Signal Processing via Orthogonal Polynomial Theory
Quantum signal processing angles admit closed-form expressions via orthogonal polynomial theory, allowing O(log(1/ε)) gate block-encodings of smooth functions through Hermite expansions and full characterization of SU(1,1)-QSP polynomials by roots.
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Quantum element-wise transforms
Quantum algorithms for element-wise polynomial matrix transforms achieve exponential space reduction in polynomial degree with corrections to prior constructions.