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.
Berry, Andrew M
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Quantum algorithm block-encodes Riccati solutions for m-particle m-hole RPA using Riesz projectors and QSVT, claiming linear system-size scaling under sparsity and polynomial cost in excitation rank m.
QKLA achieves quadratic query-complexity improvement for clipped KL estimation, yielding 2.7-7.4x fewer oracle queries than classical methods when embedded in the PC causal-discovery algorithm at moderate precision.
QRSI spans degenerate quantum eigenspaces almost surely by conjugating the Hamiltonian with random unitaries on g parallel branches and using subspace estimation, while exactly preserving the spectral gap.
citing papers explorer
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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 Solvers for Nonlinear Matrix Equations in Quantum Chemistry
Quantum algorithm block-encodes Riccati solutions for m-particle m-hole RPA using Riesz projectors and QSVT, claiming linear system-size scaling under sparsity and polynomial cost in excitation rank m.
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Quantum Causal Discovery via Amplitude Estimation of Kullback-Leibler Divergence
QKLA achieves quadratic query-complexity improvement for clipped KL estimation, yielding 2.7-7.4x fewer oracle queries than classical methods when embedded in the PC causal-discovery algorithm at moderate precision.
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Quantum Randomized Subspace Iteration
QRSI spans degenerate quantum eigenspaces almost surely by conjugating the Hamiltonian with random unitaries on g parallel branches and using subspace estimation, while exactly preserving the spectral gap.