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.
arXiv preprint arXiv:2312.09072 , year=
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A polynomial-time classical decision algorithm exactly characterizes which multivariable Laurent polynomial pairs are realizable by M-QSP and supplies a constructive implementation when the answer is yes.
Single-ancilla approximate block encoding of A = sum alpha_j H_j is achieved via generalized quantum signal processing applied to Hamiltonian simulation, yielding near-optimal depth with one or O(log log(1/epsilon)) ancilla.
Claims query-optimal bivariate-QSP simulation of non-Hermitian Hamiltonians, but the constructive angle-finding chain is circular and contradicted by the paper's own benchmarks.
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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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Polynomial time constructive decision algorithm for multivariable quantum signal processing
A polynomial-time classical decision algorithm exactly characterizes which multivariable Laurent polynomial pairs are realizable by M-QSP and supplies a constructive implementation when the answer is yes.
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Low-ancilla block encodings via Hamiltonian simulation
Single-ancilla approximate block encoding of A = sum alpha_j H_j is achieved via generalized quantum signal processing applied to Hamiltonian simulation, yielding near-optimal depth with one or O(log log(1/epsilon)) ancilla.
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Simulation of Non-Hermitian Hamiltonians with Bivariate Quantum Signal Processing
Claims query-optimal bivariate-QSP simulation of non-Hermitian Hamiltonians, but the constructive angle-finding chain is circular and contradicted by the paper's own benchmarks.