Quantum

Quantum Signal Processing Phase Factorization via Logarithmic Derivatives

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Based on a feed excerpt; full article content has not been acquired. Source evidence retrieved 14/10/2026, 12:17:26 UTC.

Briefings

A new quantum signal processing algorithm replaces Prony's method with logarithmic derivatives to factorize phase factors efficiently. The method achieves O(d log^2 d) complexity and computes phase factors in seconds with errors around 10^-12. This approach simplifies the factorization procedure for Hamiltonian simulation, eigenstate filtering, matrix inversion, and the Fermi-Dirac operator.

Key points

• The algorithm eliminates Prony's method by using the logarithmic derivative of an associated polynomial to recover unweighted power sums of roots.
• Newton-Girard identities recover polynomial coefficients without computing roots, achieving O(d log^2 d) computational complexity.

Context

Quantum signal processing requires efficient phase factor computation. The new method simplifies the factorization procedure for Hamiltonian simulation, eigenstate filtering, matrix inversion, and the Fermi-Dirac operator.

Limitations

Numerical experiments on specific quantum problems were conducted. Maximum errors are estimated at 10^-12. The source is a preprint (arXiv:2610.14259v1) with limited snapshot coverage of the full algorithm's performance across all quantum applications.

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