Weighted Quantum Signal Processing: Low-Depth Polynomial Approximation with Applications to Kolmogorov-Arnold Networks
Quantum Signal Processing is a powerful quantum framework for generating and approximating univariate polynomials. However, QSP is often limited by circuit-depth bottlenecks and parity constraints on the class of realizable polynomials. In this work, we introduce Weighted Quantum Signal Processing, an extension of QSP in which a weight function is assigned to the central rotation operator. This formulation provides a deeper understanding of QSP, which emerges as the special case of WQSP with unit weights. The choice of weights determines the structure and expressive capabilities of WQSP circuits. When the weights are natural numbers greater than one, WQSP reduces to a pruned version of QS...
| Authors | Rohit Sarma Sarkar, Rupayan Bhattacharjee, Elias F. Combarro et al. |
|---|---|
| Primary category | quant-ph |
| Published | 18 September 2026 |
| Last updated at source | 22 September 2026 |
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