Learning Quantum Signal Processing Phase Angles via Gradient Descent

This report documents a reproducible benchmark and reference implementation for learning Quantum Signal Processing (QSP) phase angles by gradient descent on a flat, JAX-traceable circuit (PennyLane is reference-only). We do not propose a new QSP algorithm; we measure when gradient training is preferable to mapped analytic solvers on a shared flat-circuit metric. On a standard degree-5 Chebyshev approximation of sin(x), Adam reaches train MSE 9.6×10⁻⁵ for seed 0—better than mapped analytic baselines (≈4.7×10⁻³) on the same circuit—and 30/30 random seeds converge below 10⁻³. Version 1.1 adds multi-seed reliability at degrees 7 and 15 (30/30 success each), an audit of Chao/pyqsp sym_qsp vs Laurent mapping, off-grid max-error evaluation, and a discussion of barren plateaus in this low-parameter QSP setting. We release degree-scaling tables, a phase-convention mapping protocol between solvers and the training circuit, audit logs, experiment results (ZIP), and an implementation note on a QSVT-template pitfall that breaks JAX autodiff. All scripts and hardcoded figure values are under Apache 2.0. Code: https://github.com/rosspeili/trainable-qsp-angles