A reproducible benchmark and JAX‑traceable implementation is now available – no analytic solver required.
Quantum Signal Processing (QSP) is one of the most elegant building blocks in quantum computing. It turns a single qubit and a handful of phase angles into a polynomial transformer: feed in a signal (x \in [-1,1]), and the circuit outputs (P(x)) for a polynomial of your choice. Hamiltonian simulation, amplitude amplification, even quantum phase estimation – all can be written as QSP with the right phase angles.
The catch? Until now, getting those phase angles meant running an analytic solver. That works, but it can be numerically fragile at high degree, and it assumes you have a closed‑form target polynomial. What if your target is defined implicitly by a loss function? What if you want to embed QSP as a differentiable layer inside a larger variational circuit?
Learning phases instead of deriving them
A new paper and open‑source implementation (DOI: 10.5281/zenodo.20645403, github.com/rosspeili/trainable-qsp-angles) shows that you can learn QSP phase angles from random initialization using gradient descent – with no analytic pre‑computation.
