Implementing quantum signal processing with adiabatic-impulse model

Quantum Signal Processing (QSP) is an algorithm that uses single-qubit dynamics to perform almost any polynomial function transformation with basic unitary operations. The Adiabatic-Impulse Model (AIM) effectively describes the evolution of a two-level quantum system under an external driving field. QSP can directly use parameters from the AIM by mapping AIM’s smooth drive profiles to the phase angles in QSP. By defining AIM parameters that control adiabatic transitions such as amplitude, frequency, and signal time one can guide the smooth variation of QSP phases to achieve stable polynomial approximations or mitigate errors in quantum circuits. That demonstrates the analogy between QSP and AIM and can be useful as a way to directly implement the QSP algorithm on quantum systems.