Efficient implementation of quantum signal processing via the adiabatic-impulse model

We investigate an analogy between quantum signal processing (QSP) and the adiabatic-impulse model (AIM) in order to implement the QSP algorithm with fast quantum logic gates. QSP is an algorithmic technique that uses single-qubit dynamics to perform a polynomial function transformation. The adiabatic-impulse model effectively describes the evolution of a two-level quantum system under a strong external driving field. We can map parameters from QSP to the AIM to implement a QSP-like evolution with nonadiabatic, high-amplitude external drives. By choosing the AIM driving parameters that control the nonadiabatic transition parameters (such as driving amplitude <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mi>A</a:mi> </a:math> , frequency <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mi>ω</b:mi> </b:math> , and signal timing), one can achieve polynomial approximations and increase robustness in quantum circuits. The analogy between QSP and AIM presented here can be useful as a way to directly implement the QSP algorithmic technique on quantum systems and show the benefits from fast Landau-Zener-Stückelberg-Majorana (LZSM) quantum logic gates in comparison with usual resonance driving gates in IBM-Q quantum processors.