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

D. O. Shendryk1,2,*, O. V. Ivakhnenko1,3,*, S. N. Shevchenko1,†, and Franco Nori3,4

  • *These authors contributed equally to this work.
  • †Contact author: sshevchenko@ilt.kharkov.ua
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Phys. Rev. A 112, 042437 – Published 27 October, 2025

DOI: https://doi.org/10.1103/gnr5-583s

Abstract

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, frequency ω, 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.

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Phys. Rev. A 112, 042437– Published 27 October, 2025
  • Received 26 June 2025
  • Accepted 24 September 2025
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