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

• URL: http://arxiv.org/abs/2506.21136v1
• Date: Thu, 26 Jun 2025 10:35:58 GMT
• Title: Efficient implementation of quantum signal processing via the adiabatic-impulse model
• Authors: D. O. Shendryk, O. V. Ivakhnenko, S. N. Shevchenko, Franco Nori,
• Abstract summary: We investigate analogy between quantum signal processing (QSP) and the adiabatic-impulse model (AIM)<n>AIM effectively describes the evolution of a two-level quantum system under strong external driving field.<n>We can map parameters from QSP to AIM to implement to QSP-like evolution with nonadiabatic, high-amplitude external drives.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Here we investigate 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 algorithm that uses single-qubit dynamics to perform a polynomial function transformation. AIM effectively describes the evolution of a two-level quantum system under strong external driving field. We can map parameters from QSP to AIM to implement QSP-like evolution with nonadiabatic, high-amplitude external drives. By choosing AIM parameters that control non-adiabatic transition parameters (such as driving amplitude $A$, frequency $\omega$, and signal timing), one can achieve polynomial approximations and increase robustness in quantum circuits. The analogy presented here between QSP and AIM can be useful as a way to directly implement the QSP algorithm on quantum systems and obtain all the benefits from the fast Landau-Zener-Stuckelberg-Majotana (LZSM) quantum logic gates.

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