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

TL;DR

This paper explores how the adiabatic-impulse model can be used to efficiently implement quantum signal processing, enabling faster quantum logic gates and improved robustness in quantum algorithms.

Contribution

It establishes an analogy between QSP and AIM, allowing direct implementation of QSP with nonadiabatic, high-amplitude drives for faster quantum operations.

Findings

Mapping QSP parameters to AIM enables polynomial transformations.

Nonadiabatic drives increase robustness of quantum circuits.

Implementation leverages Landau-Zener-Stuckelberg-Majotana gates.

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.