On multivariate polynomials achievable with quantum signal processing

Laneve, Lorenzo; Wolf, Stefan

doi:10.22331/q-2025-02-20-1641

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Journal article

On multivariate polynomials achievable with quantum signal processing

Laneve, Lorenzo ORCID Facoltà di scienze informatiche, Università della Svizzera italiana, Svizzera
Wolf, Stefan Facoltà di scienze informatiche, Università della Svizzera italiana, Svizzera

2025

Published in:

Quantum. - 2025, vol. 9, p. 1641

English Quantum signal processing (QSP) is a framework which was proven to unify and simplify a large number of known quantum algorithms, as well as discovering new ones. QSP allows one to transform a signal embedded in a given unitary using polynomials. Characterizing which polynomials can be achieved with QSP protocols is an important part of the power of this technique, and while such a characterization is well-understood in the case of univariate signals, it is unclear which multivariate polynomials can be constructed when the signal is a vector, rather than a scalar. This work uses a slightly different formalism than what is found in the literature, and uses it to find simpler necessary conditions for decomposability, as well as a sufficient condition – the first, to the best of our knowledge, proven for a (generally inhomogeneous) multivariate polynomial in the context of quantum signal processing.

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