Exact QSP angles for odd monomials

A. Kegeles; T. Keitzl; J. Renkl

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arXiv · 2504.06703

Exact QSP angles for odd monomials

A. Kegeles·T. Keitzl·J. Renkl

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Abstract

We present an analytical solution to the angle-finding problem in quantum signal processing (QSP) for monomials of odd degree. Specifically, we show that to implement a monomial of degree $ n $, where $ n $ is odd, it suffices to choose powers of a primitive $ n $-th root of unity as QSP phase angles. Our approach departs from standard numerical methods and is rooted in a group-theoretic argument. Being fully analytical, it eliminates numerical errors and reduces computational overhead in QSP implementation of odd monomials. Such use cases arise, for example, in quantum computing, where self-adjoint contractions are embedded into unitary operators acting on extended Hilbert spaces.

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BibTeX RIS

A. Kegeles, T. Keitzl, J. Renkl. 2025-04-09. Exact QSP angles for odd monomials. https://arxiv.org/abs/2504.06703

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