On multivariate polynomials achievable with quantum signal processing
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910843593031680 |
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| author | Laneve, Lorenzo Wolf, Stefan |
| author_facet | Laneve, Lorenzo Wolf, Stefan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_20823 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On multivariate polynomials achievable with quantum signal processing Laneve, Lorenzo Wolf, Stefan Quantum Physics 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. |
| title | On multivariate polynomials achievable with quantum signal processing |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2407.20823 |