Infinite quantum signal processing for arbitrary Szegő functions
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arXiv
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| Hauptverfasser: | , , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866918370267365376 |
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| author | Alexis, Michel Lin, Lin Mnatsakanyan, Gevorg Thiele, Christoph Wang, Jiasu |
| author_facet | Alexis, Michel Lin, Lin Mnatsakanyan, Gevorg Thiele, Christoph Wang, Jiasu |
| contents | We provide a complete solution to the problem of infinite quantum signal processing for the class of Szegő functions, which are functions that satisfy a logarithmic integrability condition and include almost any function that allows for a quantum signal processing representation. We do so by introducing a new algorithm called the Riemann-Hilbert-Weiss algorithm, which can compute any individual phase factor independent of all other phase factors. Our algorithm is also the first provably stable numerical algorithm for computing phase factors of any arbitrary Szegő function. The proof of stability involves solving a Riemann-Hilbert factorization problem in nonlinear Fourier analysis using elements of spectral theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_05634 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Infinite quantum signal processing for arbitrary Szegő functions Alexis, Michel Lin, Lin Mnatsakanyan, Gevorg Thiele, Christoph Wang, Jiasu Quantum Physics Numerical Analysis Classical Analysis and ODEs 68Q12, 81P68, 34L25, 42C99 We provide a complete solution to the problem of infinite quantum signal processing for the class of Szegő functions, which are functions that satisfy a logarithmic integrability condition and include almost any function that allows for a quantum signal processing representation. We do so by introducing a new algorithm called the Riemann-Hilbert-Weiss algorithm, which can compute any individual phase factor independent of all other phase factors. Our algorithm is also the first provably stable numerical algorithm for computing phase factors of any arbitrary Szegő function. The proof of stability involves solving a Riemann-Hilbert factorization problem in nonlinear Fourier analysis using elements of spectral theory. |
| title | Infinite quantum signal processing for arbitrary Szegő functions |
| topic | Quantum Physics Numerical Analysis Classical Analysis and ODEs 68Q12, 81P68, 34L25, 42C99 |
| url | https://arxiv.org/abs/2407.05634 |