Exact spin correlators of integrable quantum circuits from algebraic geometry
We calculate the correlation functions of strings of spin operators for integrable quantum circuits exactly. These observables can be used for the calibration of quantum simulation platforms. We use the algebraic Bethe Ansatz, in combination with computational algebraic geometry, to obtain analytic...
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2025-07-01
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| Series: | SciPost Physics |
| Online Access: | https://scipost.org/SciPostPhys.19.1.003 |
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| author | Arthur Hutsalyuk, Yunfeng Jiang, Balazs Pozsgay, Hefeng Xu, Yang Zhang |
| author_facet | Arthur Hutsalyuk, Yunfeng Jiang, Balazs Pozsgay, Hefeng Xu, Yang Zhang |
| author_sort | Arthur Hutsalyuk, Yunfeng Jiang, Balazs Pozsgay, Hefeng Xu, Yang Zhang |
| collection | DOAJ |
| description | We calculate the correlation functions of strings of spin operators for integrable quantum circuits exactly. These observables can be used for the calibration of quantum simulation platforms. We use the algebraic Bethe Ansatz, in combination with computational algebraic geometry, to obtain analytic results for medium-size (around 10-20 qubits) quantum circuits. The results are rational functions of the quantum circuit parameters. We obtain analytic results for such correlation functions both in the real space and Fourier space. In the real space, we analyze the short time and long time limits of the correlation functions. In Fourier space, we obtain analytic results in different parameter regimes, which exhibit qualitatively different behaviors. Using these analytic results, one can easily generate numerical data to arbitrary precision. |
| format | Article |
| id | doaj-art-b6e0bff1caa74b5b933a8a110ef7e43c |
| institution | Matheson Library |
| issn | 2542-4653 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | SciPost |
| record_format | Article |
| series | SciPost Physics |
| spelling | doaj-art-b6e0bff1caa74b5b933a8a110ef7e43c2025-07-01T12:26:13ZengSciPostSciPost Physics2542-46532025-07-0119100310.21468/SciPostPhys.19.1.003Exact spin correlators of integrable quantum circuits from algebraic geometryArthur Hutsalyuk, Yunfeng Jiang, Balazs Pozsgay, Hefeng Xu, Yang ZhangWe calculate the correlation functions of strings of spin operators for integrable quantum circuits exactly. These observables can be used for the calibration of quantum simulation platforms. We use the algebraic Bethe Ansatz, in combination with computational algebraic geometry, to obtain analytic results for medium-size (around 10-20 qubits) quantum circuits. The results are rational functions of the quantum circuit parameters. We obtain analytic results for such correlation functions both in the real space and Fourier space. In the real space, we analyze the short time and long time limits of the correlation functions. In Fourier space, we obtain analytic results in different parameter regimes, which exhibit qualitatively different behaviors. Using these analytic results, one can easily generate numerical data to arbitrary precision.https://scipost.org/SciPostPhys.19.1.003 |
| spellingShingle | Arthur Hutsalyuk, Yunfeng Jiang, Balazs Pozsgay, Hefeng Xu, Yang Zhang Exact spin correlators of integrable quantum circuits from algebraic geometry SciPost Physics |
| title | Exact spin correlators of integrable quantum circuits from algebraic geometry |
| title_full | Exact spin correlators of integrable quantum circuits from algebraic geometry |
| title_fullStr | Exact spin correlators of integrable quantum circuits from algebraic geometry |
| title_full_unstemmed | Exact spin correlators of integrable quantum circuits from algebraic geometry |
| title_short | Exact spin correlators of integrable quantum circuits from algebraic geometry |
| title_sort | exact spin correlators of integrable quantum circuits from algebraic geometry |
| url | https://scipost.org/SciPostPhys.19.1.003 |
| work_keys_str_mv | AT arthurhutsalyukyunfengjiangbalazspozsgayhefengxuyangzhang exactspincorrelatorsofintegrablequantumcircuitsfromalgebraicgeometry |