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Exact Spin Correlators of Integrable Quantum Circuits from Algebraic Geometry

Quantum Physics 2025-07-02 v2 Statistical Mechanics High Energy Physics - Theory Exactly Solvable and Integrable Systems

Abstract

We calculate the correlation functions of strings of spin operators for integrable quantum circuits exactly. These observables can be used for calibration of quantum simulation platforms. We use 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 limit 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.

Keywords

Cite

@article{arxiv.2405.16070,
  title  = {Exact Spin Correlators of Integrable Quantum Circuits from Algebraic Geometry},
  author = {Arthur Hutsalyuk and Yunfeng Jiang and Balazs Pozsgay and Hefeng Xu and Yang Zhang},
  journal= {arXiv preprint arXiv:2405.16070},
  year   = {2025}
}

Comments

discussions and references added, typos corrected, 48 pages

R2 v1 2026-06-28T16:39:52.847Z