BIMSA > BIMSA Integrable Systems Seminar Exact Spin Correlators of Integrable Quantum Circuits from Algebraic Geometry
Exact Spin Correlators of Integrable Quantum Circuits from Algebraic Geometry
Organizers
Andrii Liashyk , Nicolai Reshetikhin , Ivan Sechin , Andrey Tsiganov
Speaker
Arthur Hutsalyuk
Time
Tuesday, March 11, 2025 4:00 PM - 5:00 PM
Venue
A6-101
Online
Zoom 873 9209 0711 (BIMSA)
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.