Exact Spin Correlators of Integrable Quantum Circuits from Algebraic Geometry

TL;DR

This paper derives exact algebraic formulas for spin correlation functions in integrable quantum circuits, aiding calibration and analysis of quantum simulation platforms with precise, analytic results.

Contribution

It introduces a novel combination of algebraic Bethe Ansatz and algebraic geometry to compute exact correlation functions for medium-sized integrable quantum circuits.

Findings

Correlation functions are expressed as rational functions of circuit parameters.

Analytic results are obtained for both real space and Fourier space.

Different parameter regimes show qualitatively distinct behaviors.

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.