Exact Spin Correlators of Integrable Quantum Circuits from Algebraic Geometry

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.

discussions and references added, typos corrected, 48 pages

References in corpus (17)

• Experimental Observation of a Generalized Gibbs Ensemble
• Quantum Error Mitigation
• What is an integrable quench?
• Relaxation dynamics in the gapped XXZ spin-1/2 chain
• Formation of robust bound states of interacting microwave photons
• Observation of E8 Particles in an Ising Chain Antiferromagnet
• Finite temperature spin dynamics in a perturbed quantum critical Ising chain with an $E_8$ symmetry
• Rational $Q$-systems, Higgsing and Mirror Symmetry
• Geometric Algebra and Algebraic Geometry of Loop and Potts Models
• Conserved charges in the quantum simulation of integrable spin chains
• Popcorn Drude weights from quantum symmetry
• Magnetic excitations in the one-dimensional Heisenberg-Ising model with external fields and their experimental realizations
• Spin-$s$ Rational $Q$-system
• Dynamical quantum phase transitions
• Spaces of quasi-exponentials and representations of the Yangian Y(gl_N)
• Rational Q-systems at Root of Unity I. Closed Chains
• Bethe Ansatz Solutions for Certain Periodic Quantum Circuits

Cited by in corpus (3)

• Lanczos-Pascal approach to correlation functions in chaotic quantum systems
• Berry connection and quantum geometry in time-dependent systems with instantaneous quantum integrable field theory
• Spin-$s$ $Q$-systems: Twist and Open Boundaries