Dynamics in an exact solvable quantum magnet: benchmark for quantum computer

TL;DR

This paper investigates the dynamics of a 2D ferromagnetic J1-J2 Heisenberg model through analytical, numerical, and experimental methods, providing insights into quantum walk behavior and aiding the development of quantum computers.

Contribution

It presents the first analytical solution for magnon dynamics in this model and demonstrates experimental validation on IBM quantum processors.

Findings

Magnon exhibits ballistic propagation typical of quantum walk

Out-of-time ordered correlators reveal coupling competition

Experimental results align with theoretical predictions

Abstract

Quantum magnets are never short of novel and fascinating dynamics, yet its simulation by classical computers requires exponentially-scaled computation resources, which renders the research on large-scale many-body dynamics fiendishly difficult. In this letter, we explore the dynamic behavior of 2D large-scale ferromagnetic J1-J2 Heisenberg model both theoretically and experimentally. First, the analytical solution of magnon dynamics is obtained to show an obvious ballistic propagation of magnon, which is typical for quantum walk. Then, we verify the dynamic behavior of the system through numerical approach of exact diagonalization and tensor network method. We also calculate out-of-time ordered correlators and butterfly velocities among different lattice points, finding that they can well depict the competition between different couplings. Finally, a quantum walk experiment is designed and conducted on the basis of IBM programmable quantum processors, and the experimental results are in consistence with our theoretical predictions. Since the analytical results can be used, in principle, to predict the behavior of large-scale quantum many-body systems and even those infinitely large, this work will help facilitate further research on quantum walk and quantum many-body dynamics in large-scale lattice systems, guide future design of quantum computers, as well as popularize quantum computers until they are known and available to every household in the world.