# Floquet Engineering Heisenberg from Ising Using Constant Drive Fields for Quantum Simulation

**Authors:** Anthony N. Ciavarella, Stephan Caspar, Hersh Singh, Martin J. Savage, Pavel Lougovski  
**arXiv:** [2207.09438](https://arxiv.org/abs/2207.09438)  
**Date:** 2022-07-19  
**Summary page:** https://www.summarizepaper.com/en/paper/2207.09438v1/

## Key points

- The study explores the time-evolution of an Ising model with large driving fields over discrete time intervals
- Demonstrates effective reproduction by an XXZ-Heisenberg model at the leading order in the inverse field strength
- Dynamics of the XXX-Heisenberg model are replicated for certain orientations of the drive field
- Approximate equivalences hold true above a critical driving field strength determined by dynamical phase transitions in the Ising model
- Quantum devices capable of evolving qubits according to the Ising model could be utilized to simulate more complex systems
- Advancements in digital and analog quantum computers and simulators are enabling mapping quantum field theories onto arrays of qubits or qudits
- Quantum simulations offer polynomially scaling computational costs, potentially enabling exploration of important quantities in Standard Model physics and beyond classical computation capabilities
- Various platforms for digital quantum computation are being developed, including superconducting qubits, optical qubits, quantum dots, trapped ions, and Rydberg atoms
- These platforms support universal digital quantum computations and facilitate analog simulations efficiently

## Summary

The study explores the time-evolution of an Ising model with large driving fields over discrete time intervals and demonstrates that it can be effectively reproduced by an XXZ-Heisenberg model at the leading order in the inverse field strength. Specifically, for certain orientations of the drive field, the dynamics of the XXX-Heisenberg model are replicated. These approximate equivalences hold true above a critical driving field strength determined by dynamical phase transitions in the Ising model. The findings suggest that quantum devices capable of evolving qubits according to the Ising model could be utilized to simulate more complex systems. With advancements in digital and analog quantum computers and simulators, there is a growing interest in mapping quantum field theories onto arrays of qubits or qudits. While classical computers excel in studying static properties of quantum systems, they face challenges when dealing with time-dependent evolution and finite-density systems due to non-polynomial scaling computational resource requirements. Quantum simulations offer a promising alternative with polynomially scaling computational costs, potentially enabling the exploration of important quantities in Standard Model physics and other areas beyond classical computation capabilities. Various platforms for digital quantum computation, such as those utilizing superconducting qubits, optical qubits, quantum dots, trapped ions, and Rydberg atoms, are being developed. These platforms not only support universal digital quantum computations but also facilitate analog simulations of systems that can be mapped onto their native Hamiltonians. This approach presents opportunities for advancing scientific applications through quantum advantages and exploring new possibilities in simulating complex systems efficiently.