Quantum Simulation of Dzyaloshinsky-Moriya Interaction

TL;DR

This paper develops a genetic algorithm-based method to decompose the evolution operator of a complex quantum Hamiltonian involving Dzyaloshinsky-Moriya and Heisenberg XY interactions, enabling efficient quantum simulation and analysis of entanglement dynamics.

Contribution

It introduces a novel genetic algorithm approach for optimal unitary operator decomposition of the Dzyaloshinsky-Moriya Hamiltonian with Heisenberg XY interaction, facilitating quantum simulation.

Findings

Optimized unitary decompositions for the Hamiltonian were obtained.

Entanglement dynamics of Bell states were studied under the Hamiltonian.

Verification of entanglement preservation procedures was performed.

Abstract

Quantum simulation of a Hamiltonian H requires unitary operator decomposition (UOD) of its evolution operator, ($U=exp(-i H t)$) in terms of experimentally preferable unitaries. Here, using Genetic Algorithm optimization, we numerically evaluate the most generic UOD for the Hamiltonian, DM interaction in the presence of Heisenberg XY interaction, $H_{DH}$. Using these decompositions, we studied the entanglement dynamics of Bell state in the Hamiltonian $H_{DH}$ and verified the entanglement preservation procedure by Hou et al. [Annals of Physics 327, 292 (2012)].