Perturbational Decomposition Analysis for Quantum Ising Model with Weak Transverse Fields

TL;DR

This paper introduces a perturbational decomposition method for simulating quantum evolution in the 1D Ising model with weak transverse fields, offering improved efficiency over traditional methods in certain parameter regimes.

Contribution

It presents a novel perturbational approach tailored for the 1D Ising model with weak transverse fields, expanding the toolkit for quantum simulation techniques.

Findings

Achieves measurable improvements over Trotter decomposition in specific regimes.

Characterizes parameter regimes where the method is most effective.

Provides practical guidance for simulation strategy selection.

Abstract

This work presented a perturbational decomposition method for simulating quantum evolution under the one-dimensional Ising model with both longitudinal and transverse fields. By treating the transverse field terms as perturbations in the expansion, our approach is particularly effective in systems with moderate longitudinal fields and weak to moderate transverse fields relative to the coupling strength. Through systematic numerical exploration, we characterized parameter regimes and evolution time windows where the decomposition achieved measurable improvements over conventional Trotter decomposition methods. The developed perturbational approach and its characterized parameter space may provide practical guidance for choosing appropriate simulation strategies in different parameter regimes of the one-dimensional Ising model.