Perturbational Decomposition Analysis for Quantum Ising Model with Weak Transverse Fields

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.

10 pages, 7 figures, comments weilcomed

References in corpus (23)

• Probing many-body dynamics on a 51-atom quantum simulator
• Solving the Quantum Many-Body Problem with Artificial Neural Networks
• Direct-coupling analysis of residue co-evolution captures native contacts across many protein families
• Quantum Chemistry in the Age of Quantum Computing
• Identification of direct residue contacts in protein-protein interaction by message passing
• Scale-free correlations in bird flocks
• Observation of a Many-Body Dynamical Phase Transition with a 53-Qubit Quantum Simulator
• Quantum Phases of Matter on a 256-Atom Programmable Quantum Simulator
• A high-bias, low-variance introduction to Machine Learning for physicists
• Quantum Simulation of Antiferromagnetic Spin Chains in an Optical Lattice
• Probing Topological Spin Liquids on a Programmable Quantum Simulator
• Statistical mechanics for natural flocks of birds
• Quantum criticality in an Ising chain: experimental evidence for emergent E8 symmetry
• A simple formula for the average gate fidelity of a quantum dynamical operation
• Quantum simulation of frustrated magnetism in triangular optical lattices
• Universal digital quantum simulation with trapped ions
• Quantum Simulators: Architectures and Opportunities
• Observation of Time-Crystalline Eigenstate Order on a Quantum Processor
• Observation of topological phenomena in a programmable lattice of 1,800 qubits
• Nearly optimal lattice simulation by product formulas
• Local equilibrium in bird flocks
• Faster Digital Quantum Simulation by Symmetry Protection
• Hamiltonian simulation with nearly optimal dependence on spectral norm