The quantum transverse Ising model and its extensions play a critical role in various fields, such as statistical physics, quantum magnetism, quantum simulations, and mathematical physics. Although it does not suffer from the sign problem in most cases, the corresponding quantum Monte Carlo algorithm performs inefficiently, especially at a large longitudinal field. The main hindrance is the lack of loop update method which can strongly decrease the auto-correlation between Monte Carlo steps. Here, we successfully develop a loop algorithm with a novel merge-unmerge process. It demonstrates a great advantage over the state-of-the-art algorithm when implementing it to simulate the Rydberg atom chain and Kagome qubit ice. This advanced algorithm suits various systems, such as Rydberg atom arrays, trapped ions, quantum materials, and quantum annealers.

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• Frustrated magnetism
• Magnetic order
• Quantum computation
• Rydberg gases
• Trapped ions
• Quantum Monte Carlo
• Spin lattice models