标题： 超冷Hubbard量子模拟器的数值验证 显示英文标题

标题： Numerical validation of an ultracold Hubbard quantum simluator

摘要： 我们将形式上精确的图解蒙特卡罗（DiagMC）方法应用于探测最近在二维 Hubbard 模型的超冷原子量子模拟中实现的前所未有的低温区域 [Xu 等，Nature 642, 909 (2025)]。 在热力学极限下直接计算实验测得的可观测量，并事先控制系统误差，我们发现实验数据在所有可访问温度下都存在显著的一致性——包括最低温度，此时现有的数值基准显示出明显的偏差。 这验证了量子模拟器在此具有挑战性的区域对系统误差的控制能力，并为未来方法的发展提供了无偏基准。 我们的结果表明，经典算法在与最先进的模拟量子模拟器竞争方面仍具优势，并强调了受控数值方法在继续推进这些实验发展中的重要性。 显示英文摘要

摘要： We apply the formally exact Diagrammatic Monte Carlo (DiagMC) method to probe the unprecedentedly low-temperature regime recently achieved in an ultracold-atom quantum simulation of the 2D Hubbard model [Xu et al., Nature 642, 909 (2025)]. Computing the experimentally measured observables directly in the thermodynamic limit with a priori control of systematic errors, we find striking agreement with the experimental data across all accessible temperatures -- including the lowest, where existing numerical benchmarks show significant deviations. This validates the quantum simulator's control over systematic errors in this challenging regime and delivers unbiased benchmarks for future method development. Our results demonstrate that classical algorithms remain competitive with state-of-the-art analogue quantum simulators, and emphasise the importance of controlled numerical methods for continuing the development of these experiments.