Numerical validation of an ultracold Hubbard quantum simulator

TL;DR

This paper uses an exact numerical method to validate ultracold-atom quantum simulations of the 2D Hubbard model at very low temperatures, confirming their accuracy and providing benchmarks for future research.

Contribution

It demonstrates the effectiveness of Diagrammatic Monte Carlo in accurately simulating the 2D Hubbard model at low temperatures, validating experimental quantum simulators.

Findings

Excellent agreement with experimental data across all accessible temperatures.

Classical algorithms remain competitive with quantum simulators in this regime.

Provides unbiased benchmarks for future method development.

Abstract

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.