Quantum systems have entered a competitive regime in which classical computers must make approximations to represent highly entangled quantum states^1,2. However, in this beyond-classically-exact regime, fidelity comparisons between quantum and classical systems have so far been limited to digital quantum devices^2,3,4,5, and it remains unsolved how to estimate the actual entanglement content of experiments⁶. Here, we perform fidelity benchmarking and mixed-state entanglement estimation with a 60-atom analogue Rydberg quantum simulator, reaching a high-entanglement entropy regime in which exact classical simulation becomes impractical. Our benchmarking protocol involves extrapolation from comparisons against an approximate classical algorithm, introduced here, with varying entanglement limits. We then develop and demonstrate an estimator of the experimental mixed-state entanglement⁶, finding our experiment is competitive with state-of-the-art digital quantum devices performing random circuit evolution^2,3,4,5. Finally, we compare the experimental fidelity against that achieved by various approximate classical algorithms, and find that only the algorithm we introduce is able to keep pace with the experiment on the classical hardware we use. Our results enable a new model for evaluating the ability of both analogue and digital quantum devices to generate entanglement in the beyond-classically-exact regime, and highlight the evolving divide between quantum and classical systems.

量子系统已进入竞争状态，经典计算机必须进行近似来表示高度纠缠的量子态^1,2。然而，在这种超经典精确的情况下，量子系统和经典系统之间的保真度比较迄今为止仅限于数字量子设备^2,3,4,5，并且如何估计实验的实际纠缠内容仍然悬而未决⁶。在这里，我们使用 60 原子模拟里德堡量子模拟器进行保真度基准测试和混合态纠缠估计，达到高纠缠熵状态，在这种状态下精确的经典模拟变得不切实际。我们的基准测试协议涉及通过与此处介绍的具有不同纠缠限制的近似经典算法进行比较来推断。然后，我们开发并演示了实验混合态纠缠的估计器⁶，发现我们的实验与执行随机电路演化的最先进的数字量子设备具有竞争力^2,3,4,5。最后，我们将实验保真度与各种近似经典算法实现的保真度进行比较，发现只有我们引入的算法能够跟上我们使用的经典硬件上的实验。我们的研究结果提供了一种新模型，用于评估模拟和数字量子设备在超经典精确状态下产生纠缠的能力，并强调量子系统和经典系统之间不断发展的鸿沟。