基于随机化数据的统计学习验证量子态近似k-设计
Statistical learning on randomized data to verify quantum state approximate k-designs
AI总结：
本文提出利用随机投影测量结合最大似然估计与神经网络等统计学习方法，在数据采集规模上高效验证近似量子态k-设计的随机性，并适用于任意能生成量子设计的含噪量子平台。
摘要：
纯态随机系综在量子物理的多个方面已被证明极为重要，例如量子电路性能基准测试、量子优势检验、为多体热化提供新见解以及研究黑洞信息佯谬。尽管生成完全随机系综在实验上具有挑战性，但其近似形式同样有用，并且已知会在包括里德伯装置在内的多种物理模型中自然涌现。这些系综被称为近似量子态设计，而验证其随机性程度可能是一项代价高昂的任务，类似于对多体系统执行完整量子态层析。在这项理论工作中，与传统的频率学派方法相比，我们在数据采集规模方面高效地验证了近似量子设计的特性。具体做法是：利用随机投影测量基将复杂多体态中所蕴含的信息转化为经典数据的简洁表示，随后使用最大似然估计和神经网络等统计推断方法进行处理，并以阴影层析的预测结果作为基准进行对比。我们提出的方案将机器学习方法用于对随机化测量所得数据进行后处理，以实现对（近似）量子态k-设计的高效表征，该方案适用于任何能够生成量子设计的含噪量子平台。
英文摘要：
Random ensembles of pure states have proven to be extremely important in various aspects of quantum physics such as benchmarking the performance of quantum circuits, testing for quantum advantage, providing novel insights for many-body thermalization and studying the black hole information paradox. Although generating a fully random ensemble is experimentally challenging, approximations of it are just as useful and are known to emerge naturally in a variety of physical models, including Rydberg setups. These are referred to as approximate quantum state designs, and verifying their degree of randomness can be an expensive task, similar to performing full quantum state tomography on many-body systems. In this theoretical work, we efficiently validate the character of approximate quantum designs with respect to data size acquisition when compared to the conventional frequentist approach. This is achieved by translating the information residing in the complex many-body state into a succinct representation of classical data using a random projective measurement basis, which is then processed using methods of statistical inference such as maximum likelihood estimation and neural networks and benchmarked against the predictions of shadow tomography. Our scheme of combining machine learning methods for postprocessing the data obtained from randomized measurements for efficient characterisation of (approximate) quantum state k designs is applicable to any noisy quantum platform that can generate quantum designs.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
