具有混合统计特性的杂化光-物质系统中的量子采样
Quantum sampling in hybrid light-matter systems with mixed statistics
AI总结：
该研究结合费米子与玻色采样，提出杂化光-物质系统的混合统计量子采样网络，证明其贡献与行列式、积和式线性无关，可用于超越纯费米/玻色采样的量子应用，拓展了量子采样器功能。
AI中文摘要：
玻色采样是验证量子优势的最突出方法之一，它利用网络矩阵的积和式的计算复杂性。类似的量子采样问题采用其他表达式来表示输出概率，例如基于费米子的类似方法，其应用行列式。在这项工作中，我们研究了相互作用光-物质系统的采样设置，该设置结合了费米子采样和玻色采样。混合网络输入包含费米子和玻色子激发，对模式的输出概率进行采样会产生既非纯粹行列式也非纯粹积和式的贡献，而是一般的不变量。具体而言，我们证明了这些不变量贡献与行列式和积和式线性无关，这使得我们的混合采样网络成为超越纯费米子和玻色子采样的光-物质量子应用的理想候选者。此外，采用既非玻色统计也非费米统计的统计特性进行量子采样会产生甚至超出不变量的表达式，进一步扩展了量子采样器的功能。
英文摘要：
Boson sampling is one of the most prominent methods to verify quantum advantage, harnessing the computational complexity of the permanent of a network matrix. Similar quantum sampling problems utilize other expressions for the output probabilities, such as the fermion-based analog applying determinants. In this work, we study sampling setups of interacting light-matter systems, combining fermion and boson sampling. The mixed network input consists of fermionic and bosonic excitations. Sampling the output probability of the modes then yields contributions that are neither purely determinant nor permanent but general immanants. Specifically, we prove that these immanant contributions are linearly independent from determinants and permanents, rendering our mixed sampling network an ideal candidate for light-matter quantum application beyond pure fermion and boson sampling. Furthermore, quantum sampling with statistics that are neither bosonic nor fermionic results in expressions which even exceed immanants, further extending the functionality of quantum samplers.
