高斯玻色采样中函数计算的经典算法
Classical Algorithms for Function Computation in Gaussian Boson Sampling
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- National Laboratory of Solid State Microstructures, School of physics and college of engineering and applied sciences, and Collaborative Innovation Center of Advanced Microstructures, Nanjing University（南京大学固体微结构物理国家重点实验室、物理学院和工程与应用科学学院、先进微结构协同创新中心）
- State Key Laboratory of Novel Software Technology, Nanjing University（南京大学软件新技术国家重点实验室）
- Hefei National Laboratory（合肥国家实验室）
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中文总结 AI 辅助
本文证明在高斯玻色采样中，对于有限压缩强度输入，平均情况下所有函数期望值可经典计算，并给出逆多项式误差的经典算法，为分析线性光学量子系统提供新工具。
中文摘要 AI 辅助
高斯玻色采样（GBS）旨在通过采样由压缩输入和被动线性光学产生的光子数模式来寻求量子优势。许多提出的GBS应用转而通过将函数应用于模式分辨的光子数结果来针对函数计算——这是一种自然的实验后处理形式，产生经典输出。然而，仅采样硬度并不能决定这些任务的复杂性。通过分析固定光子数算子空间的不可约分解，我们证明在被动线性光学网络上平均情况下，对于具有有限压缩强度的输入，每个此类函数的期望值都可以经典评估。我们还提供了一种经典算法，可将该值估计到逆多项式加性误差。该结果为分析线性光学量子系统提供了新的理论工具，有助于阐明当前GBS硬度证据的起源，并激发了具有真正量子优势的GBS新应用。
英文摘要
Gaussian boson sampling (GBS) seeks quantum advantage by sampling photon-number patterns generated with squeezed inputs and passive linear optics. Many proposed GBS applications instead target function computation by applying functions to mode-resolved photon-number outcomes---a natural form of experimental postprocessing that produces classical outputs. Sampling hardness alone, however, does not determine the complexity of these tasks. By analyzing the irreducible decomposition of fixed-photon-number operator spaces, we prove that the expectation value of every such function in the average case over passive linear-optical networks can be classically evaluated for inputs with finite squeezing strength. We also provide a classical algorithm that estimates this value to inverse-polynomial additive error. The result provides new theoretical tools for analyzing linear-optical quantum systems, helps clarify the origin of current GBS hardness evidence, and inspires new applications of GBS with genuine quantum advantages.
