arXiv 2502.075712025-02-11quant-ph

通过测量辅助量子比特估计非线性物理量

Estimation of Nonlinear Physical Quantities By Measuring Ancillas

Nhat A. Nghiem, Tzu-Chieh Wei

AI总结：

针对给定量子态$ρ$的冯·诺依曼熵和雷尼熵估计问题，本文提出仅需$ρ$拷贝、通过测量少量辅助量子比特的量子算法，在非整数阶雷尼熵估计的样本复杂度和误差容限上较现有方法实现近2的幂次提升。

摘要：

本文提出了用于估计冯·诺依曼熵和雷尼熵的量子算法，这两种熵是给定量子态$ρ$的关键物理和信息论性质。尽管已有实现相同目标的研究，但部分先前成果假设存在制备目标态$ρ$纯化态的幺正变换。本文考虑仅给定$ρ$拷贝的替代场景，构建了估计目标熵的量子算法。该框架无需直接测量系统，仅通过测量少量辅助量子比特即可完成任务，且相比先前相关成果实现显著改进。例如，对于非整数阶$α$的雷尼熵，与Wang等人的研究[Phys. Rev. Applied 19, 044041 (2023)]相比，本文方法在样本复杂度（关于给定态的秩）和误差容限方面均实现近2的幂次提升。

英文摘要：

In this article, we present quantum algorithms for estimating von Neumann entropy and Renyi entropy, which are crucial physical and information-theoretical properties of a given quantum state $ρ$. Although there have been existing works that achieved the same goal, some prior developments assume the unitary that prepares the purification to the target state $ρ$. Here, we consider an alternative setting where only copies of $ρ$ are given and construct a quantum algorithm that estimates the desired entropy. Our framework can complete the given task by measuring a small number of ancilla qubits without directly measuring the system, and that it achieves significant improvement over prior relevant developments. For example, for the Renyi entropy of the order of non-integral $α$, our method achieves almost power-of-two improvement in sample complexity with respect to the rank of the given state and almost a power-of-two improvement in error tolerance compared with the work by Wang et al. [Phys. Rev. Applied 19, 044041 (2023)].

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