Optimizing Shadow Tomography with Generalized Measurements,Physical Review Letters

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Optimizing Shadow Tomography with Generalized Measurements
Physical Review Letters ( IF 8.1 ) Pub Date : 2022-11-23 , DOI: 10.1103/physrevlett.129.220502
H Chau Nguyen ₁ , Jan Lennart Bönsel ₁ , Jonathan Steinberg ₁ , Otfried Gühne ₁

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Advances in quantum technology require scalable techniques to efficiently extract information from a quantum system. Traditional tomography is limited to a handful of qubits, and shadow tomography has been suggested as a scalable replacement for larger systems. Shadow tomography is conventionally analyzed based on outcomes of ideal projective measurements on the system upon application of randomized unitaries. Here, we suggest that shadow tomography can be much more straightforwardly formulated for generalized measurements, or positive operator valued measures. Based on the idea of the least-square estimator shadow tomography with generalized measurements is both more general and simpler than the traditional formulation with randomization of unitaries. In particular, this formulation allows us to analyze theoretical aspects of shadow tomography in detail. For example, we provide a detailed study of the implication of symmetries in shadow tomography. Moreover, with this generalization we also demonstrate how the optimization of measurements for shadow tomography tailored toward a particular set of observables can be carried out.

中文翻译：

使用通用测量优化阴影层析成像

量子技术的进步需要可扩展的技术来有效地从量子系统中提取信息。传统层析成像仅限于少数几个量子位，而阴影层析成像已被建议作为大型系统的可扩展替代品。阴影断层扫描通常根据应用随机单一系统时系统上理想投影测量的结果进行分析。在这里，我们建议可以更直接地为广义测量或正算子值测量制定阴影层析成像。基于最小二乘估计的思想，具有广义测量的阴影层析成像比具有单一单元随机化的传统公式更通用和更简单。特别是，这个公式使我们能够详细分析阴影层析成像的理论方面。例如，我们详细研究了阴影层析成像中对称性的含义。此外，通过这种概括，我们还展示了如何针对一组特定的可观察量来优化阴影层析成像的测量。

更新日期：2022-11-23

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