Entanglement-Free Parameter Estimation of Generalized Pauli Channels

Junaid ur Rehman and Hyundong Shin

Department of Electronics and Information Convergence Engineering, Kyung Hee University, Korea

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We propose a parameter estimation protocol for generalized Pauli channels acting on $d$-dimensional Hilbert space. The salient features of the proposed method include product probe states and measurements, the number of measurement configurations linear in $d$, minimal post-processing, and the scaling of the mean square error comparable to that of the entanglement-based parameter estimation scheme for generalized Pauli channels. We also show that while measuring generalized Pauli operators the errors caused by the Pauli noise can be modeled as measurement errors. This makes it possible to utilize the measurement error mitigation framework to mitigate the errors caused by the generalized Pauli channels. We use this result to mitigate noise on the probe states and recover the scaling of the noiseless probes, except with a noise strength-dependent constant factor. This method of modeling Pauli channel as measurement noise can also be of independent interest in other NISQ tasks, e.g., state tomography problems, variational quantum algorithms, and other channel estimation problems where Pauli measurements have the central role.

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Cited by

[1] Steven T. Flammia and Ryan O'Donnell, "Pauli error estimation via Population Recovery", Quantum 5, 549 (2021).

[2] Steven Duplij and Raimund Vogl, "Polyadic Braid Operators and Higher Braiding Gates", Universe 7 8, 301 (2021).

[3] Syahri Ramadhani, Junaid Ur Rehman, and Hyundong Shin, "Quantum Error Mitigation for Quantum State Tomography", IEEE Access 9, 107955 (2021).

[4] Donghwa Lee, Jinil Lee, Seongjin Hong, Hyang-Tag Lim, Young-Wook Cho, Sang-Wook Han, Hyundong Shin, Junaid ur Rehman, and Yong-Su Kim, "Error-mitigated photonic variational quantum eigensolver using a single-photon ququart", Optica 9 1, 88 (2022).

[5] Muhammad Asad Ullah, Saw Nang Paing, and Hyundong Shin, "Noise-Robust Quantum Teleportation With Counterfactual Communication", IEEE Access 10, 34706 (2022).

[6] Steven T. Flammia and Ryan O'Donnell, "Pauli error estimation via Population Recovery", arXiv:2105.02885.

The above citations are from Crossref's cited-by service (last updated successfully 2022-05-20 07:05:09) and SAO/NASA ADS (last updated successfully 2022-05-20 07:05:10). The list may be incomplete as not all publishers provide suitable and complete citation data.