Entanglement-Free Parameter Estimation of Generalized Pauli Channels
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 scali...
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| Format: | Article |
| Language: | English |
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Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
2021-07-01
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| Series: | Quantum |
| Online Access: | https://quantum-journal.org/papers/q-2021-07-01-490/pdf/ |
| _version_ | 1818724329387458560 |
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| author | Junaid ur Rehman Hyundong Shin |
| author_facet | Junaid ur Rehman Hyundong Shin |
| author_sort | Junaid ur Rehman |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-17T21:24:41Z |
| format | Article |
| id | doaj.art-5d5e625686a14831ae106251982bf53c |
| institution | Directory Open Access Journal |
| issn | 2521-327X |
| language | English |
| last_indexed | 2024-12-17T21:24:41Z |
| publishDate | 2021-07-01 |
| publisher | Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften |
| record_format | Article |
| series | Quantum |
| spelling | doaj.art-5d5e625686a14831ae106251982bf53c2022-12-21T21:32:03ZengVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenQuantum2521-327X2021-07-01549010.22331/q-2021-07-01-49010.22331/q-2021-07-01-490Entanglement-Free Parameter Estimation of Generalized Pauli ChannelsJunaid ur RehmanHyundong ShinWe 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.https://quantum-journal.org/papers/q-2021-07-01-490/pdf/ |
| spellingShingle | Junaid ur Rehman Hyundong Shin Entanglement-Free Parameter Estimation of Generalized Pauli Channels Quantum |
| title | Entanglement-Free Parameter Estimation of Generalized Pauli Channels |
| title_full | Entanglement-Free Parameter Estimation of Generalized Pauli Channels |
| title_fullStr | Entanglement-Free Parameter Estimation of Generalized Pauli Channels |
| title_full_unstemmed | Entanglement-Free Parameter Estimation of Generalized Pauli Channels |
| title_short | Entanglement-Free Parameter Estimation of Generalized Pauli Channels |
| title_sort | entanglement free parameter estimation of generalized pauli channels |
| url | https://quantum-journal.org/papers/q-2021-07-01-490/pdf/ |
| work_keys_str_mv | AT junaidurrehman entanglementfreeparameterestimationofgeneralizedpaulichannels AT hyundongshin entanglementfreeparameterestimationofgeneralizedpaulichannels |