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Pauli error estimation via Population Recovery

Flammia, Steven T. and O'Donnell, Ryan (2021) Pauli error estimation via Population Recovery. Quantum, 5 . Art. No. 549. ISSN 2521-327X. doi:10.22331/q-2021-09-23-549.

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Motivated by estimation of quantum noise models, we study the problem of learning a Pauli channel, or more generally the Pauli error rates of an arbitrary channel. By employing a novel reduction to the "Population Recovery" problem, we give an extremely simple algorithm that learns the Pauli error rates of an n-qubit channel to precision ϵ in l∞ using just O(1/ϵ²) log(n/ϵ) applications of the channel. This is optimal up to the logarithmic factors. Our algorithm uses only unentangled state preparation and measurements, and the post-measurement classical runtime is just an O(1/ϵ) factor larger than the measurement data size. It is also impervious to a limited model of measurement noise where heralded measurement failures occur independently with probability ≤ 1/4. We then consider the case where the noise channel is close to the identity, meaning that the no-error outcome occurs with probability 1 - η. In the regime of small η we extend our algorithm to achieve multiplicative precision 1 ± ϵ (i.e., additive precision ϵη) using just O(1/ϵ²η) log (n/ϵ) applications of the channel.

Item Type:Article
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URLURL TypeDescription Paper
Flammia, Steven T.0000-0002-3975-0226
Additional Information:Published under CC-BY 4.0. Published: 2021-09-23. We thank Robin Harper for discussions about Pauli channels. This work was supported by ARO grant W911NF2110001. R.O. is additionally supported by NSF grant FET-1909310. This material is based upon work supported by the National Science Foundation under grant numbers listed above. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation (NSF).
Group:AWS Center for Quantum Computing, Institute for Quantum Information and Matter
Funding AgencyGrant Number
Army Research Office (ARO)W911NF2110001
Record Number:CaltechAUTHORS:20211123-173204089
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:112003
Deposited By: Tony Diaz
Deposited On:23 Nov 2021 22:09
Last Modified:23 Nov 2021 22:09

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