Adaptivity is not helpful for Pauli channel learning
Abstract: This note shows that adaptive strategies do not offer additional advantages for learning and testing Pauli channels with entangled input. First, the tight query complexity of learning Pauli channels with entangled input is established for the general norm $l_p$. In particular, the complexities for the $l_{1}$, $l_2$ and $l_\infty$ norms are improved or matched compared to previous results using entanglement in the literature. We also settle the query complexity to test if Pauli channels are white noise sources across $l_p$. Additionally, we demonstrate that the query complexity of estimating the noise level of a Pauli channel, characterized by the entropy of its error distribution and the count of non-zero probabilities, is $\Theta(4n/n)$. Further, $\Theta(4n/n)$ queries are sufficient to estimate the diamond norm between two Pauli channels.
- Clément L. Canonne. A short note on learning discrete distributions. arXiv preprint arXiv:2002.11457, 2020.
- The learnability of pauli noise. Nature Communications, 14:52, 2023. Received: 4 July 2022; Accepted: 23 December 2022; Published: 4 January 2023.
- Tight bounds on pauli channel learning without entanglement. https://arxiv.org/abs/2309.13461, 2023.
- Quantum advantages for pauli channel estimation. Phys. Rev. A, 105:032435, Mar 2022.
- Pauli error estimation via population recovery. https://arxiv.org/abs/2105.02885, 2021.
- Lower bounds on learning pauli channels. arXiv preprint arXiv:2301.09192, 2023.
- Efficient estimation of pauli channels. arXiv preprint arXiv:1907.12976, 2020.
- Modeling and simulating the noisy behavior of near-term quantum computers. Phys. Rev. A, 104:062432, Dec 2021.
- Cambyse Rouzé and Daniel Stilck França França. Efficient learning of the structure and parameters of local pauli noise channels. arXiv preprint arXiv:2307.02959, 2023.
- G. Valiant and P. Valiant. Estimating the unseen: An n/log(n)-sample estimator for entropy and support size, shown optimal via new clts. In Proceedings of the Forty-third Annual ACM Symposium on Theory of Computing, STOC ’11, pages 685–694, 2011.
- G. Valiant and P. Valiant. Estimating the unseen: Improved estimators for entropy and other properties. Journal of the ACM, 64(6), 2017.
- Bo Waggoner. lpsubscript𝑙𝑝l_{p}italic_l start_POSTSUBSCRIPT italic_p end_POSTSUBSCRIPT testing and learning of discrete distributions. https://arxiv.org/abs/1412.2314, 2015.
- Noise tailoring for scalable quantum computation via randomized compiling. Phys. Rev. A, 94:052325, Nov 2016.
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.
