Query-optimal estimation of unitary channels in diamond distance
| Autor: | Haah, Jeongwan, Kothari, Robin, O'Donnell, Ryan, Tang, Ewin |
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| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | 2023 IEEE 64th Annual Symposium on Foundations of Computer Science (FOCS), Santa Cruz, CA, USA, 2023, pp. 363-390 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1109/FOCS57990.2023.00028 |
| Popis: | We consider process tomography for unitary quantum channels. Given access to an unknown unitary channel acting on a $\textsf{d}$-dimensional qudit, we aim to output a classical description of a unitary that is $\varepsilon$-close to the unknown unitary in diamond norm. We design an algorithm achieving error $\varepsilon$ using $O(\textsf{d}^2/\varepsilon)$ applications of the unknown channel and only one qudit. This improves over prior results, which use $O(\textsf{d}^3/\varepsilon^2)$ [via standard process tomography] or $O(\textsf{d}^{2.5}/\varepsilon)$ [Yang, Renner, and Chiribella, PRL 2020] applications. To show this result, we introduce a simple technique to "bootstrap" an algorithm that can produce constant-error estimates to one that can produce $\varepsilon$-error estimates with the Heisenberg scaling. Finally, we prove a complementary lower bound showing that estimation requires $\Omega(\textsf{d}^2/\varepsilon)$ applications, even with access to the inverse or controlled versions of the unknown unitary. This shows that our algorithm has both optimal query complexity and optimal space complexity. Comment: 43 pages; v2, minor edits for referee comments |
| Databáze: | arXiv |
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