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We study the task of agnostic tomography: given copies of an unknown $n$-qubit state $\rho$ which has fidelity $\tau$ with some state in a given class $C$, find a state which has fidelity $\ge \tau - \epsilon$ with $\rho$.
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Adriano Barenco, Charles H Bennett, Richard Cleve, David P DiVincenzo, Norman Margolus, Peter Shor, Tycho Sleator, John A Smolin, and Harald Weinfurter, Elementary gates for quantum computation , Physical Review A 52
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Yevgeniy Dodis, Yael Tauman Kalai, and Shachar Lovett, On cryptography with auxiliary input , Proceedings of the Forty-first Annual ACM Symposium on Theory of Computing, pp. 621–630, 2009
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Michael A. Nielsen and Isaac L. Chuang, Quantum Computation and Quantum Information , Cambridge University Press, Cambridge, 2010
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Krzysztof Pietrzak, Cryptography from learning parity with noise , International Conference on Current Trends in Theory and Practice of Computer Science, pp. 99–114, Springer, 2012
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Konrad Banaszek, Marcus Cramer, and David Gross, Focus on quantum tomography , New Journal of Physics 15
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Ashley Montanaro, Learning stabilizer states by Bell sampling , arXiv:1707.04012 (2017), 1707.04012
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2018
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Zhengfeng Ji, Yi-Kai Liu, and Fang Song, Pseudorandom quantum states , Advances in Cryptology–CRYPTO 2018: 38th Annual International Cryptology Conference, Santa Barbara, CA, USA, August 19–23, 2018, Proceedings, Part III 38, pp. 126–152, Springer, 2018
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Jeongwan Haah, Robin Kothari, and Ewin Tang, Learning quantum Hamiltonians from high-temperature Gibbs states and real-time evolutions , Nature Physics (2024)
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