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Beating full state tomography for unentangled spectrum estimation

https://doi.org/10.1137/1.9781611978971.120

Pelecanos, Angelos; Tan, Xinyu; Tang, Ewin; Wright, John (January 2026, Society for Industrial and Applied Mathematics)

Free, publicly-accessible full text available January 1, 2027
Efficient Approximate Unitary Designs from Random Pauli Rotations

https://doi.org/10.1109/FOCS61266.2024.00036

Haah, Jeongwan; Liu, Yunchao; Tan, Xinyu (October 2024, IEEE)

We construct random walks on simple Lie groups that quickly converge to the Haar measure for all moments up to order t. The spectral gap of this random walk is shown to be Ω(1/t), which coincides with the best previously known bound for a random walk on the permutation group on {0, 1}^n. This implies that the walk gives an ε-approximate unitary t-design. Our simple proof uses quadratic Casimir operators of Lie algebras.
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Approximate unitary 3-designs from transvection Markov chains

https://doi.org/10.1007/s10623-021-01000-4

Tan, Xinyu; Rengaswamy, Narayanan; Calderbank, Robert (September 2022, Designs, Codes and Cryptography)

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