# Approximate 3-designs and partial decomposition of the Clifford group representation using transvections

@inproceedings{Singal2021Approximate3A, title={Approximate 3-designs and partial decomposition of the Clifford group representation using transvections}, author={Tanmay Singal and Min-Hsiu Hsieh}, year={2021} }

X iv :2 11 1. 13 67 8v 2 [ qu an tph ] 1 9 Ju n 20 22 Approximate 3-designs and partial decomposition of the Clifford group representation using transvections Tanmay Singal∗ Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University, Grudziadzka 5/7, 87-100 Toruń, Poland Physics Division, National Center for Theoretical Sciences, Taipei 10617, Taiwan Department of Physics, National Taiwan University, No.1 Sec. 4., Roosevelt Road, Taipei 106, Taiwan…

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It is proved that the Clifford group is a 3-design, showing that it is a better approximation to Haar-random unitaries than previously expected and characterizing how well random Clifford elements approximateHaar- random unitaries.

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Unitary $t$-designs are a ubiquitous tool in many research areas, including randomized benchmarking, quantum process tomography, and scrambling. Despite the intensive efforts of many researchers,…

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Unitary $t$-designs are probabilistic ensembles of unitary matrices whose first $t$ statistical moments match that of the full unitary group endowed with the Haar measure. In prior work, we showed…

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A fast algorithm is provided that decomposes any Clifford gate as a minimal product of Clifford transvections and can be directly used for computing the support of any given Clifford gate.