# 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 1 [ qu an tph ] 2 6 N ov 2 02 1 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,…

Approximate unitary 3-designs from transvection Markov chains

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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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We give an algorithm which produces a unique element of the Clifford group on n qubits ( Cn ) from an integer 0≤i<Cn (the number of elements in the group). The algorithm involves O(n 3) operations…

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The design described here was originally discovered by Cleve et al. (2016), but the connection to classical codes is new, which significantly simplifies the description of the design and its translation to circuits.