# The Clifford group fails gracefully to be a unitary 4-design

@article{Zhu2016TheCG, title={The Clifford group fails gracefully to be a unitary 4-design}, author={Huangjun Zhu and Richard Kueng and Markus Grassl and David Gross}, journal={arXiv: Quantum Physics}, year={2016} }

A unitary t-design is a set of unitaries that is "evenly distributed" in the sense that the average of any t-th order polynomial over the design equals the average over the entire unitary group. In various fields -- e.g. quantum information theory -- one frequently encounters constructions that rely on matrices drawn uniformly at random from the unitary group. Often, it suffices to sample these matrices from a unitary t-design, for sufficiently high t. This results in more explicit…

## 42 Citations

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A comprehensive mathematical theory of the stabilizerRank and the related approximate stabilizer rank is developed and a suite of classical simulation algorithms with broader applicability and significantly improved performance over the previous state-of-the-art are presented.

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