# Multiqubit Clifford groups are unitary 3-designs

@article{Zhu2017MultiqubitCG, title={Multiqubit Clifford groups are unitary 3-designs}, author={Huangjun Zhu}, journal={Physical Review A}, year={2017}, volume={96}, pages={062336} }

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, little is known about unitary $t$-designs with $t\geq3$ in the literature. We show that the multiqubit Clifford group in any even prime-power dimension is not only a unitary 2-design, but also a 3-design. Moreover, it is a minimal 3-design except for dimension~4. As an immediate consequence, any orbit…

## 98 Citations

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