# Approximate unitary 3-designs from transvection Markov chains

@article{Tan2022ApproximateU3, title={Approximate unitary 3-designs from transvection Markov chains}, author={Xinyu Tan and Narayanan Rengaswamy and Robert Calderbank}, journal={Designs, Codes and Cryptography}, year={2022} }

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 that the automorphism group of classical $\mathbb{Z}_4$-linear Kerdock codes maps to a unitary $2$-design, which established a new classical-quantum connection via graph states. In this paper, we construct a Markov process that mixes this Kerdock $2$-design with symplectic transvections, and show that…

## One Citation

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

- Physics
- 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,…

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