Hadamard-Free Circuits Expose the Structure of the Clifford Group

@article{Bravyi2021HadamardFreeCE,
  title={Hadamard-Free Circuits Expose the Structure of the Clifford Group},
  author={S. Bravyi and D. Maslov},
  journal={IEEE Transactions on Information Theory},
  year={2021},
  volume={67},
  pages={4546-4563}
}
  • S. Bravyi, D. Maslov
  • Published 2021
  • Computer Science, Physics, Mathematics
  • IEEE Transactions on Information Theory
The Clifford group plays a central role in quantum randomized benchmarking, quantum tomography, and error correction protocols. Here we study the structural properties of this group. We show that any Clifford operator can be uniquely written in the canonical form <inline-formula> <tex-math notation="LaTeX">$F_{1}HSF_{2}$ </tex-math></inline-formula>, where <inline-formula> <tex-math notation="LaTeX">$H$ </tex-math></inline-formula> is a layer of Hadamard gates, <inline-formula> <tex-math… Expand

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