• Corpus ID: 238215341

Bounds on stabilizer measurement circuits and obstructions to local implementations of quantum LDPC codes

@article{Delfosse2021BoundsOS,
  title={Bounds on stabilizer measurement circuits and obstructions to local implementations of quantum LDPC codes},
  author={Nicolas Delfosse and Michael Beverland and Maxime Tremblay},
  journal={ArXiv},
  year={2021},
  volume={abs/2109.14599}
}
In this work we establish lower bounds on the size of Clifford circuits that measure a family of commuting Pauli operators. Our bounds depend on the interplay between a pair of graphs: the Tanner graph of the set of measured Pauli operators, and the connectivity graph which represents the qubit connections required to implement the circuit. For local-expander quantum codes, which are promising for low-overhead quantum error correction, we prove that any syndrome extraction circuit implemented… 

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1Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany 2Department of Physics and Astronomy, University of Sheffield, Sheffield S3 7RH, United Kingdom 3Centre for

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