# 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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