Quantized Graphs and Quantum Error Correction

Zhengwei Liu au Mathematical Science Center and Department of Mathematics, Tsinghua University, Beijing 100084, China

Mathematical Physics Quantum Algebra arXiv subject: High Energy Physics - Theory (hep-th) mathscidoc:2207.22008

2019.10
Graph theory is important in information theory. We introduce a quantization process on graphs and apply the quantized graphs in quantum information. The quon language provides a mathematical theory to study such quantized graphs in a general framework. We give a new method to construct graphical quantum error correcting codes on quantized graphs and characterize all optimal ones. We establish a further connection to geometric group theory and construct quantum low-density parity-check stabilizer codes on the Cayley graphs of groups. Their logical qubits can be encoded by the ground states of newly constructed exactly solvable models with translation-invariant local Hamiltonians. Moreover, the Hamiltonian is gapped in the large limit when the underlying group is infinite.
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@inproceedings{zhengwei2019quantized,
  title={Quantized Graphs and Quantum Error Correction},
  author={Zhengwei Liu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220707161144095018581},
  year={2019},
}
Zhengwei Liu. Quantized Graphs and Quantum Error Correction. 2019. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220707161144095018581.
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