#  Seminar, Zhengwei Liu (Tsinghua University), Quantized Graphs and Quantum Error Correction 

 



####  calendar\_today Date and Time 

 **February 4, 2020** 

 03:30PM - 03:30PM EST 

####  pin\_drop Location 

 **Jefferson 356**  



 

 



 

   ![Zhengwei Liu](/sites/g/files/omnuum6611/files/styles/hwp_1_1__360x360_scale/public/mathpicture/files/zhengwei_2020.jpg?itok=z7OTXRiR) 

 

 **Title:** Quantized Graphs and Quantum Error Correction

 **Abstract:** 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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