Tradeoffs for reliable quantum information storage in 2D systems

@article{Bravyi2010TradeoffsFR,
  title={Tradeoffs for reliable quantum information storage in 2D systems},
  author={Sergey Bravyi and David Poulin and Barbara M. Terhal},
  journal={Physical review letters},
  year={2010},
  volume={104 5},
  pages={050503}
}
We ask whether there are fundamental limits on storing quantum information reliably in a bounded volume of space. To investigate this question, we study quantum error correcting codes specified by geometrically local commuting constraints on a 2D lattice of finite-dimensional quantum particles. For these 2D systems, we derive a tradeoff between the number of encoded qubits k, the distance of the code d, and the number of particles n. It is shown that kd{2}=O(n) where the coefficient in O(n… CONTINUE READING

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