Tradeoffs for Reliable Quantum Information Storage in Surface Codes and Color Codes

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Provided by: INRIA
Topic: Storage
Format: PDF
The generalization of Low Density Parity-Check (LDPC) codes to the quantum setting is far from evident. The fact that most of the constructions of quantum LDPC codes have bounded minimum distance illustrates this difficulty. Such a distance is not sufficient for a family of quantum LDPC codes. Topological constructions of quantum LDPC codes allow the user to obtain a growing minimum distance, but their dimension is generally small. The construction of families of non-zero rate quantum LDPC codes with unbounded minimum distance is highly non trivial.
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