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Quantum Error Correction Fault Tolerance
Quantum Foundations
On the Hardnesses of Several Quantum Decoding Problems
arXiv
Authors: Kao-Yueh Kuo, Chung-Chin Lu
Year
2013
Paper ID
8438
Status
Preprint
Abstract Read
~2 min
Abstract Words
98
Citations
N/A
Abstract
We classify the time complexities of three important decoding problems for quantum stabilizer codes. First, regardless of the channel model, quantum bounded distance decoding is shown to be NP-hard, like what Berlekamp, McEliece and Tilborg did for classical binary linear codes in 1978. Then over the depolarizing channel, the decoding problems for finding a most likely error and for minimizing the decoding error probability are also shown to be NP-hard. Our results indicate that finding a polynomial-time decoding algorithm for general stabilizer codes may be impossible, but this, on the other hand, strengthens the foundation of quantum code-based cryptography.
Why This Paper Matters
- This paper contributes to the Quantum Foundations research area in the Quantum Articles archive.
- It adds a 2013 reference point for readers tracking recent quantum research.
- We classify the time complexities of three important decoding problems for quantum stabilizer codes.
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