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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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