NP-hardness of decoding quantum error-correction codes
- Statistical Laboratory, University of Cambridge, Cambridge, United Kingdom. (United Kingdom)
- Department of Computer Science, University of Tokyo, Tokyo, Japan. (Japan)
Although the theory of quantum error correction is intimately related to classical coding theory and, in particular, one can construct quantum error-correction codes (QECCs) from classical codes with the dual-containing property, this does not necessarily imply that the computational complexity of decoding QECCs is the same as their classical counterparts. Instead, decoding QECCs can be very much different from decoding classical codes due to the degeneracy property. Intuitively, one expects degeneracy would simplify the decoding since two different errors might not and need not be distinguished in order to correct them. However, we show that general quantum decoding problem is NP-hard regardless of the quantum codes being degenerate or nondegenerate. This finding implies that no considerably fast decoding algorithm exists for the general quantum decoding problems and suggests the existence of a quantum cryptosystem based on the hardness of decoding QECCs.
- OSTI ID:
- 21546748
- Journal Information:
- Physical Review. A, Vol. 83, Issue 5; Other Information: DOI: 10.1103/PhysRevA.83.052331; (c) 2011 American Institute of Physics; ISSN 1050-2947
- Country of Publication:
- United States
- Language:
- English
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