skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: NP-hardness of decoding quantum error-correction codes

Abstract

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.

Authors:
 [1];  [2]
  1. Statistical Laboratory, University of Cambridge, Cambridge, United Kingdom. (United Kingdom)
  2. Department of Computer Science, University of Tokyo, Tokyo, Japan. (Japan)
Publication Date:
OSTI Identifier:
21546748
Resource Type:
Journal Article
Journal Name:
Physical Review. A
Additional Journal Information:
Journal Volume: 83; Journal Issue: 5; Other Information: DOI: 10.1103/PhysRevA.83.052331; (c) 2011 American Institute of Physics; Journal ID: ISSN 1050-2947
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGORITHMS; COMPUTER CODES; CORRECTIONS; CRYPTOGRAPHY; ERRORS; QUANTUM STATES; MATHEMATICAL LOGIC

Citation Formats

Hsieh, Min-Hsiu, and Le Gall, Francois. NP-hardness of decoding quantum error-correction codes. United States: N. p., 2011. Web. doi:10.1103/PHYSREVA.83.052331.
Hsieh, Min-Hsiu, & Le Gall, Francois. NP-hardness of decoding quantum error-correction codes. United States. https://doi.org/10.1103/PHYSREVA.83.052331
Hsieh, Min-Hsiu, and Le Gall, Francois. 2011. "NP-hardness of decoding quantum error-correction codes". United States. https://doi.org/10.1103/PHYSREVA.83.052331.
@article{osti_21546748,
title = {NP-hardness of decoding quantum error-correction codes},
author = {Hsieh, Min-Hsiu and Le Gall, Francois},
abstractNote = {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.},
doi = {10.1103/PHYSREVA.83.052331},
url = {https://www.osti.gov/biblio/21546748}, journal = {Physical Review. A},
issn = {1050-2947},
number = 5,
volume = 83,
place = {United States},
year = {Sun May 15 00:00:00 EDT 2011},
month = {Sun May 15 00:00:00 EDT 2011}
}