Concatenated Quantum Codes Constructible in Polynomial Time: Efficient Decoding and Error Correction
Mitsuru Hamada
备注：
16 pages, 3 figures. Ver.4: Title changed. Ver.3: Due to a request of the AE of the journal, the present version has become a combination of (thoroughly revised) quant-ph/0610194 and the former quant-ph/0610195. Problem formulations of polynomial complexity are strictly followed. An erroneous instance of a lower bound on minimum distance was removed
发表信息：
IEEE Trans. on Information Theory, vol. 54, no. 12, pp. 5689--5704, 2008
A method for concatenating quantum error-correcting codes is presented. The method is applicable to a wide class of quantum error-correcting codes known as Calderbank-Shor-Steane (CSS) codes. As a result, codes that achieve a high rate in the Shannon theoretic sense and that are decodable in polynomial time are presented. The rate is the highest among those known to be achievable by CSS codes. Moreover, the best known lower bound on the greatest minimum distance of codes constructible in polynomial time is improved for a wide range.
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University of Sydney（悉尼大学）；Chalmers University of Technology（查尔姆斯理工大学）；Freie Universität Berlin（柏林自由大学）；Helmholtz-Zentrum Berlin für Materialien und Energie（柏林亥姆霍兹材料能源中心）；École Normale Supérieure, PSL University（巴黎高等师范学院，PSL大学）
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Exact Maximum Likelihood Decoding beyond Treewidth via Rank-Decomposition Dynamic Programming
Centre for Quantum Technologies, National University of Singapore（新加坡国立大学量子技术中心）；Science, Mathematics and Technology Cluster, Singapore University of Technology and Design（新加坡科技设计大学科学、数学与技术集群）
We present and analyze protocols for fault-tolerant quantum computing using color codes. We present circuit-level schemes for extracting the error syndrome of these codes fault-tolerantly. We further present an integer-program-based decoding algorithm for identifying the most likely error given the syndrome. We simulated our syndrome extraction and decoding algorithms against three physically-motivated noise models using Monte Carlo methods, and used the simulations to estimate the corresponding accuracy thresholds for fault-tolerant quantum error correction. We also used a self-avoiding walk …
Quantum error correction allows to actively correct errors occurring in a quantum computation when the noise is weak enough. To make this error correction competitive information about the specific noise is required. Traditionally, this information is obtained by benchmarking the device before operation. We address the question of what can be learned from only the measurements done during decoding. Such estimation of noise models was proposed for surface codes, exploiting their special structure, and in the limit of low error rates also for other codes. However, so far it has been unclear unde…
Entropic Rigidity in Quantum Memories: How Geometry and Algebra Control the Onset of Degeneracy Corrections
Beijing Academy of Quantum Information Sciences（北京量子信息科学研究院）；Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所）；University of Chinese Academy of Sciences（中国科学院大学）
