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Quantum stabilizer codes and beyond
2022The importance of quantum error correction in paving the way to build a practical quantum computer is no longer in doubt. Despite the large body of literature in quantum coding theory, many important questions, especially those centering on the issue of "good codes" are unresolved.
Ivan B Djordjevic
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Quantum Circuits for Stabilizer Codes
2005 IEEE International Symposium on Circuits and Systems, 2005Stabilizer codes constitute an important class of quantum error correction codes. This paper examines the sign-generation circuit based on controlled phase flip (Z) gates, and presents quantum circuits for efficient encoding and decoding of the [5,1,3] stabilizer code.
Chien-Hsing Wu 0002 +2 more
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Optimization of Quantum Circuits for Stabilizer Codes
IEEE Transactions on Circuits and Systems I: Regular PapersKeshab K Parhi
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LP Decoding of Quantum Stabilizer Codes
2018 IEEE International Symposium on Information Theory (ISIT), 2018Linear programming (LP) decoding is an approach for decoding classical codes, especially for decoding low-density parity-check codes. In this paper, we initiate the study of LP decoding for stabilizer quantum error-correction codes. In particular, we formulate different polytope relaxations, we introduce pseudoweights to analyze the effect of ...
July X. Li, Pascal O. Vontobel
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Quantum stabilizer codes from difference sets
2013 IEEE International Symposium on Information Theory, 2013In this work we have developed a new method to construct general quantum stabilizer codes of variable block size by adopting the notion of a difference set. The proposed method comprises an efficient way to obtain the difference set, and from that set the construction of a quantum stabilizer code, which we refer to as a DSS (Difference Set Stabilizer ...
Yixuan Xie +2 more
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Generate Seed Generators for Quantum Stabilizer Codes
2009 WRI World Congress on Computer Science and Information Engineering, 2009Stabilizer is a very important description method of quantum error-correcting code. Before to generate quantum codes based on the stabilizer it needs to generate seed generator. The problem of finding seed generators is transformed into the problems of determining linear independence or linear dependence of vectors and finding the solutions of ...
Fangying Xiao, Hanwu Chen
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Construction of minimal trellises for quantum stabilizer codes
Science China Information Sciences, 2012The size of vertex set of quantum trellises affects the efficiency of decoding algorithms, which can be improved by reducing the number of vertices. Based on the standard check matrix of stabilizer codes, an algorithm to construct trellis-oriented generators for quantum stabilizer codes is presented.
Fangying Xiao, Hanwu Chen
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Factor-graph representations of stabilizer quantum codes
2016 54th Annual Allerton Conference on Communication, Control, and Computing (Allerton), 2016We study normal factor graph (NFG) representations of stabilizer quantum error-correction codes (QECCs), in particular NFG representations of the stabilizer label code and the normalizer label code associated with a stabilizer QECC. The structure of the NFGs we are using is such that the (symplectic) self-orthogonality constraint that stabilizer label ...
July X. Li, Pascal O. Vontobel
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DETERMINISTIC QUANTUM KEY DISTRIBUTION USING STABILIZER QUANTUM CODE
International Journal of Quantum Information, 2007Employing a stabilizer quantum code (SQC), a quantum deterministic communication scheme is proposed to transmit secret messages with unconditional security. The proposed scheme has great capacity to transmit the messages since the utilized SQC can encode more than one qubit of the secret message in the message transmission phase for one scheme run. By
Guo, Ying, Zeng, Guihua
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