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Decoding sparse quantum codes can be accomplished by syndrome-based decoding through using the sum-product algorithm (SPA). We significantly improve this decoding scheme by developing a new feedback adjustment strategy for the standard SPA. In our feedback strategy, we exploit not only the syndrome but also the values of the frustrated checks on individual qubits of the code and the channel model. Consequently, our decoding algorithm, on the one hand, can break the symmetric degeneracy, and on the other hand, can feed back more useful information to the SPA decoder to help the decoder determine a valid output, thereby significantly improving the decoding ability of the decoder. Moreover, our algorithm does not increase the measurement complexity compared with the previous method, but takes full advantage of the measured information.
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Keywords:
- sparse quantum codes /
- sum-product algorithm /
- quantum error-correcting codes /
- quantum information
[1] Liu W J, Chen H W, Ma T H, Li Z Q, Liu Z H, Hu W B 2009 Chin. Phys. B 18 4105
[2] Wang X B 2004 Phys. Rev. Lett. 92 077902
[3] Li C Y, Li X H, Deng F G, Zhou H Y 2008 Chin. Phys. B 17 2352
[4] Gallager R G 1962 IRE Trans. Inform. Theory 8 21
[5] Li Z, Xing L J 2008 Acta Phys. Sin. 57 28 (in Chinese) [李 卓、 邢莉娟 2008 57 28]
[6] MacKay D J C, Mitchison G J, McFadden P L 2004 IEEE Trans. Inform. Theory 50 2315
[7] Wang Y J, Bai B M, Zhao W B, Wang X M 2009 Int. J. Quantum Inf. 7 1373
[8] Li Y, Zeng G H, Moon H L 2009 Chin. Phys. B 18 4154
[9] Poulin D, Chung Y 2008 Quantum Inform. Comput. 8 987
[10] Camara T, Ollivier H, Tillich J P 2007 Proceedings of the International Symposium on Information Theory Nice, France, June 2007 p811
[11] Gottesman D 1996 Phys. Rev. A 54 1862
[12] Calderbank A R, Rains E M, Shor P W, Sloane N J A 1997 Phys. Rev. Lett. 78 405
[13] Steane A M 1996 Phys. Rev. Lett. 77 793
[14] Calderbank A R, Shor P W 1996 Phys. Rev. A 54 1098
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[1] Liu W J, Chen H W, Ma T H, Li Z Q, Liu Z H, Hu W B 2009 Chin. Phys. B 18 4105
[2] Wang X B 2004 Phys. Rev. Lett. 92 077902
[3] Li C Y, Li X H, Deng F G, Zhou H Y 2008 Chin. Phys. B 17 2352
[4] Gallager R G 1962 IRE Trans. Inform. Theory 8 21
[5] Li Z, Xing L J 2008 Acta Phys. Sin. 57 28 (in Chinese) [李 卓、 邢莉娟 2008 57 28]
[6] MacKay D J C, Mitchison G J, McFadden P L 2004 IEEE Trans. Inform. Theory 50 2315
[7] Wang Y J, Bai B M, Zhao W B, Wang X M 2009 Int. J. Quantum Inf. 7 1373
[8] Li Y, Zeng G H, Moon H L 2009 Chin. Phys. B 18 4154
[9] Poulin D, Chung Y 2008 Quantum Inform. Comput. 8 987
[10] Camara T, Ollivier H, Tillich J P 2007 Proceedings of the International Symposium on Information Theory Nice, France, June 2007 p811
[11] Gottesman D 1996 Phys. Rev. A 54 1862
[12] Calderbank A R, Rains E M, Shor P W, Sloane N J A 1997 Phys. Rev. Lett. 78 405
[13] Steane A M 1996 Phys. Rev. Lett. 77 793
[14] Calderbank A R, Shor P W 1996 Phys. Rev. A 54 1098
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