References

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  1. Kschischang, F. R., Frey, B. J., & Loeliger, H.-A. (2001). Factor graphs and the sum-product algorithm. IEEE Transactions on Information Theory, 47(2), 498–519.
  2. Hagenauer, J., Offer, E., & Papke, L. (1996). Iterative decoding of binary block and convolutional codes. IEEE Transactions on Information Theory, 42(2), 429–445.
  3. Barenco, A., Bennett, C. H., Cleve, R., DiVincenzo, D. P., Margolus, N., Shor, P., Sleator, T., Smolin, J. A., & Weinfurter, H. (1995). Elementary gates for quantum computation. Physical Review A, 52(5), 3457.
  4. Wang, Y.-J., Sanders, B. C., Bai, B.-M., & Wang, X.-M. (2012). Enhanced feedback iterative decoding of sparse quantum codes. IEEE Transactions on Information Theory, 58(2), 1231–1241.
  5. Chen, J., Tanner, R. M., Jones, C., & Li, Y. (2005). Improved min-sum decoding algorithms for irregular LDPC codes. Proceedings. International Symposium on Information Theory, 2005. ISIT 2005., 449–453.
  6. Rigby, A., Olivier, J. C., & Jarvis, P. (2019). Modified belief propagation decoders for quantum low-density parity-check codes. Physical Review A, 100(1), 012330.
  7. Panteleev, P., & Kalachev, G. (2019). Degenerate Quantum LDPC Codes With Good Finite Length Performance. ArXiv Preprint ArXiv:1904.02703.
  8. MacKay, D. J. C., & Mac Kay, D. J. C. (2003). Information theory, inference and learning algorithms. Cambridge university press.
  9. Zarei, M. H., & Montakhab, A. (2018). Dual correspondence between classical spin models and quantum Calderbank-Shor-Steane states. Physical Review A, 98(1), 012337.
  10. Nielsen, M. A., & Chuang, I. (2002). Quantum computation and quantum information. AAPT.
  11. Muller, M., Rivas, A., Martinez, E. A., Nigg, D., Schindler, P., Monz, T., Blatt, R., & Martin-Delgado, M. A. (2016). Iterative Phase Optimization of Elementary Quantum Error Correcting Codes (Open Access, Publisher’s Version). Swansea University Swansea United Kingdom.
  12. Rosenblum, S., Reinhold, P., Mirrahimi, M., Jiang, L., Frunzio, L., & Schoelkopf, R. J. (2018). Fault-tolerant detection of a quantum error. Science, 361(6399), 266–270.
  13. Linke, N. M., Gutierrez, M., Landsman, K. A., Figgatt, C., Debnath, S., Brown, K. R., & Monroe, C. (2017). Fault-tolerant quantum error detection. Science Advances, 3(10), e1701074.
  14. Pokharel, B., Anand, N., Fortman, B., & Lidar, D. A. (2018). Demonstration of fidelity improvement using dynamical decoupling with superconducting qubits. Physical Review Letters, 121(22), 220502.
  15. Li, C.-K., Lyles, S., & Poon, Y.-T. (2019). Error correlation schemes for fully correlated quantum channels protecting both quantum and classical information. ArXiv Preprint ArXiv:1905.10228.
  16. Córcoles, A. D., Magesan, E., Srinivasan, S. J., Cross, A. W., Steffen, M., Gambetta, J. M., & Chow, J. M. (2015). Demonstration of a quantum error detection code using a square lattice of four superconducting qubits. Nature Communications, 6, 6979.
  17. Hu, L., Ma, Y., Cai, W., Mu, X., Xu, Y., Wang, W., Wu, Y., Wang, H., Song, Y. P., Zou, C.-L., & others. (2019). Quantum error correction and universal gate set operation on a binomial bosonic logical qubit. Nature Physics, 15(5), 503.
  18. Zeng, W., Ashikhmin, A., Woolls, M., & Pryadko, L. P. (2019). Quantum convolutional data-syndrome codes. 2019 IEEE 20th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC), 1–5. https://doi.org/10.1109/SPAWC.2019.8815487 DOI
  19. Chamberland, C., & Beverland, M. E. (2018). Flag fault-tolerant error correction with arbitrary distance codes. Quantum, 2(53), 10–22331.
  20. Preskill, J. (2018). Quantum Computing in the NISQ era and beyond. Quantum, 2, 79.
  21. Campbell, E. T., Terhal, B. M., & Vuillot, C. (2017). Roads towards fault-tolerant universal quantum computation. Nature, 549(7671), 172–179.
  22. Guth, L., & Lubotzky, A. (2014). Quantum error correcting codes and 4-dimensional arithmetic hyperbolic manifolds. Journal of Mathematical Physics, 55(8), 082202.
  23. Tillich, J.-P., & Zémor, G. (2013). Quantum LDPC codes with positive rate and minimum distance proportional to the square root of the blocklength. IEEE Transactions on Information Theory, 60(2), 1193–1202.
  24. Gottesman, D. (1998). The Heisenberg representation of quantum computers. ArXiv Preprint Quant-Ph/9807006.
  25. Zeng, W., & Pryadko, L. P. (2019). Higher-Dimensional Quantum Hypergraph-Product Codes with Finite Rates. Physical Review Letters, 122(23), 230501.
  26. Liu, Y.-H., & Poulin, D. (2018). Neural Belief-Propagation Decoders for Quantum Error-Correcting Codes. ArXiv Preprint ArXiv:1811.07835.
  27. Ashikhmin, A., Lai, C.-Y., & Brun, T. (2016). Correction of data and syndrome errors by stabilizer codes. ArXiv Preprint ArXiv:1602.01545.
  28. Yoder, T. J. (2019). Optimal quantum subsystem codes in 2-dimensions. ArXiv Preprint ArXiv:1901.06319.
  29. Leverrier, A., Tillich, J.-P., & Zémor, G. (2015). Quantum expander codes. Foundations of Computer Science (FOCS), 2015 IEEE 56th Annual Symposium On, 810–824.
  30. Fawzi, O., Grospellier, A., & Leverrier, A. (2018). Constant overhead quantum fault-tolerance with quantum expander codes. 2018 IEEE 59th Annual Symposium on Foundations of Computer Science (FOCS), 743–754.
  31. Hastings, M. B. (2016). Weight reduction for quantum codes. ArXiv Preprint ArXiv:1611.03790.
  32. Grassl, M., Shor, P. W., & Zeng, B. (2009). Generalized concatenation for quantum codes. Information Theory, 2009. ISIT 2009. IEEE International Symposium On, 953–957.
  33. Forney, G. D. (1965). Concatenated codes.
  34. Pyndiah, R. M. (1998). Near-optimum decoding of product codes: Block turbo codes. IEEE Transactions on Communications, 46(8), 1003–1010.
  35. Kahale, N., & Urbanke, R. (1998). On the minimum distance of parallel and serially concatenated codes. Information Theory, 1998. Proceedings. 1998 IEEE International Symposium On, 31.
  36. Huang, T. D. H., Chang, C.-Y., Zheng, Y.-X., Su, Y. T., & others. (2007). Product Codes and Parallel Concatenated Product Codes. WCNC, 94–99.
  37. Rankin, D. M., & Gulliver, T. A. (2001). Single parity check product codes. IEEE Transactions on Communications, 49(8), 1354–1362.
  38. Elias, P. (1954). Error-free coding. Transactions of the IRE Professional Group on Information Theory, 4(4), 29–37.
  39. Zeng, W., & Pryadko, L. P. (2018). Higher-dimensional quantum hypergraph-product codes. ArXiv Preprint ArXiv:1810.01519.
  40. Ashikhmin, A. E., Lai, C.-Y., & Brun, T. A. (2014). Robust quantum error syndrome extraction by classical coding. ISIT, 546–550.
  41. Ollivier, H., & Tillich, J.-P. (2006). Trellises for stabilizer codes: definition and uses. Physical Review A, 74(3), 032304.
  42. Viterbi, A. (1967). Error bounds for convolutional codes and an asymptotically optimum decoding algorithm. IEEE Transactions on Information Theory, 13(2), 260–269.
  43. Forney, G. D. (1973). The viterbi algorithm. Proceedings of the IEEE, 61(3), 268–278.
  44. Lin, S., & Costello, D. J. (2001). Error control coding. Pearson Education India.
  45. Johannesson, R., & Zigangirov, K. S. (2015). Fundamentals of convolutional coding (Vol. 15). John Wiley & Sons.
  46. Sidorenko, V., & Zyablov, V. (1994). Decoding of convolutional codes using a syndrome trellis. IEEE Transactions on Information Theory, 40(5), 1663–1666.
  47. Wolf, J. K., & Viterbi, A. J. (1996). On the weight distribution of linear block codes formed from convolutional codes. IEEE Transactions on Communications, 44(9), 1049–1051.
  48. Bocharova, I. E., & Kudryashov, B. D. (1997). Rational rate punctured convolutional codes for soft-decision Viterbi decoding. IEEE Transactions on Information Theory, 43(4), 1305–1313.
  49. Fossorier, M. P. C., Lin, S., & Costello, D. J. (1999). On the weight distribution of terminated convolutional codes. IEEE Transactions on Information Theory, 45(5), 1646–1648.
  50. Cedervall, M. L., & Johannesson, R. (1989). A fast algorithm for computing distance spectrum of convolutional codes. IEEE Transactions on Information Theory, 35(6), 1146–1159.
  51. Mason, S. J. (1956). Feedback theory: Further properties of signal flow graphs.
  52. Ashikhmin, A., Lai, C.-Y., & Brun, T. A. (2014). Robust quantum error syndrome extraction by classical coding. Information Theory (ISIT), 2014 IEEE International Symposium On, 546–550.
  53. Ding, B., Zhang, T., & Ge, G. (2015). New constructions of quantum MDS convolutional codes derived from generalized Reed-Solomon codes. ArXiv Preprint ArXiv:1511.01616.
  54. Gütschow, J. (2010). Representation of convolutional stabilizer codes as Clifford memory channels. CORNER, EU Project Number FP7-ICT-213681 (Internal Report).
  55. Tan, P., & Li, J. (2012). Quantum convolutional codes: Practical syndrome decoder. Information Sciences and Systems (CISS), 2012 46th Annual Conference On, 1–6.
  56. Babar, Z., Nguyen, H. V., Botsinis, P., Alanis, D., Chandra, D., Ng, S. X., Maunder, R. G., & Hanzo, L. (2016). Fully-Parallel Quantum Turbo Decoder. IEEE Access, 4, 6073–6085.
  57. La Guardia, G. G. (2016). Asymmetric quantum convolutional codes. Quantum Information Processing, 15(1), 167–183.
  58. Zhu, S., Wang, L., & Kai, X. (2015). New optimal quantum convolutional codes. International Journal of Quantum Information, 13(03), 1550019.
  59. Zhang, G., Chen, B., & Li, L. (2015). A construction of MDS quantum convolutional codes. International Journal of Theoretical Physics, 54(9), 3182–3194.
  60. Grassl, M. (2006). Convolutional and block quantum error-correcting codes. Information Theory Workshop, 2006. ITW’06 Chengdu. IEEE, 144–148.
  61. Wilde, M. M., Houshmand, M., & Hosseini-Khayat, S. (2011). Examples of minimal-memory, non-catastrophic quantum convolutional encoders. Information Theory Proceedings (ISIT), 2011 IEEE International Symposium On, 450–454.
  62. Tan, P., & Li, J. (2007). On construction of two classes of efficient quantum error-correction codes. Information Theory, 2007. ISIT 2007. IEEE International Symposium On, 2106–2110.
  63. Wang, X., Qian, H., Xiang, W., Xu, J., & Huang, H. (2013). An efficient ML decoder for tail-biting codes based on circular trap detection. IEEE Transactions on Communications, 61(4), 1212–1221.
  64. Chen, J., Li, J., Huang, Y., & Lin, J. (2015). Some families of asymmetric quantum codes and quantum convolutional codes from constacyclic codes. Linear Algebra and Its Applications, 475, 186–199.
  65. Chen, J., Li, J., Yang, F., & Huang, Y. (2015). Nonbinary quantum convolutional codes derived from negacyclic codes. International Journal of Theoretical Physics, 54(1), 198–209.
  66. Aly, S. A. (2008). On quantum and classical error control codes: constructions and applications. ArXiv Preprint ArXiv:0812.5104.
  67. Houshmand, M., Hosseini-Khayat, S., & Wilde, M. M. (2013). Minimal-memory, noncatastrophic, polynomial-depth quantum convolutional encoders. IEEE Transactions on Information Theory, 59(2), 1198–1210.
  68. Wilde, M. M. (2009). Logical operators of quantum codes. Physical Review A, 79(6), 062322.
  69. Aly, S. A. (2008). Asymmetric and symmetric subsystem BCH codes and beyond. ArXiv Preprint ArXiv:0803.0764.
  70. Gluesing-Luerssen, H., & Schneider, G. (2008). On the MacWilliams identity for convolutional codes. IEEE Transactions on Information Theory, 54(4), 1536–1550.
  71. Babar, Z., Ng, S. X., & Hanzo, L. (2015). EXIT-chart-aided near-capacity quantum turbo code design. IEEE Transactions on Vehicular Technology, 64(3), 866–875.
  72. La Guardia, G. G. (2014). On classical and quantum MDS-convolutional BCH codes. IEEE Transactions on Information Theory, 60(1), 304–312.
  73. Aly, S. A., Grassl, M., Klappenecker, A., Rotteler, M., & Sarvepalli, P. K. (2007). Quantum convolutional BCH codes. Information Theory, 2007. CWIT’07. 10th Canadian Workshop On, 180–183.
  74. Grassl, M., & Rotteler, M. (2007). Constructions of quantum convolutional codes. Information Theory, 2007. ISIT 2007. IEEE International Symposium On, 816–820.
  75. Tan, P., & Li, J. (2010). Efficient quantum stabilizer codes: LDPC and LDPC-convolutional constructions. IEEE Transactions on Information Theory, 56(1), 476–491.
  76. Brun, T. A., Devetak, I., & Hsieh, M.-H. (2014). Catalytic quantum error correction. IEEE Transactions on Information Theory, 60(6), 3073–3089.
  77. Wilde, M. M., & Brun, T. A. (2010). Entanglement-assisted quantum convolutional coding. Physical Review A, 81(4), 042333.
  78. La Guardia, G. G. (2009). Constructions of new families of nonbinary quantum codes. Physical Review A, 80(4), 042331.
  79. Poulin, D., & Chung, Y. (2008). On the iterative decoding of sparse quantum codes. ArXiv Preprint ArXiv:0801.1241.
  80. Ollivier, H., & Tillich, J.-P. (2003). Description of a quantum convolutional code. Physical Review Letters, 91(17), 177902.
  81. Poulin, D., Tillich, J.-P., & Ollivier, H. (2009). Quantum serial turbo codes. IEEE Transactions on Information Theory, 55(6), 2776–2798.
  82. Fujiwara, Y. (2014). Ability of stabilizer quantum error correction to protect itself from its own imperfection. Physical Review A, 90(6), 062304.
  83. Pelchat, E., & Poulin, D. (2013). Degenerate viterbi decoding. IEEE Transactions on Information Theory, 59(6), 3915–3921.
  84. Kovalev, A. A., Dumer, I., & Pryadko, L. P. (2011). Design of additive quantum codes via the code-word-stabilized framework. Physical Review A, 84(6), 062319.
  85. Forney, G. D., Grassl, M., & Guha, S. (2007). Convolutional and tail-biting quantum error-correcting codes. IEEE Transactions on Information Theory, 53(3), 865–880.
  86. Paler, A., Devitt, S., Nemoto, K., & Polian, I. (2014). Software-based pauli tracking in fault-tolerant quantum circuits. Design, Automation and Test in Europe Conference and Exhibition (DATE), 2014, 1–4.
  87. Lidar, D. A., & Biham, O. (1997). Simulating Ising spin glasses on a quantum computer. Physical Review E, 56(3), 3661.
  88. Breuckmann, N. P., Duivenvoorden, K., Michels, D., & Terhal, B. M. (2016). Local decoders for the 2D and 4D toric code. ArXiv Preprint ArXiv:1609.00510.
  89. Katzgraber, H. G., & Andrist, R. S. (2013). Stability of topologically-protected quantum computing proposals as seen through spin glasses. Journal of Physics: Conference Series, 473(1), 012019. http://stacks.iop.org/1742-6596/473/i=1/a=012019
  90. Poulin, D. (2005). Stabilizer Formalism for Operator Quantum Error Correction. Phys. Rev. Lett., 95(23), 230504. https://doi.org/10.1103/PhysRevLett.95.230504 DOI
  91. Bacon, D. (2006). Operator quantum error-correcting subsystems for self-correcting quantum memories. Phys. Rev. A, 73(1), 012340. https://doi.org/10.1103/PhysRevA.73.012340 DOI
  92. Dennis, E., Kitaev, A., Landahl, A., & Preskill, J. (2002). Topological quantum memory. J. Math. Phys., 43, 4452. http://dx.doi.org/10.1063/1.1499754
  93. Napp, J., & Preskill, J. (2013). Optimal Bacon-Shor codes. Quantum Information & Computation, 13(5-6), 490–510. http://www.rintonpress.com/xxqic13/qic-13-56/0490-0510.pdf
  94. Bravyi, S. (2011). Subsystem codes with spatially local generators. Physical Review A, 83(1), 012320.
  95. Nishimori, H. (1981). Internal energy, specific heat and correlation function of the bond-random Ising model. Progress of Theoretical Physics, 66(4), 1169–1181.
  96. Suchara, M., Bravyi, S., & Terhal, B. (2011). Constructions and noise threshold of topological subsystem codes. Journal of Physics A: Mathematical and Theoretical, 44(15), 155301.
  97. Katzgraber, H. G., & Andrist, R. S. (2013). Stability of topologically-protected quantum computing proposals as seen through spin glasses. Journal of Physics: Conference Series, 473(1), 012019.
  98. Kovalev, A. A., & Pryadko, L. P. (2013). Spin glass reflection of the decoding transition for quantum error correcting codes. ArXiv Preprint ArXiv:1311.7688.
  99. Dumer, I., Kovalev, A. A., & Pryadko, L. P. (2015). Thresholds for correcting errors, erasures, and faulty syndrome measurements in degenerate quantum codes. Physical Review Letters, 115(5), 050502.
  100. Calderbank, A. R., Rains, E. M., Shor, P. W., & Sloane, N. J. A. (1996). Quantum error correction via codes over GF (4). ArXiv Preprint Quant-Ph/9608006.
  101. Sourlas, N. (1989). Spin-glass models as error-correcting codes. Nature, 339(6227), 693–695.
  102. Wegner, F. J. (1971). Duality in generalized Ising models and phase transitions without local order parameters. Journal of Mathematical Physics, 12(10), 2259–2272.
  103. Nishimori, H. (2001). Statistical physics of spin glasses and information processing: an introduction (Vol. 111). Clarendon Press.
  104. Holsztynski, W., & Slawny, J. (1979). Phase transitions in ferromagnetic spin systems at low temperatures. Communications in Mathematical Physics, 66(2), 147–166. https://doi.org/10.1007/BF01197332 DOI
  105. Devitt, S. J., Munro, W. J., & Nemoto, K. (2013). Quantum error correction for beginners. Reports on Progress in Physics, 76(7), 076001. http://stacks.iop.org/0034-4885/76/i=7/a=076001
  106. Gallager, R. (1962). Low-density parity-check codes. IRE Transactions on Information Theory, 8(1), 21–28.
  107. Gottesman, D. (1997). Stabilizer codes and quantum error correction. ArXiv Preprint Quant-Ph/9705052.
  108. Gottesman, D. (2009). An introduction to quantum error correction and fault-tolerant quantum computation. Quantum Information Science and Its Contributions to Mathematics, Proceedings of Symposia in Applied Mathematics, 68, 13–58.
  109. Dumer, I., Kovalev, A., & Pryadko, L. (2017). Distance verification for classical and quantum LDPC codes. IEEE Transactions on Information Theory.
  110. Gottesman, D. (1996). Class of quantum error-correcting codes saturating the quantum Hamming bound. Physical Review A, 54(3), 1862.
  111. Shor, P. W. (1995). Scheme for reducing decoherence in quantum computer memory. Physical Review A, 52(4), R2493.
  112. Kitaev, A. Y. (2003). Fault-tolerant quantum computation by anyons. Annals of Physics, 303(1), 2–30.
  113. Dennis, E., Kitaev, A., Landahl, A., & Preskill, J. (2002). Topological quantum memory. Journal of Mathematical Physics, 43(9), 4452–4505.
  114. Bravyi, S. B., & Kitaev, A. Y. (1998). Quantum codes on a lattice with boundary. ArXiv Preprint Quant-Ph/9811052.
  115. Kubica, A., Yoshida, B., & Pastawski, F. (2015). Unfolding the color code. New Journal of Physics, 17(8), 083026.
  116. Bombı́n Héctor. (2010). Topological subsystem codes. Physical Review A, 81(3), 032301.
  117. Richardson, T. J., & Urbanke, R. L. (2001). The capacity of low-density parity-check codes under message-passing decoding. IEEE Transactions on Information Theory, 47(2), 599–618.
  118. Sipser, M., & Spielman, D. A. (1996). Expander codes. IEEE Transactions on Information Theory, 42(6), 1710–1722.
  119. MacKay, D. J. C. (1999). Good error-correcting codes based on very sparse matrices. IEEE Transactions on Information Theory, 45(2), 399–431.
  120. Berrou, C., Glavieux, A., & Thitimajshima, P. (1993). Near Shannon limit error-correcting coding and decoding: Turbo-codes. 1. Communications, 1993. ICC’93 Geneva. Technical Program, Conference Record, IEEE International Conference On, 2, 1064–1070.
  121. Gottesman, D. (2013). Fault-tolerant quantum computation with constant overhead. ArXiv Preprint ArXiv:1310.2984.
  122. Bravyi, S., & Hastings, M. B. (2014). Homological product codes. Proceedings of the Forty-Sixth Annual ACM Symposium on Theory of Computing, 273–282.
  123. Shor, P. W. (1994). Algorithms for quantum computation: Discrete logarithms and factoring. Foundations of Computer Science, 1994 Proceedings., 35th Annual Symposium On, 124–134.
  124. Shor, P. W. (1999). Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM Review, 41(2), 303–332.
  125. Grover, L. K. (1996). A fast quantum mechanical algorithm for database search. Proceedings of the Twenty-Eighth Annual ACM Symposium on Theory of Computing, 212–219.
  126. Grover, L. K. (2001). From Schrödinger’s equation to the quantum search algorithm. American Journal of Physics, 69(7), 769–777.
  127. Yoder, T. J., & Kim, I. H. (2016). The surface code with a twist. ArXiv Preprint ArXiv:1612.04795.
  128. Bombin, H., & Martin-Delgado, M. A. (2009). Quantum measurements and gates by code deformation. Journal of Physics A: Mathematical and Theoretical, 42(9), 095302.
  129. Bombin, H. (2011). Clifford gates by code deformation. New Journal of Physics, 13(4), 043005.
  130. Knill, E., & Laflamme, R. (1996). Concatenated quantum codes. ArXiv Preprint Quant-Ph/9608012.
  131. Crosswhite, G. M., & Bacon, D. (2011). Automated searching for quantum subsystem codes. Physical Review A, 83(2), 022307.
  132. Yoshida, B. (2012). Studying many-body physics through quantum coding theory [PhD thesis]. Massachusetts Institute of Technology.
  133. Filler, T. (2009). Simplification of the Belief propagation algorithm. online lecture note. http://dde.binghamton.edu/filler/mct/lectures/22/mct-lect22-v0.pdf
  134. Freeman, B., & Torralba, A. (2010). Lecture 7: graphical models and belief propagation. http://helper.ipam.ucla.edu/publications/gss2013/gss2013_11344.pdf