Abstract
Quantum computing stands at the forefront of technological advancement, offering the promise of solving complex problems at unprecedented speeds. This potential, however, is hindered by the inherent susceptibility of quantum information to errors stemming from decoherence and quantum noise. Quantum error-correcting codes (QECCs) have emerged as a pivotal solution to safeguard quantum data, thereby unleashing the full potential of quantum computers.
This research paper focuses on the creation of QECCs by employing a concatenated code approach, which demonstrates the ability to significantly enhance the resilience of quantum information to errors. Our study delves into the fundamental principles of quantum error correction and explores the utilization of concatenated codes as an innovative strategy for improving the fault tolerance of quantum computing systems.
Keywords:
: Concatenated code; Quantum error-correcting codes; Construction of QECCs.
References
[1] A. R. Calderbank, E. M. Rains, P. M. Shor, and N. J. Sloane. Quantum error correction via codes over gf (4). IEEE Transactions on Information Theory, 44(4):1369-1387, 1998.
[2] C. Carlet, C. Güneri, F. Özbudak, and P. Solé. A new concatenated type construction for lcd codes and isometry codes. Discrete Mathematics, 341(3):830-835, 2018.
[3] H. Chen, S. Ling, and C. Xing. Asymptotically good quantum codes exceeding the ashikhmin-litsyn-tsfasman bound. IEEE Transactions on Information Theory, 47(5):2055-2058, 2001.
[4] K. Feng, S. Ling, and C. Xing. Asymptotic bounds on quantum codes from algebraic geometry codes. IEEE transactions on information theory, 52(3):986-991, 2006.
[5] M. Grassl, T. Beth, and M. Roetteler. On optimal quantum codes. International Journal of Quantum Information, 2(01):55-64, 2004.
[6] W. C. Huffman and V. Pless. Fundamentals of error-correcting codes. Cambridge university press, 2010.
[7] A. Ketkar, A. Klappenecker, S. Kumar, and P. K. Sarvepalli. Nonbinary stabilizer codes over finite fields. IEEE transactions on information theory, 52(11):4892-4914, 2006.
[8] A. Klappenecker and P. K. Sarvepalli. Clifford code constructions of operator quantum error-correcting codes. IEEE transactions on information theory, 54(12):5760-5765, 2008.
[9] G. G. La Guardia and R. Palazzo Jr. Constructions of new families of nonbinary css codes. Discrete mathematics, 310(21):2935-2945, 2010.
[10] R. Li and X. Li. Binary construction of quantum codes of minimum distance three and four. IEEE Transactions on Information Theory, 50(6):13311335,2004.
[11] S. Ling and C. Xing. Coding theory: a first course. Cambridge University Press, 2004.
[12] G. Seroussi and A. Lempel. Factorization of symmetric matrices and trace orthogonal bases in finite fields. SIAM Journal on Computing, 9(4):758767,1980.
[13] P. W. Shor. Scheme for reducing decoherence in quantum computer memory. Physical review A, 52(4):R2493, 1995.
[14] A. M. Steane. Simple quantum error-correcting codes. Physical Review A, 54(6):4741, 1996.
[15] X.-K. Xu, J. Zhang, and M. Small. Rich-club connectivity dominates assortativity and transitivity of complex networks. Physical Review E, 82(4):046117, 2010.
