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High-rate quantum low-density parity-check codes assisted by reliable qubits

Yuichiro Fujiwara, Alexander Gruner and Peter Vandendriessche (UGent)
(2015) IEEE TRANSACTIONS ON INFORMATION THEORY. 61(4). p.1860-1878
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Abstract
Quantum error correction is an important building block for reliable quantum information processing. A challenging hurdle in the theory of quantum error correction is that it is significantly more difficult to design error-correcting codes with desirable properties for quantum information processing than for traditional digital communications and computation. A typical obstacle to constructing a variety of strong quantum error-correcting codes is the complicated restrictions imposed on the structure of a code. Recently, promising solutions to this problem have been proposed in quantum information science, where in principle any binary linear code can be turned into a quantum error-correcting code by assuming a small number of reliable quantum bits. This paper studies how best to take advantage of these latest ideas to construct desirable quantum error-correcting codes of very high information rate. Our methods exploit structured high-rate low-density parity-check codes available in the classical domain and provide quantum analogues that inherit their characteristic low decoding complexity and high error correction performance even at moderate code lengths. Our approach to designing high-rate quantum error-correcting codes also allows for making direct use of other major syndrome decoding methods for linear codes, making it possible to deal with a situation where promising quantum analogues of low-density parity-check codes are difficult to find.
Keywords
Quantum error correction, low-density parity-check code, combinatorial design, entanglement-assisted quantum error-correcting code, STEINER TRIPLE-SYSTEMS, ERROR-CORRECTING CODES, TRAPPING SETS, ENTANGLEMENT, DESIGNS, CONSTRUCTION, REALIZATION, CIRCUITS, MATRICES, RANK

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MLA
Fujiwara, Yuichiro, et al. “High-Rate Quantum Low-Density Parity-Check Codes Assisted by Reliable Qubits.” IEEE TRANSACTIONS ON INFORMATION THEORY, vol. 61, no. 4, 2015, pp. 1860–78, doi:10.1109/tit.2015.2398436.
APA
Fujiwara, Y., Gruner, A., & Vandendriessche, P. (2015). High-rate quantum low-density parity-check codes assisted by reliable qubits. IEEE TRANSACTIONS ON INFORMATION THEORY, 61(4), 1860–1878. https://doi.org/10.1109/tit.2015.2398436
Chicago author-date
Fujiwara, Yuichiro, Alexander Gruner, and Peter Vandendriessche. 2015. “High-Rate Quantum Low-Density Parity-Check Codes Assisted by Reliable Qubits.” IEEE TRANSACTIONS ON INFORMATION THEORY 61 (4): 1860–78. https://doi.org/10.1109/tit.2015.2398436.
Chicago author-date (all authors)
Fujiwara, Yuichiro, Alexander Gruner, and Peter Vandendriessche. 2015. “High-Rate Quantum Low-Density Parity-Check Codes Assisted by Reliable Qubits.” IEEE TRANSACTIONS ON INFORMATION THEORY 61 (4): 1860–1878. doi:10.1109/tit.2015.2398436.
Vancouver
1.
Fujiwara Y, Gruner A, Vandendriessche P. High-rate quantum low-density parity-check codes assisted by reliable qubits. IEEE TRANSACTIONS ON INFORMATION THEORY. 2015;61(4):1860–78.
IEEE
[1]
Y. Fujiwara, A. Gruner, and P. Vandendriessche, “High-rate quantum low-density parity-check codes assisted by reliable qubits,” IEEE TRANSACTIONS ON INFORMATION THEORY, vol. 61, no. 4, pp. 1860–1878, 2015.
@article{8531964,
  abstract     = {{Quantum error correction is an important building block for reliable quantum information processing. A challenging hurdle in the theory of quantum error correction is that it is significantly more difficult to design error-correcting codes with desirable properties for quantum information processing than for traditional digital communications and computation. A typical obstacle to constructing a variety of strong quantum error-correcting codes is the complicated restrictions imposed on the structure of a code. Recently, promising solutions to this problem have been proposed in quantum information science, where in principle any binary linear code can be turned into a quantum error-correcting code by assuming a small number of reliable quantum bits. This paper studies how best to take advantage of these latest ideas to construct desirable quantum error-correcting codes of very high information rate. Our methods exploit structured high-rate low-density parity-check codes available in the classical domain and provide quantum analogues that inherit their characteristic low decoding complexity and high error correction performance even at moderate code lengths. Our approach to designing high-rate quantum error-correcting codes also allows for making direct use of other major syndrome decoding methods for linear codes, making it possible to deal with a situation where promising quantum analogues of low-density parity-check codes are difficult to find.}},
  author       = {{Fujiwara, Yuichiro and Gruner, Alexander and Vandendriessche, Peter}},
  issn         = {{0018-9448}},
  journal      = {{IEEE TRANSACTIONS ON INFORMATION THEORY}},
  keywords     = {{Quantum error correction,low-density parity-check code,combinatorial design,entanglement-assisted quantum error-correcting code,STEINER TRIPLE-SYSTEMS,ERROR-CORRECTING CODES,TRAPPING SETS,ENTANGLEMENT,DESIGNS,CONSTRUCTION,REALIZATION,CIRCUITS,MATRICES,RANK}},
  language     = {{eng}},
  number       = {{4}},
  pages        = {{1860--1878}},
  title        = {{High-rate quantum low-density parity-check codes assisted by reliable qubits}},
  url          = {{http://doi.org/10.1109/tit.2015.2398436}},
  volume       = {{61}},
  year         = {{2015}},
}
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