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On the Exploration of Quantum Polar Stabilizer Codes and Quantum Stabilizer Codes with High Coding Rate [PDF]
EntropyInspired by classical polar codes, whose coding rate can asymptotically achieve the Shannon capacity, researchers are trying to find their analogs in the quantum information field, which are called quantum polar codes.
Zhengzhong Yi +3 more
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Stabilizer codes for open quantum systems [PDF]
Scientific Reports, 2023 The Lindblad master equation describes the evolution of a large variety of open quantum systems. An important property of some open quantum systems is the existence of decoherence-free subspaces.
Francisco Revson F. Pereira +2 more
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Quantum Stabilizer Codes and Classical Linear Codes [PDF]
Physical Review A, 1996 We show that within any quantum stabilizer code there lurks a classical binary linear code with similar error-correcting capabilities, thereby demonstrating new connections between quantum codes and classical codes.
A. Ekert +13 more
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Quantum stabilizer codes, lattices, and CFTs [PDF]
Journal of High Energy Physics, 2021 There is a rich connection between classical error-correcting codes, Euclidean lattices, and chiral conformal field theories. Here we show that quantum error-correcting codes, those of the stabilizer type, are related to Lorentzian lattices and non ...
Anatoly Dymarsky, Alfred Shapere
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Nonbinary quantum stabilizer codes [PDF]
IEEE Transactions on Information Theory, 2001 6 ...
A Ashikhmin, E Knill
exaly +3 more sources
Quantum LDPC Codes Based on Cocyclic Block Matrices [PDF]
Entropy, 2023 Motivated by a family of binary cocyclic block matrices over GF(2), we proposed a construction method to gain the stabilizer of long-length quantum error-correction codes (QECCs).
Yuan Li, Ying Guo
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Quantum Stabilizer Codes from Maximal Curves [PDF]
IEEE Transactions on Information Theory, 2013 A curve attaining the Hasse-Weil bound is called a maximal curve. Usually classical error-correcting codes obtained from a maximal curve have good parameters.
Jin, Lingfei
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Hardness of Decoding Quantum Stabilizer Codes [PDF]
IEEE Transactions on Information Theory, 2015 In this article we address the computational hardness of optimally decoding a quantum stabilizer code. Much like classical linear codes, errors are detected by measuring certain check operators which yield an error syndrome, and the decoding problem consists of determining the most likely recovery given the syndrome. The corresponding classical problem
Pavithran Iyer, David Poulin
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Universal Decoding of Quantum Stabilizer Codes via Classical Guesswork
IEEE Access, 2023 A universal decoding scheme is conceived for quantum stabilizer codes (QSCs) by appropriately adapting the ‘guessing random additive noise decoding’ (GRAND) philosophy of classical domain codes.
Daryus Chandra +5 more
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Stabilizer formalism for generalized concatenated quantum codes [PDF]
2013 IEEE International Symposium on Information Theory, 2013 The concept of generalized concatenated quantum codes (GCQC) provides a systematic way for constructing good quantum codes from short component codes. We introduce a stabilizer formalism for GCQCs, which is achieved by defining quantum coset codes.
Grassl, Markus +3 more
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