Results 11 to 20 of about 1,386 (248)
Nonadditive Quantum Error-Correcting Code [PDF]
Physical Review Letters, 2008 We report the first nonadditive quantum error-correcting code, namely, a $((9,12,3))$ code which is a 12-dimensional subspace within a 9-qubit Hilbert space, that outperforms the optimal stabilizer code of the same length by encoding more levels while correcting arbitrary single-qubit errors.
Yu, S., Chen, Q., Lai, C.H., Oh, C.H.
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Entropy of a Quantum Error Correction Code [PDF]
Open Systems & Information Dynamics, 2008 We define and investigate the notion of entropy for quantum error correcting codes. The entropy of a code for a given quantum channel has a number of equivalent realisations, such as through the coefficients associated with the Knill-Laflamme conditions and the entropy exchange computed with respect to any initial state supported on the code.
David W. Kribs +2 more
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Theory of quantum error-correcting codes [PDF]
Physical Review A, 1997 34 pages in LaTex, 1 figures, the paper is also available at http://qso.lanl.gov/qc/
Knill, Emanuel, Laflamme, Raymond
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An explicit construction of quantum codes from one-generator generalized quasi-cyclic codes [PDF]
MATEC Web of Conferences, 2021 In this paper, we take advantage of a class of one-generator generalized quasi-cyclic (GQC) codes of index 2 to construct quantum error-correcting codes.
Yao Yu, Ma Yuena, Li Husheng, Lv Jingjie
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Asymmetric quantum error-correcting codes [PDF]
Physical Review A, 2007 The noise in physical qubits is fundamentally asymmetric: in most devices, phase errors are much more probable than bit flips. We propose a quantum error correcting code which takes advantage of this asymmetry and shows good performance at a relatively small cost in redundancy, requiring less than a doubling of the number of physical qubits for error ...
Ioffe, Lev, Mezard, Marc
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Homological error correction: Classical and quantum codes [PDF]
Journal of Mathematical Physics, 2007 We prove several theorems characterizing the existence of homological error correction codes both classically and quantumly. Not every classical code is homological, but we find a family of classical homological codes saturating the Hamming bound. In the quantum case, we show that for nonorientable surfaces it is impossible to construct homological ...
Bombin, H., Martin-Delgado, M. A.
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Quantum Convolutional Error Correction Codes [PDF]
Physical Review A, 1998 I report two general methods to construct quantum convolutional codes for quantum registers with internal $N$ states. Using one of these methods, I construct a quantum convolutional code of rate 1/4 which is able to correct one general quantum error for every eight consecutive quantum registers.
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A combinatorial approach to quantum error correcting codes [PDF]
Discrete Mathematics, Algorithms and Applications, 2014 Motivated from the theory of quantum error correcting codes, we investigate a combinatorial problem that involves a symmetric n-vertices colorable graph and a group of operations (coloring rules) on the graph: find the minimum sequence of operations that maps between two given graph colorings.
German Luna +3 more
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Error Correction of Quantum Reference Frame Information
PRX Quantum, 2021 The existence of quantum error-correcting codes is one of the most counterintuitive and potentially technologically important discoveries of quantum-information theory.
Patrick Hayden +3 more
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Quantum error correction with the semion code
New Journal of Physics, 2019 Abstract We present a full quantum error correcting procedure with the semion code: an off-shell extension of the double-semion model. We construct open-string operators that recover the quantum memory from arbitrary errors and closed-string operators that implement the basic logical operations for information processing. Physically, the
Dauphinais, Guillaume +3 more
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