Results 11 to 20 of about 2,043 (254)
Foliated Quantum Error-Correcting Codes [PDF]
Physical Review Letters, 2016 We show how to construct a large class of quantum error-correcting codes, known as Calderbank-Steane-Shor codes, from highly entangled cluster states. This becomes a primitive in a protocol that foliates a series of such cluster states into a much larger cluster state, implementing foliated quantum error correction.
Bolt, A. +3 more
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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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Optimal universal quantum error correction via bounded reference frames
Physical Review Research, 2022 Error correcting codes with a universal set of transversal gates are a desideratum for quantum computing. Such codes, however, are ruled out by the Eastin-Knill theorem.
Yuxiang Yang +4 more
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An Application of p-Fibonacci Error-Correcting Codes to Cryptography
Mathematics, 2021 In addition to their usefulness in proving one’s identity electronically, identification protocols based on zero-knowledge proofs allow designing secure cryptographic signature schemes by means of the Fiat–Shamir transform or other similar constructs ...
Emanuele Bellini +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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Quantum error correction and large $N$
SciPost Physics, 2021 In recent years quantum error correction (QEC) has become an important part of AdS/CFT. Unfortunately, there are no field-theoretic arguments about why QEC holds in known holographic systems.
Alexey Milekhin
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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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