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50
On quantum and classical BCH codes,” in
 Proc. 2007 IEEE Intl. Symp. Inform. Theory,
, 2007
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An introduction to quantum error correction and faulttolerant quantum computation
, 2009
"... Abstract. Quantum states are very delicate, so it is likely some sort of quantum error correction will be necessary to build reliable quantum computers. ..."
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Cited by 25 (2 self)
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Abstract. Quantum states are very delicate, so it is likely some sort of quantum error correction will be necessary to build reliable quantum computers.
A class of quantum LDPC codes constructed from finite geometries
 in Proc. IEEE GlobeCom
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Clifford code constructions of operator quantum errorcorrecting codes
, 2006
"... Recently, operator quantum errorcorrecting codes have been proposed to unify and generalize decoherence free subspaces, noiseless subsystems, and quantum errorcorrecting codes. This note introduces a natural construction of such codes in terms of Clifford codes, an elegant generalization of stabil ..."
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Cited by 12 (5 self)
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Recently, operator quantum errorcorrecting codes have been proposed to unify and generalize decoherence free subspaces, noiseless subsystems, and quantum errorcorrecting codes. This note introduces a natural construction of such codes in terms of Clifford codes, an elegant generalization of stabilizer codes due to Knill. Charactertheoretic methods are used to derive a simple method to construct operator quantum errorcorrecting codes from any classical additive code over a finite field, which obviates the need for selforthogonal codes. Introduction. One of the main challenges in quantum information processing is the protection of the quantum information against various sources of errors. A possible remedy is given by encoding the quantum information in a subspace C of the state space H of the quantum system. If such a quantum errorcorrecting code C is wellchosen, then many errors can be
Subsystem codes
 44th Annual Allerton Conference on Communication, Control, and Computing
, 2006
"... Abstract — We investigate various aspects of operator quantum errorcorrecting codes or, as we prefer to call them, subsystem codes. We give various methods to derive subsystem codes from classical codes. We give a proof for the existence of subsystem codes using a counting argument similar to the q ..."
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Cited by 9 (8 self)
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Abstract — We investigate various aspects of operator quantum errorcorrecting codes or, as we prefer to call them, subsystem codes. We give various methods to derive subsystem codes from classical codes. We give a proof for the existence of subsystem codes using a counting argument similar to the quantum GilbertVarshamov bound. We derive linear programming bounds and other upper bounds. We answer the question whether or not there exist [[n, n −2d+2, r> 0, d]]q subsystem codes. Finally, we compare stabilizer and subsystem codes with respect to the required number of syndrome qudits. I.
Boolean functions, projection operators, and quantum error correcting codes
 IEEE Trans. Inf. Theory
"... AbstractThis paper describes a common mathematical framework for the design of additive and nonadditive Quantum Error Correcting Codes. It is based on a correspondence between boolean functions and projection operators. The new framework extends to operator quantum error correcting codes. I. ..."
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Cited by 8 (1 self)
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AbstractThis paper describes a common mathematical framework for the design of additive and nonadditive Quantum Error Correcting Codes. It is based on a correspondence between boolean functions and projection operators. The new framework extends to operator quantum error correcting codes. I.
Graphbased classification of selfdual additive codes over finite fields
 Adv. Math. Commun
, 2009
"... Abstract. Quantum stabilizer states over Fm can be represented as selfdual additive codes over F m 2. These codes can be represented as weighted graphs, and orbits of graphs under the generalized local complementation operation correspond to equivalence classes of codes. We have previously used thi ..."
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Cited by 8 (4 self)
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Abstract. Quantum stabilizer states over Fm can be represented as selfdual additive codes over F m 2. These codes can be represented as weighted graphs, and orbits of graphs under the generalized local complementation operation correspond to equivalence classes of codes. We have previously used this fact to classify selfdual additive codes over F4. In this paper we classify selfdual additive codes over F9, F16, and F25. Assuming that the classical MDS conjecture holds, we are able to classify all selfdual additive MDS codes over F9 by using an extension technique. We prove that the minimum distance of a selfdual additive code is related to the minimum vertex degree in the associated graph orbit. Circulant graph codes are introduced, and a computer search reveals that this set contains many strong codes. We show that some of these codes have highly regular graph representations. 1.
Remarkable Degenerate Quantum Stabilizer Codes Derived from Duadic Codes
, 2006
"... Abstract — Good quantum codes, such as quantum MDS codes, are typically nondegenerate, meaning that errors of small weight require active errorcorrection, which is—paradoxically—itself prone to errors. Decoherence free subspaces, on the other hand, do not require active error correction, but perfor ..."
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Cited by 5 (1 self)
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Abstract — Good quantum codes, such as quantum MDS codes, are typically nondegenerate, meaning that errors of small weight require active errorcorrection, which is—paradoxically—itself prone to errors. Decoherence free subspaces, on the other hand, do not require active error correction, but perform poorly in terms of minimum distance. In this paper, examples of degenerate quantum codes are constructed that have better minimum distance than decoherence free subspaces and allow some errors of small weight that do not require active error correction. In particular, two new families of [[n, 1, ≥ √ n]]q degenerate quantum codes are derived from classical duadic codes. I.
Quantum convolutional codes derived from reedsolomon and reedmuller codes,” arXiv:quantph/0701037
, 2007
"... Abstract — Convolutional stabilizer codes promise to make quantum communication more reliable with attractive online encoding and decoding algorithms. This paper introduces a new approach to convolutional stabilizer codes based on direct limit constructions. Two families of quantum convolutional cod ..."
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Cited by 5 (1 self)
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Abstract — Convolutional stabilizer codes promise to make quantum communication more reliable with attractive online encoding and decoding algorithms. This paper introduces a new approach to convolutional stabilizer codes based on direct limit constructions. Two families of quantum convolutional codes are derived from generalized ReedSolomon codes and from ReedMuller codes. A Singleton bound for pure convolutional stabilizer codes is given. I.