Nonbinary quantum stabilizer codes

By Alexei E. Ashikhmin, Emanuel Knill. IEEE Transactions on Information Theory, 2000

642 citations recorded by the source corpus.

We define and show how to construct nonbinary quantum stabilizer codes. Our approach is based on nonbinary error bases. It generalizes the relationship between self-orthogonal codes over F/sub 4/ and binary quantum codes to one between self-orthogonal codes over F(q/sup 2/) and q-ary quantum codes for any prime power q.

Subfields: Artificial Intelligence, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/1ac528d2c9ba61d778a1a6bf96de92f179e31599

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In Computational Theory and Mathematics

Citations in the corpus

Nonbinary Stabilizer Codes Over Finite Fields (2005, methodology): “We ﬁrst recall the following characterization of detectable errors (see also [4]; the interested reader can ﬁnd a more general approach in [59], [60]).”
An Introduction to Quantum Error Correction and Fault-Tolerant Quantum Computation (2009, background): “There is a natural generalization of stabilizer codes to this case [ 29 ], and a variety of qudit stabilizer codes are known (e.g., [ 1, 7, 26 ]).”
Stabilizer states and Clifford operations for systems of arbitrary dimensions and modular arithmetic (2004, background): “The n-qud it generalized Pauli group and Clifford group and the related concepts of stabilizer codes and states have been studied in various levels of detail in a number of papers [6, 7, 8, 9, 10, 11, 12, 13, 14, 15].”
Quantum channels and memory effects (2012, background): “For non binary codes the reader may refer to (Ashikhmin and Knill, 2001; Ketkar et al., 2006; Knill, 1996).”
Fundamentals of quantum information theory (2002, neutral): “[70,38,4]).”
Entanglement-assisted capacity of a quantum channel and the reverse Shannon theorem (2001, methodology): “In this paper, we advance quantum information theory by proving a capacity formula for quantum channels which holds when the sender and receiver have access to shared quantum entangled states which can be used in the communication protocol.”
Quantum error-correcting codes associated with graphs (2000, background): “The order of the group determines the type of systems for which errors are corrected so that, e.g., the two-element group corresponds to the qubit case (Compare [5–8] for other constructions of non-binary codes).”
On optimal quantum codes (2003, background): “q Theorem 10 puncture code P (C) weights in P (C) 2 [[4, 2, 2]]2 [4, 3, 2]2 2, 4 3 [[9, 7, 2]]3 [9, 8, 2]3 2–9 [[9, 5, 3]]3 [9, 5, 4]3 4–9 4 [[16, 14, 2]]4 [16, 15, 2]4 2–16 [[16, 12, 3]]4 [16, 12, 4]4 4–16 [[16, 10, 4]]4 [16, 7, 8]4 8, 10, 12, 14, 16 5 [[25, 23, 2]]5 [25, 24, 2]5 2–25 [[25, 21, 3]]”