On optimal quantum codes

By M. Grassl, T. Beth, M. Roetteler. 2003

297 citations recorded by the source corpus.

We present families of quantum error-correcting codes which are optimal in the sense that the minimum distance is maximal. These maximum distance separable (MDS) codes are defined over q-dimensional quantum systems, where q is an arbitrary prime power. It is shown that codes with parameters 〚n, n - 2d + 2, d〛q exist for all 3≤n≤q and 1≤d≤n/2+1. We also present quantum MDS codes with parameters 〚q2, q2-2d+2, d〛q for 1≤d≤q which additionally give rise to shortened codes 〚q2-s, q2-2d+2-s, d〛q for some s.

Subfields: Artificial Intelligence, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/db497a748d24d4959851709b3d6768757cb45165

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In Artificial Intelligence

In Computational Theory and Mathematics

Citations in the corpus

Nonbinary Stabilizer Codes Over Finite Fields (2005, methodology): “Digital Object Identiﬁer 10.1109/TIT.2006.883612 some results were generalized to the case of nonbinary stabilizer codes [1], [3], [4], [16], [23], [24], [34], [35], [41], [48], [50], [57], [65], [71], [80], [84], [86], [87], but the theory is not nearly as complete as in the binary case.”
Holographic quantum error-correcting codes: toy models for the bulk/boundary correspondence (2015, methodology): “A construction with v ∝ O(√n) was later proposed [56].”
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].”