Quantum Code Constructions

2020 ◽  
pp. 57-124
Author(s):  
Giuliano Gadioli La Guardia
Keyword(s):  
Quantum Code ◽  
Code Constructions

Cracking the quantum code

Physics World ◽  
2020 ◽  
Vol 33 (7) ◽  
pp. 46-*
Author(s):  
Kate Gardner
Keyword(s):  
Quantum Code

ON TWO PROBLEMS OF ASYMMETRIC QUANTUM CODES

2014 ◽  
Vol 28 (06) ◽  
pp. 1450017 ◽  
Author(s):  
RUIHU LI ◽  
GEN XU ◽  
LUOBIN GUO
Keyword(s):  
Cyclic Codes ◽  
Error Correcting Codes ◽  
Bch Code ◽  
Quantum Codes ◽  
Quantum Code ◽  
Asymmetric Quantum ◽  
Asymmetric Quantum Codes ◽  
Special Cases ◽  
Quantum Error ◽  
Better Than

In this paper, we discuss two problems on asymmetric quantum error-correcting codes (AQECCs). The first one is on the construction of a [[12, 1, 5/3]]2 asymmetric quantum code, we show an impure [[12, 1, 5/3 ]]2 exists. The second one is on the construction of AQECCs from binary cyclic codes, we construct many families of new asymmetric quantum codes with dz> δ max +1 from binary primitive cyclic codes of length n = 2m-1, where δ max = 2⌈m/2⌉-1 is the maximal designed distance of dual containing narrow sense BCH code of length n = 2m-1. A number of known codes are special cases of the codes given here. Some of these AQECCs have parameters better than the ones available in the literature.

scholarly journals On maximum-likelihood decoding with circuit-level errors

Quantum ◽  
2020 ◽  
Vol 4 ◽  
pp. 304
Author(s):  
Leonid P. Pryadko
Keyword(s):  
Maximum Likelihood ◽  
Probability Distribution ◽  
Error Probability ◽  
Ldpc Codes ◽  
Quantum Codes ◽  
Quantum Code ◽  
Maximum Likelihood Decoding ◽  
Measurement Circuit ◽  
Equivalence Group ◽  
Error Probability Distribution

Error probability distribution associated with a given Clifford measurement circuit is described exactly in terms of the circuit error-equivalence group, or the circuit subsystem code previously introduced by Bacon, Flammia, Harrow, and Shi. This gives a prescription for maximum-likelihood decoding with a given measurement circuit. Marginal distributions for subsets of circuit errors are also analyzed; these generate a family of related asymmetric LDPC codes of varying degeneracy. More generally, such a family is associated with any quantum code. Implications for decoding highly-degenerate quantum codes are discussed.

scholarly journals On cyclotomic cosets and code constructions

2016 ◽  
Vol 488 ◽  
pp. 302-319 ◽  
Author(s):  
Giuliano G. La Guardia ◽  
Marcelo M.S. Alves
Keyword(s):  
Cyclotomic Cosets ◽  
Code Constructions

scholarly journals Subspace code constructions

2020 ◽  
Author(s):  
Antonio Cossidente ◽  
Giuseppe Marino ◽  
Francesco Pavese
Keyword(s):  
Code Constructions

scholarly journals Z6-Code Constructions of the Leech Lattice and the Niemeier Lattices

2002 ◽  
Vol 23 (5) ◽  
pp. 573-581 ◽  
Author(s):  
Masaaki Harada ◽  
Masaaki Kitazume
Keyword(s):  
Leech Lattice ◽  
Code Constructions
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