Stabilizer quantum codes defined by trace-depending polynomials

Galindo, Carlos; Hernando, Fernando; Helena, Martín-Cruz,; Ruano, Diego

doi:10.1016/j.ffa.2022.102138

Cited by 3 publications

(2 citation statements)

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“…There is an extensive study of quantum error-correcting codes, see for example the papers [ 3 , 4 , 11 , 12 , 31 , 33 , 52 ] for the binary case and [ 5 , 6 , 9 , 14 , 21 , 24 , 27 , 32 , 35 , 40 , 41 , 47 , 51 ] for the general case. Many of the known quantum error-correcting codes are stabilizer codes.…”

Section: Introductionmentioning

confidence: 99%

MDS, Hermitian almost MDS, and Gilbert–Varshamov quantum codes from generalized monomial-Cartesian codes

Barbero-Lucas,

Hernando,

Martín-Cruz

et al. 2024

Quantum Inf Process

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We construct new stabilizer quantum error-correcting codes from generalized monomial-Cartesian codes. Our construction uses an explicitly defined twist vector, and we present formulas for the minimum distance and dimension. Generalized monomial-Cartesian codes arise from polynomials in m variables. When $$m=1$$ m = 1 our codes are MDS, and when $$m=2$$ m = 2 and our lower bound for the minimum distance is 3, the codes are at least Hermitian almost MDS. For an infinite family of parameters, when $$m=2$$ m = 2 we prove that our codes beat the Gilbert–Varshamov bound. We also present many examples of our codes that are better than any known code in the literature.

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Section: Introductionmentioning

confidence: 99%

MDS, Hermitian almost MDS, and Gilbert–Varshamov quantum codes from generalized monomial-Cartesian codes

Barbero-Lucas,

Hernando,

Martín-Cruz

et al. 2024

Quantum Inf Process

Self Cite

View full text Add to dashboard Cite

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“…Many of these codes satisfy K = q k , for some nonnegative integer k, and then their parameters are expressed as [[n, k, d]] q ; abusing the notation we say that k is the dimension of these codes. QECCs were first introduced in the binary case [10,22,9,4,5] and later in the general case [7,3,30,1,32,11,17,18], where we have cited only some references of a vast literature on the subject. QECCs in the nonbinary case are convenient for fault-tolerant quantum computation [43,31,23,36].…”

Section: Introductionmentioning

confidence: 99%