Entanglement-assisted quantum error-correcting codes over arbitrary finite fields

Galindo, Carlos; Hernando, Fernando; Matsumoto, Ryutaroh; Ruano, Diego

doi:10.1007/s11128-019-2234-5

Cited by 74 publications

(81 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Using a suitable basis of F q over F p , an isomorphism of F p -linear spaces φ : F 2r p → F 2 q can be given, providing an isomorphism of F p -linear spaces [21], the results of EAQECCs over F p can be extended to F q and the product · s instead of · ts . Indeed, the following result holds:…”

Section: Asymmetric Eaqeccsmentioning

confidence: 99%

“…Next we will count the quantity of triples (v, [21,Proposition 4] and the fact that the rank of a matrix and its transpose coincide, we deduce that…”

Section: A Gilbert-varshamov Bound For Asymmetric Eaqeccsmentioning

confidence: 99%

“…Some constructions of this type for binary codes (and also for codes over finite fields F p , p prime) can be found in the literature [26,34,44]. The case when the codes are supported in an arbitrary finite field has been described in [21].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Asymmetric Entanglement-Assisted Quantum Error-Correcting Codes and BCH Codes

et al. 2020

Self Cite

View full text Add to dashboard Cite

The concept of asymmetric entanglement-assisted quantum error-correcting code (asymmetric EAQECC) is introduced in this article. Codes of this type take advantage of the asymmetry in quantum errors since phase-shift errors are more probable than qudit-flip errors. Moreover, they use pre-shared entanglement between encoder and decoder to simplify the theory of quantum error correction and increase the communication capacity. Thus, asymmetric EAQECCs can be constructed from any pair of classical linear codes over an arbitrary field. Their parameters are described and a Gilbert-Varshamov bound is presented. Explicit parameters of asymmetric EAQECCs from BCH codes are computed and examples exceeding the introduced Gilbert-Varshamov bound are shown.2010 Mathematics Subject Classification. 81P70; 94B65; 94B05.

show abstract

Section: Asymmetric Eaqeccsmentioning

confidence: 99%

“…Next we will count the quantity of triples (v, [21,Proposition 4] and the fact that the rank of a matrix and its transpose coincide, we deduce that…”

Section: A Gilbert-varshamov Bound For Asymmetric Eaqeccsmentioning

confidence: 99%

See 1 more Smart Citation

Asymmetric Entanglement-Assisted Quantum Error-Correcting Codes and BCH Codes

et al. 2020

Self Cite

View full text Add to dashboard Cite

show abstract

“…This EA framework provides the power to construct quantum codes from any group of quantum operators operating over the qudits leading to the construction of codes with better error correction capability [10]. All known quantum error correction codes based on finite fields [2] [5] [6] [11] [12] are special cases of this construction. Using the proposed framework in [10], quantum codes can be constructed from well-known classical codes, such as Reed-Solomon (RS) codes [13], etc.…”

Section: Introductionmentioning

confidence: 99%

Encoding of Nonbinary Entanglement-Unassisted and Assisted Stabilizer Codes

Nadkarni

Garani

2021

IEEE Trans. Quantum Eng.

View full text Add to dashboard Cite

Quantum coding schemes over qudits using pre-shared entanglement between the encoder and decoder can provide better error correction capability than without it. In this paper, we develop procedures for constructing encoding operators for entanglement-unassisted and entanglement-assisted qudit stabilizer codes over F p k , with p prime and k ≥ 1 from first principles, generalizing prior works on qubit based codes and codes that work over F p . We also provide quantum encoding architectures based on the proposed encoding procedures using one and two qudit gates, useful towards realizing coded quantum computing and communication systems using qudits.INDEX TERMS Quantum error correction, Entanglement-assisted codes, Encoding architecture, Qudit stabilizer codes, Non-binary codes. 1 The encoding circuit complexity linearly increases with codelength. To realize the practical implementation of large length codes, we need to construct all the stabilizers or their extensions from a carefully chosen group of quantum operators, making it a computationally challenging problem.2 Preliminary version on the encoding procedure for entanglementunassisted stabilizer codes over qudits was presented at IEEE Globecom 2018, Abu Dhabi [14].

show abstract

“…With this new formalism, entanglement-assisted quantum stabilizer codes can be constructed from any classical linear code giving rise to entanglement-assisted quantum error-correcting codes (EAQECCs). Recently, nonbinary generalization of EAQECCs was studied [4], [10]. On the other hand, until very recently, no researcher had studied entanglementassisted asymmetric quantum error correction, though its necessity and importance seem pretty obvious at hindsight.…”

Section: Introductionmentioning

confidence: 99%