scholarly journals Quantum codes from codes over Gaussian integers with respect to the Mannheim metric

2012 ◽  
Vol 12 (9&10) ◽  
pp. 813-819
Author(s):  
Mehmet Ozen ◽  
Murat Guzeltepe
Keyword(s):  
Quantum Codes ◽  
Gaussian Integers ◽  
Mannheim Metric ◽  
Better Than

In this paper, some nonbinary quantum codes using classical codes over Gaussian integers are obtained. Also, some of our quantum codes are better than or comparable with those known before, (for instance $[[8,2,5]]_{4+i}$).

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.

New families of asymmetric quantum BCH codes

2011 ◽  
Vol 11 (3&4) ◽  
pp. 239-252
Author(s):  
Giuliano G. La Guardia
Keyword(s):  
Phase Shift ◽  
Quantum Systems ◽  
Bch Codes ◽  
Quantum Codes ◽  
Asymmetric Quantum ◽  
The Asymmetry ◽  
Better Than

Several families of nonbinary asymmetric quantum Bose-Chaudhuri-Hocquenghem (BCH) codes are presented in this paper. These quantum codes have parameters better than the ones available in the literature. Additionally, such codes can be applied in quantum systems where the asymmetry between qudit-flip and phase-shift errors is large.

Surface codes and color codes associated with non-orientable surfaces

2021 ◽  
Vol 21 (13&14) ◽  
pp. 1135-1153
Author(s):  
Debashis Bhowmik ◽  
Dipendu Maity ◽  
Eduardo Brandani Da Silva
Keyword(s):  
Current Work ◽  
Quantum Codes ◽  
Orientable Surfaces ◽  
Better Than

Silva et al. produced quantum codes related to topology and coloring, which are associated with tessellations on the orientable surfaces of genus $\ge 1$ and the non-orientable surfaces of the genus 1. Current work presents an approach to build quantum surface and color codes} on non-orientable surfaces of genus $ \geq 2n+1 $ for $n\geq 1$. We also present several tables of new surface and color codes related to non-orientable surfaces. These codes have the ratios $k/n$ and $d/n$ better than the codes obtained from orientable surfaces.

NEW QUANTUM CODES CONSTRUCTED FROM A CLASS OF IMPRIMITIVE BCH CODES

2013 ◽  
Vol 11 (01) ◽  
pp. 1350006 ◽  
Author(s):  
YANG LIU ◽  
YUENA MA ◽  
YOUQIAN FENG ◽  
RUIHU LI
Keyword(s):  
Lower Bound ◽  
Prime Power ◽  
Careful Analysis ◽  
Bch Codes ◽  
Bch Code ◽  
Quantum Codes ◽  
Narrow Sense ◽  
Cyclotomic Cosets ◽  
Steane Construction ◽  
Better Than

By a careful analysis on cyclotomic cosets, the maximal designed distance δnew of narrow-sense imprimitive Euclidean dual containing q-ary BCH code of length [Formula: see text] is determined, where q is a prime power and l is odd. Our maximal designed distance δnew of dual containing narrow-sense BCH codes of length n improves upon the lower bound δmax for maximal designed distances of dual containing narrow-sense BCH codes given by Aly et al. [IEEE Trans. Inf. Theory53 (2007) 1183]. A series of non-narrow-sense dual containing BCH codes of length n, including the ones whose designed distances can achieve or exceed δnew, are given, and their dimensions are computed. Then new quantum BCH codes are constructed from these non-narrow-sense imprimitive BCH codes via Steane construction, and these new quantum codes are better than previous results in the literature.

Entanglement-assisted quantum codes from quaternary codes of dimension five

2017 ◽  
Vol 15 (03) ◽  
pp. 1750017 ◽  
Author(s):  
Liangdong Lu ◽  
Ruihu Li ◽  
Luobin Guo
Keyword(s):  
Noise Suppression ◽  
Error Correcting Codes ◽  
Quantum Codes ◽  
Optimal Codes ◽  
Maximal Entanglement ◽  
Quaternary Codes ◽  
Almost All ◽  
Quantum Error ◽  
Better Than

Maximal-entanglement entanglement-assisted quantum error-correcting codes (EAQE-CCs) can achieve the EA-hashing bound asymptotically and a higher rate and/or better noise suppression capability may be achieved by exploiting maximal entanglement. In this paper, we discussed the construction of quaternary zero radical (ZR) codes of dimension five with length [Formula: see text]. Using the obtained quaternary ZR codes, we construct many maximal-entanglement EAQECCs with very good parameters. Almost all of these EAQECCs are better than those obtained in the literature, and some of these EAQECCs are optimal codes.

SYMMETRIC AND ASYMMETRIC QUANTUM CODES

2013 ◽  
Vol 11 (05) ◽  
pp. 1350047 ◽  
Author(s):  
KENZA GUENDA ◽  
T. AARON GULLIVER
Keyword(s):  
Mds Codes ◽  
Quantum Codes ◽  
Asymmetric Quantum ◽  
Asymmetric Quantum Codes ◽  
Special Cases ◽  
Minimum Distances ◽  
Css Construction ◽  
The Relationship ◽  
Dual Case ◽  
Better Than

The asymmetric CSS construction is extended to the Hermitian dual case. New infinite families of quantum symmetric and asymmetric codes are constructed. In particular, new quantum codes are obtained from binary BCH codes and MDS codes. These codes have known minimum distances and thus the relationship between the rate gain and minimum distance is given explicitly. The codes obtained are shown to have parameters better than those of previous codes. A number of known codes are special cases of the codes given here.

Construction of quantum negacyclic BCH codes

2018 ◽  
Vol 16 (07) ◽  
pp. 1850059 ◽  
Author(s):  
Xiaoshan Kai ◽  
Ping Li ◽  
Shixin Zhu
Keyword(s):  
Positive Integer ◽  
Prime Power ◽  
Bch Codes ◽  
Quantum Codes ◽  
Negacyclic Codes ◽  
Cyclotomic Cosets ◽  
Better Than

Let [Formula: see text] be an odd prime power and [Formula: see text] be a positive integer. Maximum designed distance such that negacyclic BCH codes over [Formula: see text] of length [Formula: see text] are Hermitian dual-containing codes is given. The dimension of such Hermitian dual-containing negacyclic codes is completely determined by analyzing cyclotomic cosets. Quantum negacyclic BCH codes of length [Formula: see text] are obtained by using Hermitian construction. The constructed quantum negacyclic BCH codes produce new quantum codes with parameters better than those obtained from quantum BCH codes.

scholarly journals New quantum codes from metacirculant graphs via self-dual additive $\mathbb{F}_4$-codes

2022 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Padmapani Seneviratne ◽  
Martianus Frederic Ezerman
Keyword(s):  
Quantum Codes ◽  
Additive Codes ◽  
First Time ◽  
Better Than

<p style='text-indent:20px;'>We use symplectic self-dual additive codes over <inline-formula><tex-math id="M1">\begin{document}$ \mathbb{F}_4 $\end{document}</tex-math></inline-formula> obtained from metacirculant graphs to construct, for the first time, <inline-formula><tex-math id="M2">\begin{document}$ \left[\kern-0.15em\left[ {\ell, 0, d} \right]\kern-0.15em\right] $\end{document}</tex-math></inline-formula> qubit codes with parameters <inline-formula><tex-math id="M3">\begin{document}$ (\ell,d) \in \{(78, 20), (90, 21), (91, 22), (93,21),(96,22)\} $\end{document}</tex-math></inline-formula>. Secondary constructions applied to the qubit codes result in many new qubit codes that perform better than the previous best-known.</p>

scholarly journals Loss tolerance with a concatenated graph state

2013 ◽  
Vol 13 (11&12) ◽  
pp. 995-1006
Author(s):  
David A. Herrera-Marti ◽  
Terry Rudolph
Keyword(s):  
Quantum Computation ◽  
Loss Rate ◽  
Quantum Codes ◽  
Graph State ◽  
Universal Quantum ◽  
Loss Tolerance ◽  
Qubit Loss ◽  
Logical Qubit ◽  
Better Than ◽  
Loss Rates

A new way of addressing loss errors is introduced which combines ideas from measurement-based quantum computation and concatenated quantum codes, allowing for universal quantum computation. It is shown that for the case where qubit loss is detected upon measurement, the scheme performs well under $23\%$ loss rate. For loss rates below $10\%$ this approach performs better than the best scheme known up to date \cite{varnava2006loss}. If lost qubits are tagged prior to measurement, it can tolerate up to $50\%$ loss. The overhead per logical qubit is shown to be significantly lower than other schemes. The obtention of the threshold is entirely analytic.

scholarly journals On quantum tensor product codes

2017 ◽  
Vol 17 (13&14) ◽  
pp. 1105-1122
Author(s):  
Jihao Fan ◽  
Yonghui Li ◽  
Min-Hsiu Hsieh ◽  
Hanwu Chen
Keyword(s):  
Tensor Product ◽  
Error Correction ◽  
Mds Codes ◽  
Quantum Codes ◽  
Multiple Quantum ◽  
Parity Check ◽  
Product Codes ◽  
Burst Error ◽  
Quantum Error ◽  
Better Than

We present a general framework for the construction of quantum tensor product codes (QTPC). In a classical tensor product code (TPC), its parity check matrix is constructed via the tensor product of parity check matrices of the two component codes. We show that by adding some constraints on the component codes, several classes of dual-containing TPCs can be obtained. By selecting different types of component codes, the proposed method enables the construction of a large family of QTPCs and they can provide a wide variety of quantum error control abilities. In particular, if one of the component codes is selected as a burst-error-correction code, then QTPCs have quantum multiple-burst-error-correction abilities, provided these bursts fall in distinct subblocks. Compared with concatenated quantum codes (CQC), the component code selections of QTPCs are much more flexible than those of CQCs since only one of the component codes of QTPCs needs to satisfy the dual-containing restriction. We show that it is possible to construct QTPCs with parameters better than other classes of quantum error-correction codes (QECC), e.g., CQCs and quantum BCH codes. Many QTPCs are obtained with parameters better than previously known quantum codes available in the literature. Several classes of QTPCs that can correct multiple quantum bursts of errors are constructed based on reversible cyclic codes and maximum-distance-separable (MDS) codes.

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