scholarly journals Binary construction of quantum codes of minimum distances five and six

2008 ◽  
Vol 308 (9) ◽  
pp. 1603-1611 ◽  
Author(s):  
Ruihu Li ◽  
Xueliang Li
Keyword(s):  
Quantum Codes ◽  
Minimum Distances

Entanglement-assisted quantum codes achieving the quantum singleton bound but violating the quantum hamming bound

2014 ◽  
Vol 14 (13&14) ◽  
pp. 1107-1116
Author(s):  
Ruihu Li ◽  
Luobin Guo ◽  
Zongben Xu
Keyword(s):  
Error Correction ◽  
Infinite Family ◽  
Error Correcting Codes ◽  
Quantum Codes ◽  
Singleton Bound ◽  
Minimum Distances ◽  
Quantum Error

We give an infinite family of degenerate entanglement-assisted quantum error-correcting codes (EAQECCs) which violate the EA-quantum Hamming bound for non-degenerate EAQECCs and achieve the EA-quantum Singleton bound, thereby proving that the EA-quantum Hamming bound does not asymptotically hold for degenerate EAQECCs. Unlike the previously known quantum error-correcting codes that violate the quantum Hamming bound by exploiting maximally entangled pairs of qubits, our codes do not require local unitary operations on the entangled auxiliary qubits during encoding. The degenerate EAQECCs we present are constructed from classical error-correcting codes with poor minimum distances, which implies that, unlike the majority of known EAQECCs with large minimum distances, our EAQECCs take more advantage of degeneracy and rely less on the error correction capabilities of classical 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.

On non-binary quantum repeated-root cyclic codes

2014 ◽  
Vol 12 (03) ◽  
pp. 1450010 ◽  
Author(s):  
Liqi Wang ◽  
Shixin Zhu
Keyword(s):  
Cyclic Codes ◽  
Quantum Codes ◽  
Mds Code ◽  
Characteristic P ◽  
Minimum Distances

In this paper, based on the Steane's enlargement construction, three classes of non-binary quantum codes are constructed from classical repeated-root cyclic codes of length 2ps over 𝔽q with odd characteristic p. The exact minimum distances of these quantum codes are determined. This construction yields a quantum MDS code with parameters [[2p, 2p - 4, 3]]p and two good quantum codes with parameters [[2p, 2p - 7, 4]]p and [[2p, 2p - 10, 5]]p.

scholarly journals Encoding classical information in gauge subsystems of quantum codes

2022 ◽  
Author(s):  
Andrew Nemec ◽  
Andreas Klappenecker
Keyword(s):  
Quantum Information ◽  
Linear Codes ◽  
Explicit Construction ◽  
Quantum Codes ◽  
Classical Information ◽  
Hybrid Code ◽  
Gauge Fixing ◽  
Minimum Distances

In this paper, we show how to construct hybrid quantum-classical codes from subsystem codes by encoding the classical information into the gauge qudits using gauge fixing. Unlike previous work on hybrid codes, we allow for two separate minimum distances, one for the quantum information and one for the classical information. We give an explicit construction of hybrid codes from two classical linear codes using Bacon–Casaccino subsystem codes, as well as several new examples of good hybrid code.

Image registration with a computer driven S.T.E.M.

1978 ◽  
Vol 36 (1) ◽  
pp. 98-99
Author(s):  
A.M.H. Schepman ◽  
J.A.P. van der Voort ◽  
J.E. Mellema
Keyword(s):  
Spot Size ◽  
Scanning Transmission Electron Microscope ◽  
Small Computer ◽  
Structural Studies ◽  
Area Of Interest ◽  
Transmission Electron ◽  
Scanning Transmission ◽  
Specimen Area ◽  
On Line ◽  
Minimum Distances

A Scanning Transmission Electron Microscope (STEM) was coupled to a small computer. The system (see Fig. 1) has been built using a Philips EM400, equipped with a scanning attachment and a DEC PDP11/34 computer with 34K memory. The gun (Fig. 2) consists of a continuously renewed tip of radius 0.2 to 0.4 μm of a tungsten wire heated just below its melting point by a focussed laser beam (1). On-line operation procedures were developped aiming at the reduction of the amount of radiation of the specimen area of interest, while selecting the various imaging parameters and upon registration of the information content. Whereas the theoretical limiting spot size is 0.75 nm (2), routine resolution checks showed minimum distances in the order 1.2 to 1.5 nm between corresponding intensity maxima in successive scans. This value is sufficient for structural studies of regular biological material to test the performance of STEM over high resolution CTEM.

scholarly journals Solutions of Modular Bootstrap Constraints from Quantum Codes

2021 ◽  
Vol 126 (16) ◽  
Author(s):  
Anatoly Dymarsky ◽  
Alfred Shapere
Keyword(s):  
Quantum Codes

Constacyclic codes over mixed alphabets and their applications in constructing new quantum codes

2021 ◽  
Vol 20 (4) ◽  
Author(s):  
Hai Q. Dinh ◽  
Sachin Pathak ◽  
Tushar Bag ◽  
Ashish Kumar Upadhyay ◽  
Woraphon Yamaka
Keyword(s):  
Quantum Codes ◽  
Constacyclic Codes

scholarly journals Quantum repeaters based on concatenated bosonic and discrete-variable quantum codes

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Filip Rozpędek ◽  
Kyungjoo Noh ◽  
Qian Xu ◽  
Saikat Guha ◽  
Liang Jiang
Keyword(s):  
Continuous Variable ◽  
Quantum Codes ◽  
Discrete Variable ◽  
Long Distance ◽  
Concatenated Code ◽  
Different Types ◽  
Optical Modes ◽  
Distance Communication ◽  
Quantum Repeaters ◽  
Quantum Error

AbstractWe propose an architecture of quantum-error-correction-based quantum repeaters that combines techniques used in discrete- and continuous-variable quantum information. Specifically, we propose to encode the transmitted qubits in a concatenated code consisting of two levels. On the first level we use a continuous-variable GKP code encoding the qubit in a single bosonic mode. On the second level we use a small discrete-variable code. Such an architecture has two important features. Firstly, errors on each of the two levels are corrected in repeaters of two different types. This enables for achieving performance needed in practical scenarios with a reduced cost with respect to an architecture for which all repeaters are the same. Secondly, the use of continuous-variable GKP code on the lower level generates additional analog information which enhances the error-correcting capabilities of the second-level code such that long-distance communication becomes possible with encodings consisting of only four or seven optical modes.

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