scholarly journals Quantum codes from algebraic curves with automorphisms

2008 ◽  
Vol 11 (2) ◽  
pp. 383 ◽  
Author(s):  
Shaska
Keyword(s):  
Algebraic Curves ◽  
Quantum Codes

GEOMETRIC THEORY OF MULTIDIMENSIONAL INTERPOLATION

2020 ◽  
Vol 2020 (1) ◽  
pp. 9-16
Author(s):  
Evgeniy Konopatskiy
Keyword(s):  
Response Function ◽  
Algebraic Curves ◽  
Geometric Theory ◽  
Analytical Description ◽  
Geometric Interpretation ◽  
Affine Geometry ◽  
Mathematical Apparatus ◽  
Multidimensional Interpolation ◽  
Pass Through

The paper presents a geometric theory of multidimensional interpolation based on invariants of affine geometry. The analytical description of geometric interpolants is performed within the framework of the mathematical apparatus BN-calculation using algebraic curves that pass through preset points. A geometric interpretation of the interaction of parameters, factors, and the response function is presented, which makes it possible to generalize the geometric theory of multidimensional interpolation in the direction of increasing the dimension of space. The conceptual principles of forming the tree of the geometric interpolant model as a geometric basis for modeling multi-factor processes and phenomena are described.

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.

scholarly journals Real plane algebraic curves with prescribed singularities

Topology ◽  
1993 ◽  
Vol 32 (4) ◽  
pp. 845-856 ◽  
Author(s):  
Eugenii Shustin
Keyword(s):  
Algebraic Curves ◽  
Real Plane
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