Quantum stabilizer codes from difference sets

2013 ◽  
Author(s):  
Yixuan Xie ◽  
Jinhong Yuan ◽  
Robert Malaney
Keyword(s):  
Difference Sets ◽  
Stabilizer Codes ◽  
Quantum Stabilizer Codes

scholarly journals New Constructions of Quantum Stabilizer Codes Based on Difference Sets

Symmetry ◽  
2018 ◽  
Vol 10 (11) ◽  
pp. 655 ◽  
Author(s):  
Duc Nguyen ◽  
Sunghwan Kim
Keyword(s):  
Difference Sets ◽  
Combinatorial Design ◽  
Inner Product ◽  
Code Construction ◽  
Stabilizer Codes ◽  
Stabilizer Code ◽  
The Difference ◽  
Symplectic Inner Product ◽  
Quantum Stabilizer Code ◽  
Quantum Stabilizer Codes

In this paper, new conditions on parameters in difference sets are derived to satisfy symplectic inner product, and new constructions of quantum stabilizer codes are proposed from the conditions. The conversion of the difference sets into parity-check matrices is first explained. Then, the proposed code construction is composed of three steps, which are to choose the generators of quantum stabilizer code, to determine the quantum stabilizer groups, and to determine subspace codewords with large minimum distance. The quantum stabilizer codes with various length are also presented to explain the practicality of the code construction. The proposed design can be applied to quantum stabilizer code construction based on combinatorial design.

New construction of binary and nonbinary quantum stabilizer codes based on symmetric matrices

2019 ◽  
Vol 33 (24) ◽  
pp. 1950274 ◽  
Author(s):  
Duc Manh Nguyen ◽  
Sunghwan Kim
Keyword(s):  
Inner Product ◽  
Symmetric Matrices ◽  
Parity Check ◽  
Stabilizer Codes ◽  
Construction Methods ◽  
Singleton Bound ◽  
New Construction ◽  
Symplectic Inner Product ◽  
Quantum Stabilizer Codes

In this paper, we propose two construction methods for binary and nonbinary quantum stabilizer codes based on symmetric matrices. In the first construction, we use the identity and symmetric matrices to generate parity-check matrices that satisfy the symplectic inner product (SIP) for the construction of quantum stabilizer codes. In the second construction, we modify the first construction to generate parity-check matrices based on the Calderbank–Shor–Stean structure for the construction of quantum stabilizer codes. The binary and nonbinary quantum stabilizer codes whose parameters achieve equality of the quantum singleton bound are investigated with the code lengths ranging from 4 to 12.

scholarly journals Nonbinary quantum stabilizer codes

2001 ◽  
Vol 47 (7) ◽  
pp. 3065-3072 ◽  
Author(s):  
A. Ashikhmin ◽  
E. Knill
Keyword(s):  
Stabilizer Codes ◽  
Quantum Stabilizer Codes

A novel construction for quantum stabilizer codes based on binary formalism

2020 ◽  
Vol 34 (08) ◽  
pp. 2050059 ◽  
Author(s):  
Duc Manh Nguyen ◽  
Sunghwan Kim
Keyword(s):  
Minimum Distance ◽  
Binary Vector ◽  
Quantum Codes ◽  
Quantum Code ◽  
Parity Check Matrix ◽  
Stabilizer Codes ◽  
Check Matrix ◽  
Stabilizer Code ◽  
Quantum Stabilizer Code ◽  
Quantum Stabilizer Codes

In this research, we propose a novel construction of quantum stabilizer code based on a binary formalism. First, from any binary vector of even length, we generate the parity-check matrix of the quantum code from a set composed of elements from this vector and its relations by shifts via subtraction and addition. We prove that the proposed matrices satisfy the condition constraint for the construction of quantum codes. Finally, we consider some constraint vectors which give us quantum stabilizer codes with various dimensions and a large minimum distance with code length from six to twelve digits.

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