A quantum stabilizer code associated with cluster states

2017 ◽  
Author(s):  
Dan Song ◽  
Zhengwen Cao ◽  
Shuanghao Zhang ◽  
Jie Feng ◽  
Yan Li ◽  
...  
Keyword(s):  
Cluster States ◽  
Stabilizer Code ◽  
Quantum Stabilizer Code

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.

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.

scholarly journals The Nonexistence of a $[[{13,5,4}]]$-Quantum Stabilizer Code

2011 ◽  
Vol 57 (7) ◽  
pp. 4788-4793 ◽  
Author(s):  
Jürgen Bierbrauer ◽  
Richard Fears ◽  
Stefano Marcugini ◽  
Fernanda Pambianco
Keyword(s):  
Stabilizer Code ◽  
Quantum Stabilizer Code

scholarly journals High-dimensional one-way quantum processing implemented on d-level cluster states

2018 ◽  
Vol 15 (2) ◽  
pp. 148-153 ◽  
Author(s):  
Christian Reimer ◽  
Stefania Sciara ◽  
Piotr Roztocki ◽  
Mehedi Islam ◽  
Luis Romero Cortés ◽  
...  
Keyword(s):  
High Dimensional ◽  
Cluster States ◽  
Level Cluster

scholarly journals Cluster states in11B

2014 ◽  
Vol 66 ◽  
pp. 03007 ◽  
Author(s):  
A.N. Danilov ◽  
A.S. Demyanova ◽  
A.A. Ogloblin ◽  
S.V. Dmitriev ◽  
T.L. Belyaeva ◽  
...  
Keyword(s):  
Cluster States

THE INTERACTION OF A NUCLEON AND ALPHA CONDENSATE

2008 ◽  
Vol 17 (10) ◽  
pp. 2106-2109 ◽  
Author(s):  
AKIHIRO TOHSAKI
Keyword(s):  
Pauli Principle ◽  
Numerical Results ◽  
Microscopic Model ◽  
Cluster States ◽  
Equidistant Spectrum ◽  
Composite Bosons ◽  
Spectrum Model

A nucleon is available for examining the property of α-condensate, which consists of composite bosons. Only a microscopic model, which fully takes into account the Pauli principle between all the constituent nucleons, can play its role. We give numerical results by equidistant spectrum model for the system of a neutron and 3α-cluster states. We discuss whether an extra nucleon can exist in the center of α-condensate or not.

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