New Classes of LDPC Stabilizer Codes Using Ideas from Matrix Scrambling

Author(s):  
P. Tan ◽  
J. Li
Keyword(s):  
2016 ◽  
Vol 16 (3&4) ◽  
pp. 237-250
Author(s):  
Yongsoo Hwang ◽  
Jun Heo

A graph state and a graph code respectively are defined based on a mathematical simple graph. In this work, we examine a relation between a graph state and a graph code both obtained from the same graph, and show that a graph state is a superposition of logical qubits of the related graph code. By using the relation, we first discuss that a local complementation which has been used for a graph state can be useful for searching locally equivalent stabilizer codes, and second provide a method to find a stabilizer group of a graph code.


2018 ◽  
Vol 97 (13) ◽  
Author(s):  
A. T. Schmitz ◽  
Han Ma ◽  
Rahul M. Nandkishore ◽  
S. A. Parameswaran

2009 ◽  
Vol 9 (5&6) ◽  
pp. 487-499
Author(s):  
S.S. Bullock ◽  
D.P. O'Leary

In this paper, we study the complexity of Hamiltonians whose groundstate is a stabilizer code. We introduce various notions of $k$-locality of a stabilizer code, inherited from the associated stabilizer group. A choice of generators leads to a Hamiltonian with the code in its groundspace. We establish bounds on the locality of any other Hamiltonian whose groundspace contains such a code, whether or not its Pauli tensor summands commute. Our results provide insight into the cost of creating an energy gap for passive error correction and for adiabatic quantum computing. The results simplify in the cases of XZ-split codes such as Calderbank-Shor-Steane stabilizer codes and topologically-ordered stabilizer codes arising from surface cellulations.


2016 ◽  
Vol 6 (3) ◽  
Author(s):  
Theodore J. Yoder ◽  
Ryuji Takagi ◽  
Isaac L. Chuang

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