Construction and complement circuit of a quantum stabilizer code with length 7

2016 ◽  
Author(s):  
Duc Manh Nguyen ◽  
Sunghwan Kim
Keyword(s):  
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

Locality bounds on Hamiltonians for stabilizer codes

2009 ◽  
Vol 9 (5&6) ◽  
pp. 487-499
Author(s):  
S.S. Bullock ◽  
D.P. O'Leary
Keyword(s):  
Quantum Computing ◽  
Error Correction ◽  
Energy Gap ◽  
Stabilizer Codes ◽  
Adiabatic Quantum Computing ◽  
Group A ◽  
Stabilizer Code ◽  
Stabilizer Group ◽  
The Cost ◽  
Insight Into

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.

A stabilizer code for uncorrelated errors can correct spatially correlated ones

2007 ◽  
Vol 40 (24) ◽  
pp. F457-F463 ◽  
Author(s):  
T Hayashi ◽  
T Arimitsu ◽  
S Kitajima ◽  
F Shibata
Keyword(s):  
Spatially Correlated ◽  
Stabilizer Code

scholarly journals On subsystem codes beating the quantum Hamming or Singleton bound

2007 ◽  
Vol 463 (2087) ◽  
pp. 2887-2905 ◽  
Author(s):  
Andreas Klappenecker ◽  
Pradeep Kiran Sarvepalli
Keyword(s):  
The Other ◽  
Maximum Distance ◽  
Open Problems ◽  
Prime Field ◽  
Stabilizer Codes ◽  
Singleton Bound ◽  
Other Hand ◽  
Maximum Distance Separable ◽  
Linear Subsystem ◽  
Stabilizer Code

Subsystem codes are a generalization of noiseless subsystems, decoherence-free subspaces and stabilizer codes. We generalize the quantum Singleton bound to q -linear subsystem codes. It follows that no subsystem code over a prime field can beat the quantum Singleton bound. On the other hand, we show the remarkable fact that there exist impure subsystem codes beating the quantum Hamming bound. A number of open problems concern the comparison in the performance of stabilizer and subsystem codes. One of the open problems suggested by Poulin's work asks whether a subsystem code can use fewer syndrome measurements than an optimal q -linear maximum distance separable stabilizer code while encoding the same number of qudits and having the same distance. We prove that linear subsystem codes cannot offer such an improvement under complete decoding.

Sign in / Sign up

Export Citation Format

Share Document