scholarly journals Degenerate Quantum LDPC Codes With Good Finite Length Performance

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 585
Author(s):  
Pavel Panteleev ◽  
Gleb Kalachev
Keyword(s):  
Minimum Distance ◽  
Belief Propagation ◽  
Fault Tolerant ◽  
Large Family ◽  
Parity Check ◽  
Product Codes ◽  
Medium Length ◽  
Surface Code ◽  
Depolarizing Channel ◽  
Better Than

We study the performance of medium-length quantum LDPC (QLDPC) codes in the depolarizing channel. Only degenerate codes with the maximal stabilizer weight much smaller than their minimum distance are considered. It is shown that with the help of OSD-like post-processing the performance of the standard belief propagation (BP) decoder on many QLDPC codes can be improved by several orders of magnitude. Using this new BP-OSD decoder we study the performance of several known classes of degenerate QLDPC codes including hypergraph product codes, hyperbicycle codes, homological product codes, and Haah's cubic codes. We also construct several interesting examples of short generalized bicycle codes. Some of them have an additional property that their syndromes are protected by small BCH codes, which may be useful for the fault-tolerant syndrome measurement. We also propose a new large family of QLDPC codes that contains the class of hypergraph product codes, where one of the used parity-check matrices is square. It is shown that in some cases such codes have better performance than hypergraph product codes. Finally, we demonstrate that the performance of the proposed BP-OSD decoder for some of the constructed codes is better than for a relatively large surface code decoded by a near-optimal decoder.

scholarly journals The small stellated dodecahedron code and friends

2018 ◽  
Vol 376 (2123) ◽  
pp. 20170323 ◽  
Author(s):  
J. Conrad ◽  
C. Chamberland ◽  
N. P. Breuckmann ◽  
B. M. Terhal
Keyword(s):  
Quantum Mechanics ◽  
Fault Tolerant ◽  
Three Dimensional ◽  
Foundations Of Quantum Mechanics ◽  
Quantum Code ◽  
Contemporary Society ◽  
Parity Check ◽  
Logical Qubits ◽  
Surface Code ◽  
Logical Qubit

We explore a distance-3 homological CSS quantum code, namely the small stellated dodecahedron code, for dense storage of quantum information and we compare its performance with the distance-3 surface code. The data and ancilla qubits of the small stellated dodecahedron code can be located on the edges respectively vertices of a small stellated dodecahedron, making this code suitable for three-dimensional connectivity. This code encodes eight logical qubits into 30 physical qubits (plus 22 ancilla qubits for parity check measurements) in contrast with one logical qubit into nine physical qubits (plus eight ancilla qubits) for the surface code. We develop fault-tolerant parity check circuits and a decoder for this code, allowing us to numerically assess the circuit-based pseudo-threshold. This article is part of a discussion meeting issue ‘Foundations of quantum mechanics and their impact on contemporary society’.

scholarly journals On quantum tensor product codes

2017 ◽  
Vol 17 (13&14) ◽  
pp. 1105-1122
Author(s):  
Jihao Fan ◽  
Yonghui Li ◽  
Min-Hsiu Hsieh ◽  
Hanwu Chen
Keyword(s):  
Tensor Product ◽  
Error Correction ◽  
Mds Codes ◽  
Quantum Codes ◽  
Multiple Quantum ◽  
Parity Check ◽  
Product Codes ◽  
Burst Error ◽  
Quantum Error ◽  
Better Than

We present a general framework for the construction of quantum tensor product codes (QTPC). In a classical tensor product code (TPC), its parity check matrix is constructed via the tensor product of parity check matrices of the two component codes. We show that by adding some constraints on the component codes, several classes of dual-containing TPCs can be obtained. By selecting different types of component codes, the proposed method enables the construction of a large family of QTPCs and they can provide a wide variety of quantum error control abilities. In particular, if one of the component codes is selected as a burst-error-correction code, then QTPCs have quantum multiple-burst-error-correction abilities, provided these bursts fall in distinct subblocks. Compared with concatenated quantum codes (CQC), the component code selections of QTPCs are much more flexible than those of CQCs since only one of the component codes of QTPCs needs to satisfy the dual-containing restriction. We show that it is possible to construct QTPCs with parameters better than other classes of quantum error-correction codes (QECC), e.g., CQCs and quantum BCH codes. Many QTPCs are obtained with parameters better than previously known quantum codes available in the literature. Several classes of QTPCs that can correct multiple quantum bursts of errors are constructed based on reversible cyclic codes and maximum-distance-separable (MDS) codes.

scholarly journals Fault-Tolerant Gates on Hypergraph Product Codes

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Anirudh Krishna ◽  
David Poulin
Keyword(s):  
Fault Tolerant ◽  
Product Codes

scholarly journals Perturbed Adaptive Belief Propagation Decoding for High-Density Parity-Check Codes

2020 ◽  
pp. 1-1
Author(s):  
Li Deng ◽  
Zilong Liu ◽  
Yong Liang Guan ◽  
Xiaobei Liu ◽  
Chaudhry Adnan Aslam ◽  
...  
Keyword(s):  
Belief Propagation ◽  
High Density ◽  
Parity Check ◽  
Parity Check Codes

scholarly journals FAULT-TOLERANT MULTI-AGENT EXACT BELIEF PROPAGATION

2009 ◽  
Vol 25 (1) ◽  
pp. 1-30 ◽  
Author(s):  
Xiangdong An ◽  
Nick Cercone
Keyword(s):  
Belief Propagation ◽  
Fault Tolerant ◽  
Multi Agent

FAULT TOLERANT ROUTING IN HYPERCUBES AND STAR GRAPHS

1996 ◽  
Vol 06 (01) ◽  
pp. 127-136 ◽  
Author(s):  
QIAN-PING GU ◽  
SHIETUNG PENG
Keyword(s):  
Free Path ◽  
Fault Tolerant ◽  
Linear Time ◽  
Time Efficiency ◽  
Routing Problem ◽  
Star Graphs ◽  
Linear Time Algorithms ◽  
Better Than

In this paper, we give two linear time algorithms for node-to-node fault tolerant routing problem in n-dimensional hypercubes Hn and star graphs Gn. The first algorithm, given at most n−1 arbitrary fault nodes and two non-fault nodes s and t in Hn, finds a fault-free path s→t of length at most [Formula: see text] in O(n) time, where d(s, t) is the distance between s and t. Our second algorithm, given at most n−2 fault nodes and two non-fault nodes s and t in Gn, finds a fault-free path s→t of length at most d(Gn)+3 in O(n) time, where [Formula: see text] is the diameter of Gn. When the time efficiency of finding the routing path is more important than the length of the path, the algorithms in this paper are better than the previous ones.

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