Related papers: Linked-Cluster Technique for Finding the Distance …
We survey the existing techniques for calculating code distances of classical codes and apply these techniques to generic quantum codes. For classical and quantum LDPC codes, we also present a new linked-cluster technique. It reduces…
The techniques of distance verification known for general linear codes are re-applied to quantum stabilizer codes. Then distance verification is addressed for classical and quantum LDPC codes. New complexity bounds for distance verification…
The distance of a classical or quantum code is a key figure of merit which reflects its capacity to detect errors. Quantum LDPC code families have considerable promise in reducing the overhead required for fault-tolerant quantum…
The problem of finding code distance has been long studied for the generic ensembles of linear codes and led to several algorithms that substantially reduce exponential complexity of this task. However, no asymptotic complexity bounds are…
We give a construction of quantum LDPC codes of dimension $\Theta(\log N)$ and distance $\Theta(N/\log N)$ as the code length $N\to\infty$. Using a product of chain complexes this construction also provides a family of quantum LDPC codes of…
Existence of quantum low-density parity-check (LDPC) codes whose minimal distance scales linearly with the number of qubits is a major open problem in quantum information. Its practical interest stems from the need to protect information in…
We examine LDPC codes decoded using linear programming (LP). Four contributions to the LP framework are presented. First, a new method of tightening the LP relaxation, and thus improving the LP decoder, is proposed. Second, we present an…
We give a construction of Quantum Low-Density Parity Check (QLDPC) codes with near-optimal rate-distance tradeoff and efficient list decoding up to the Johnson bound in polynomial time. Previous constructions of list decodable good distance…
An appropriate distance metric is crucial for categorical data clustering, as the distance between categorical data cannot be directly calculated. However, the distances between attribute values usually vary in different clusters induced by…
In this paper, a construction of a pair of "regular" quasi-cyclic LDPC codes as ingredient codes for a quantum error-correcting code is proposed. That is, we find quantum regular LDPC codes with various weight distributions. Furthermore our…
Low-density parity check (LDPC) codes are an important class of codes with many applications. Two algebraic methods for constructing regular LDPC codes are derived -- one based on nonprimitive narrow-sense BCH codes and the other directly…
This paper introduces a construction of quantum CSS codes from a tuple of component CSS codes and two collections of subsets. The resulting codes have parallelizable encoding and syndrome measurement circuits and built-in redundancy in the…
The current best asymptotic lower bound on the minimum distance of quantum LDPC codes with fixed non-zero rate is logarithmic in the blocklength. We propose a construction of quantum LDPC codes with fixed non-zero rate and prove that the…
Due to their fast decoding algorithms, quantum generalizations of low-density parity check, or LDPC, codes have been investigated as a solution to the problem of decoherence in fragile quantum states. However, the additional twisted inner…
Clustering is an important part of many modern data analysis pipelines, including network analysis and data retrieval. There are many different clustering algorithms developed by various communities, and it is often not clear which…
Two methods for constructing quantum LDPC codes are presented. We explain how to overcome the difficulty of finding a set of low weight generators for the stabilizer group of the code. Both approaches are based on some graph representation…
Two upper bounds on the minimum distance of type-1 quasi-cyclic low-density parity-check (QC LDPC) codes are derived. The necessary condition is given for the minimum code distance of such codes to grow linearly with the code length.
Crowdsourced, or human computation based clustering algorithms usually rely on relative distance comparisons, as these are easier to elicit from human workers than absolute distance information. A relative distance comparison is a statement…
LDPC convolutional codes have been shown to be capable of achieving the same capacity-approaching performance as LDPC block codes with iterative message-passing decoding. In this paper, asymptotic methods are used to calculate a lower bound…
Quantum error correction (QEC) is critical for practical realization of fault-tolerant quantum computing, and recently proposed families of quantum low-density parity-check (QLDPC) code are prime candidates for advanced QEC hardware…