Related papers: A simple decoder for topological codes
Rotation symmetric bosonic codes are an attractive encoding for qubits into oscillator degrees of freedom, particularly in superconducting qubit experiments. While these codes can tolerate considerable loss and dephasing, they will need to…
A method is described which allows to evaluate efficiently a polynomial in a (possibly trivial) extension of the finite field of its coefficients. Its complexity is shown to be lower than that of standard techniques when the degree of the…
Decoding algorithms based on approximate tensor network contraction have proven tremendously successful in decoding 2D local quantum codes such as surface/toric codes and color codes, effectively achieving optimal decoding accuracy. In this…
The training complexity of deep learning-based channel decoders scales exponentially with the codebook size and therefore with the number of information bits. Thus, neural network decoding (NND) is currently only feasible for very short…
We show that here standard decoding algorithms for generic linear codes over a finite field can speeded up by a factor which is essentially the size of the finite field by reducing it to a low weight codeword problem and working in the…
We present a comprehensive framework for structured sparse coding and modeling extending the recent ideas of using learnable fast regressors to approximate exact sparse codes. For this purpose, we develop a novel block-coordinate proximal…
In this paper we describe how to leverage higher-order unification to type check a dependently typed language with meta-variables. The literature usually presents the unification algorithm as a standalone component, however the need to…
In many areas of applied geometric/numeric computational mathematics, including geo-mapping, computer vision, computer graphics, finite element analysis, medical imaging, geometric design, and solid modeling, one has to compute incidences,…
Tensor codes are a generalisation of matrix codes. Such codes are defined as subspaces of order-r tensors for which the ambient space is endowed with the tensor-rank as a metric. A class of these codes was introduced by Roth, who also…
This chapter studies the problem of decomposing a tensor into a sum of constituent rank one tensors. While tensor decompositions are very useful in designing learning algorithms and data analysis, they are NP-hard in the worst-case. We will…
Computational topology is an area that revisits topological problems from an algorithmic point of view, and develops topological tools for improved algorithms. We survey results in computational topology that are concerned with graphs drawn…
We propose a new strategy to decode color codes, which is based on the projection of the error onto three surface codes. This provides a method to transform every decoding algorithm of surface codes into a decoding algorithm of color codes.…
We prove the existence of topological quantum error correcting codes with encoding rates $k/n$ asymptotically approaching the maximum possible value. Explicit constructions of these topological codes are presented using surfaces of…
Neural architecture search methods are able to find high performance deep learning architectures with minimal effort from an expert. However, current systems focus on specific use-cases (e.g. convolutional image classifiers and recurrent…
A set of linearly constrained permutation matrices are proposed for constructing a class of permutation codes. Making use of linear constraints imposed on the permutation matrices, we can formulate a minimum Euclidian distance decoding…
The design of decoding algorithms is a significant technological component in the development of fault-tolerant quantum computers. Often design of quantum decoders is inspired by classical decoding algorithms, but there are no general…
Topological subsystem color codes add to the advantages of topological codes an important feature: error tracking only involves measuring 2-local operators in a two dimensional setting. Unfortunately, known methods to compute with them were…
In this paper we address the problem of decoding linearized Reed-Solomon (LRS) codes beyond their unique decoding radius. We analyze the complexity in order to evaluate if the considered problem is of cryptographic relevance, i.e., can be…
The development of multicore architectures supporting parallel data processing has led to a paradigm shift, which affects communication systems significantly. This article provides a scalable parallel approach of an iterative LDPC decoder,…
Polar codes provably achieve the capacity of a wide array of channels under successive decoding. This assumes infinite precision arithmetic. Given the successive nature of the decoding algorithm, one might worry about the sensitivity of the…