Related papers: Degenerate Viterbi decoding
A novel decoding algorithm is developed for general quantum convolutional codes. Exploiting useful ideas from classical coding theory, the new decoder introduces two innovations that drastically reduce the decoding complexity compared to…
Quantum convolutional code was introduced recently as an alternative way to protect vital quantum information. To complete the analysis of quantum convolutional code, I report a way to decode certain quantum convolutional codes based on the…
The most famous error-decoding algorithm for convolutional codes is the Viterbi algorithm. In this paper, we present a new reduced complexity version of this algorithm which can be applied to a class of binary convolutional codes with…
Efficient and accurate decoding of quantum error-correcting codes is essential for fault-tolerant quantum computation, however, it is challenging due to the degeneracy of errors, the complex code topology, and the large space for logical…
We consider the problem of optimally decoding a quantum error correction code -- that is to find the optimal recovery procedure given the outcomes of partial "check" measurements on the system. In general, this problem is NP-hard. However,…
Decoding of convolutional codes poses a significant challenge for coding theory. Classical methods, based on e.g. Viterbi decoding, suffer from being computationally expensive and are restricted therefore to codes of small complexity. Based…
We present a quantum Viterbi algorithm (QVA) with better than classical performance under certain conditions. In this paper the proposed algorithm is applied to decoding classical convolutional codes, for instance; large constraint length…
In this article we address the computational hardness of optimally decoding a quantum stabilizer code. Much like classical linear codes, errors are detected by measuring certain check operators which yield an error syndrome, and the…
A striking feature of quantum error correcting codes is that they can sometimes be used to correct more errors than they can uniquely identify. Such degenerate codes have long been known, but have remained poorly understood. We provide a…
Quantum error correction offers a promising path for performing quantum computations with low errors. Although a fully fault-tolerant execution of a quantum algorithm remains unrealized, recent experimental developments, along with…
Surface codes are among the best candidates to ensure the fault-tolerance of a quantum computer. In order to avoid the accumulation of errors during a computation, it is crucial to have at our disposal a fast decoding algorithm to quickly…
Quantum error correction is essential for realizing scalable quantum computation. Among various approaches, low-density parity-check codes over higher-order Galois fields have shown promising performance due to their structured sparsity and…
This paper presents a comprehensive guide to designing minimal trellises for both non-degenerate and degenerate decoding of quantum stabilizer codes. For non-degenerate decoding, various strategies are explored, leveraging insights from…
We construct a hybrid quantum-classical Viterbi decoder for the classical error-correcting codes. Viterbi decoding is a trellis-based procedure for maximum likelihood decoding of classical error-correcting codes. In this article, we…
The quantum paradigm presents a phenomenon known as degeneracy that should improve the performance of quantum error correcting codes. However, the effects of this mechanism are sometimes ignored when evaluating the performance of sparse…
Mapping an error syndrome to the error operator is the core of quantum decoding network and is also the key step of recovery. The definitions of the bit-flip error syndrome matrix and the phase-flip error syndrome matrix were presented, and…
A Viterbi-like decoding algorithm is proposed in this paper for generalized convolutional network error correction coding. Different from classical Viterbi algorithm, our decoding algorithm is based on minimum error weight rather than the…
We examine the efficiency of pure, nondegenerate quantum-error correction-codes for Pauli channels. Specifically, we investigate if correction of multiple errors in a block is more efficient than using a code that only corrects one error…
We introduce a convergent iterative algorithm for finding the optimal coding and decoding operations for an arbitrary noisy quantum channel. This algorithm does not require any error syndrome to be corrected completely, and hence also finds…
We propose a general framework for decoding quantum error-correcting codes with generative modeling. The model utilizes autoregressive neural networks, specifically Transformers, to learn the joint probability of logical operators and…