Related papers: Diagnosis of weaknesses in modern error correction…
Low-density parity-check codes with irregular constructions have been recently shown to outperform the most advanced error-correcting codes to date. In this paper we apply methods of statistical physics to study the typical properties of…
Efficient decoding is crucial to high-throughput and power-sensitive wireless communication scenarios. A theoretical analysis of the performance-complexity tradeoff toward low-complexity decoding is required for a better understanding of…
We work out a theory of approximate quantum error correction that allows us to derive a general lower bound for the entanglement fidelity of a quantum code. The lower bound is given in terms of Kraus operators of the quantum noise. This…
We show that the problem of designing a quantum information error correcting procedure can be cast as a bi-convex optimization problem, iterating between encoding and recovery, each being a semidefinite program. For a given encoding…
We investigate the performance of a quantum error-correcting code when pushed beyond its intended capacity to protect information against errors, presenting formulae for the probability of failure when the errors affect more qudits than…
We present relaxed criteria for quantum error correction which are useful when the specific dominant noise process is known. These criteria have no classical analogue. As an example, we provide a four-bit code which corrects for a single…
In the setting of error-correcting codes with feedback, Alice wishes to communicate a $k$-bit message $x$ to Bob by sending a sequence of bits over a channel while noiselessly receiving feedback from Bob. It has been long known (Berlekamp,…
Guessing random additive noise decoding (GRAND) is a universal decoding paradigm that decodes by repeatedly testing error patterns until identifying a codeword, where the ordering of tests is generated by the received channel values. On one…
Automatic speech recognition (ASR) systems often encounter difficulties in accurately recognizing rare words, leading to errors that can have a negative impact on downstream tasks such as keyword spotting, intent detection, and text…
Error correction in automatic speech recognition (ASR) aims to correct those incorrect words in sentences generated by ASR models. Since recent ASR models usually have low word error rate (WER), to avoid affecting originally correct tokens,…
Current hardware for quantum computing suffers from high levels of noise, and so to achieve practical fault-tolerant quantum computing will require powerful and efficient methods to correct for errors in quantum circuits. Here, we explore…
There are well known necessary and sufficient conditions for a quantum code to correct a set of errors. We study weaker conditions under which a quantum code may correct errors with probabilities that may be less than one. We work with…
This work constructs codes that are efficiently decodable from a constant fraction of \emph{worst-case} insertion and deletion errors in three parameter settings: (i) Binary codes with rate approaching 1; (ii) Codes with constant rate for…
Error correction techniques remain effective to refine outputs from automatic speech recognition (ASR) models. Existing end-to-end error correction methods based on an encoder-decoder architecture process all tokens in the decoding phase,…
Quantum error mitigation has been proposed as a means to combat unwanted and unavoidable errors in near-term quantum computing without the heavy resource overheads required by fault tolerant schemes. Recently, error mitigation has been…
Even with the recent rapid developments in quantum hardware, noise remains the biggest challenge for the practical applications of any near-term quantum devices. Full quantum error correction cannot be implemented in these devices due to…
Recent progress in quantum cryptography and quantum computers has given hope to their imminent practical realization. An essential element at the heart of the application of these quantum systems is a quantum error correction scheme. We…
A fault-tolerant quantum computation requires an efficient means to detect and correct errors that accumulate in encoded quantum information. In the context of machine learning, neural networks are a promising new approach to quantum error…
Quantum metrology stands as a leading application of quantum science and technology, yet noise often constrains its precision and sensitivity. In near-term quantum metrology, existing protocols largely depend on virtual state purification,…
We present a method of concatenated quantum error correction in which improved classical processing is used with existing quantum codes and fault-tolerant circuits to more reliably correct errors. Rather than correcting each level of a…