Related papers: Degenerate Viterbi decoding
The decoding of error syndromes of surface codes with classical algorithms may slow down quantum computation. To overcome this problem it is possible to implement decoding algorithms based on artificial neural networks. This work reports a…
We introduce a quantum Viterbi decoding algorithm for hidden quantum Markov models (HQMMs) motivated by quantum information processing and quantum algorithms. Given a finite sequence of measurement outcomes, the algorithm identifies hidden…
Quantum technologies have the potential to solve certain computationally hard problems with polynomial or super-polynomial speedups when compared to classical methods. Unfortunately, the unstable nature of quantum information makes it prone…
Erasures are the primary type of errors in physical systems dominated by leakage errors. While quantum error correction (QEC) using stabilizer codes can combat erasure errors, it remains unknown which constructions achieve capacity…
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…
Quantum low-density parity-check codes are promising candidates for low-overhead fault-tolerant quantum computing, but degeneracy is known to impair the convergence of belief-propagation (BP) decoding of these codes. In this work, we show…
We describe the theory of quantum convolutional error correcting codes. These codes are aimed at protecting a flow of quantum information over long distance communication. They are largely inspired by their classical analogs which are used…
Quantum error correction, which utilizes logical qubits that are encoded as redundant multiple physical qubits to find and correct errors in physical qubits, is indispensable for practical quantum computing. Surface code is considered to be…
The use of deep neural network for decoding error control code will encounter two problems, namely, the high-precision requirements of the error control code and the complexity of the neural network due to the long code. In this paper, a…
An iterative decoding algorithm for convolutional codes is presented. It successively processes $N$ consecutive blocks of the received word in order to decode the first block. A bound is presented showing which error configurations can be…
In this paper, we propose a new erasure decoding algorithm for convolutional codes using the generator matrix. This implies that our decoding method also applies to catastrophic convolutional codes in opposite to the classic approach using…
We present a theory of quantum serial turbo-codes, describe their iterative decoding algorithm, and study their performances numerically on a depolarization channel. Our construction offers several advantages over quantum LDPC codes. First,…
Dense coding with non-maximally entangled states has been investigated in many different scenarios. We revisit this problem for protocols adopting the standard encoding scheme. In this case, the set of possible classical messages cannot be…
Efficient high-performance decoding of topological stabilizer codes has the potential to crucially improve the balance between logical failure rates and the number and individual error rates of the constituent qubits. High-threshold…
Quantum error correction (QEC) enables reliable computation on noisy hardware by encoding logical information across many physical qubits and periodically measuring parities to detect errors. A decoder is the classical algorithm that uses…
Quantum information needs to be protected by quantum error-correcting codes due to imperfect physical devices and operations. One would like to have an efficient and high-performance decoding procedure for the class of quantum stabilizer…
Though the theory of quantum error correction is intimately related to the classical coding theory, in particular, one can construct quantum error correction codes (QECCs) from classical codes with the dual containing property, this does…
To improve the efficiency of the encoding and the decoding is the important problem in the quantum error correction. In a preceding work, a general algorithm for decoding the stabilizer code is shown. This paper will show an decoding which…
Belief-propagation (BP) decoders play a vital role in modern coding theory, but they are not suitable to decode quantum error-correcting codes because of a unique quantum feature called error degeneracy. Inspired by an exact mapping between…
Error probability distribution associated with a given Clifford measurement circuit is described exactly in terms of the circuit error-equivalence group, or the circuit subsystem code previously introduced by Bacon, Flammia, Harrow, and…