Related papers: Degenerate quantum erasure decoding
Locally repairable codes (LRCs) were originally introduced to enable efficient recovery from erasures in distributed storage systems by accessing only a small number of other symbols. While their structural properties-such as bounds and…
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…
We study the performance of medium-length quantum LDPC (QLDPC) codes in the depolarizing channel. Only degenerate codes with the maximal stabilizer weight much smaller than their minimum distance are considered. It is shown that with the…
Hardware-friendly quantum low-density parity-check (QLDPC) decoders are commonly built upon belief propagation (BP) processing. Yet, quantum degeneracy often prevents BP from achieving reliable convergence. To overcome this fundamental…
Quantum computing is poised to solve practically useful problems which are computationally intractable for classical supercomputers. However, the current generation of quantum computers are limited by errors that may only partially be…
Quantum error correction (QEC) is essential for enabling quantum advantages, with decoding as a central algorithmic primitive. Owing to its importance and intrinsic difficulty, substantial effort has been made to QEC decoder design, among…
Quantum computers have the potential to solve certain complex problems in a much more efficient way than classical computers. Nevertheless, current quantum computer implementations are limited by high physical error rates. This issue is…
Realizing the full potential of quantum computation requires quantum error correction (QEC), with most recent breakthrough demonstrations of QEC using the surface code. QEC codes use multiple noisy physical qubits to encode information in…
Qubit loss errors constitute a dominant source of noise in many quantum hardware systems, particularly in neutral atom quantum computers. We develop a theoretical framework to effectively detect and correct loss errors in logical algorithms…
A fundamental requirement for enabling fault-tolerant quantum information processing is an efficient quantum error-correcting code (QECC) that robustly protects the involved fragile quantum states from their environment. Just as classical…
Decoding quantum error-correcting codes is a key challenge in enabling fault-tolerant quantum computation. In the classical setting, linear programming (LP) decoders offer provable performance guarantees and can leverage fast practical…
Quantum computing has the potential to solve problems that are intractable for classical systems, yet the high error rates in contemporary quantum devices often exceed tolerable limits for useful algorithm execution. Quantum Error…
Quantum low-density parity-check (QLDPC) codes are promising candidates for error correction in quantum computers. One of the major challenges in implementing QLDPC codes in quantum computers is the lack of a universal decoder. In this…
Fault tolerance in quantum protocols requires contributions from error-correcting codes and their suitable decoders. Quantum Low-Density Parity Check (QLDPC) codes are one of the most explored quantum codes that have good coding rate and…
Quantum burst error correction codes (QBECCs) are of great importance to deal with the memory effect in quantum channels. As the most important family of QBECCs, quantum cyclic codes (QCCs) play a vital role in the correction of burst…
Decoding sparse quantum codes can be accomplished by syndrome-based decoding using a belief propagation (BP) algorithm.We significantly improve this decoding scheme by developing a new feedback adjustment strategy for the standard BP…
The recent success in constructing asymptotically good quantum low-density parity-check (QLDPC) codes makes this family of codes a promising candidate for error-correcting schemes in quantum computing. However, conventional belief…
Error correction allows a quantum computer to preserve states long beyond the decoherence time of its physical qubits. Key to any scheme of error correction is the decoding algorithm, which estimates the error state of qubits from the…
Large-scale quantum computers promise transformative speedups, but their viability hinges on fast and reliable quantum error correction (QEC). At the center of QEC are decoders-classical algorithms running on hardware such as FPGAs, GPUs,…
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…