Related papers: Improved belief propagation is sufficient for real…

We introduce a decoding framework for correlated errors in quantum LDPC codes under circuit-level noise. The core of our approach is a graph augmentation and rewiring for interference (GARI) method, which modifies the correlated detector…

Quantum error correction (QEC) is essential for scalable quantum computing. However, it requires classical decoders that are fast and accurate enough to keep pace with quantum hardware. While quantum low-density parity-check codes have…

Quantum relays are central to both quantum communication and distributed quantum computing, enabling long-distance transmission and modular architectures. Unlike classical repeaters, quantum repeaters preserve coherence without amplifying…

We propose a decoder for quantum low density parity check (LDPC) codes based on a beam search heuristic guided by belief propagation (BP). Our beam search decoder applies to all quantum LDPC codes and achieves different speed-accuracy…

Repetition code forms a fundamental basis for quantum error correction experiments. To date, it stands as the sole code that has achieved large distances and extremely low error rates. Its applications span the spectrum of evaluating…

We present a new family of quantum low-density parity-check codes, which we call radial codes, obtained from the lifted product of a specific subset of classical quasi-cyclic codes. The codes are defined using a pair of integers $(r,s)$ and…

Real-time decoding is crucial for fault-tolerant quantum computing but likely requires specialized hardware such as field-programmable gate arrays (FPGAs), whose parallelism can alter relative algorithmic performance. We analyze…

Polar codes are newly discovered capacity-achieving codes, which have attracted lots of research efforts. Polar codes can be efficiently decoded by the low-complexity successive cancelation (SC) algorithm and the SC list (SCL) decoding…

We introduce a new method for decoding short and moderate length linear block codes with dense parity-check matrix representations of cyclic form, termed multiple-bases belief-propagation (MBBP). The proposed iterative scheme makes use of…

One of the fundamental challenges in enabling fault-tolerant quantum computation is realising fast enough quantum decoders. We present a new two-stage decoder that accelerates the decoding cycle and boosts accuracy. In the first stage, a…

In this work, a relay channel is studied in which a source encoder communicates with a destination decoder through a number of out-of-band relays that are connected to the decoder through capacity-constrained digital backhaul links. This…

Efficient decoding to estimate error locations from outcomes of syndrome measurement is the prerequisite for quantum error correction. Decoding in presence of circuit-level noise including measurement errors should be considered in case of…

Lowering the resource overhead needed to achieve fault-tolerant quantum computation is crucial to building scalable quantum computers. We show that adapting conventional maximum likelihood (ML) decoders to a small subset of efficiently…

There has been a rise in decoding quantum error correction codes with neural network based decoders, due to the good decoding performance achieved and adaptability to any noise model. However, the main challenge is scalability to larger…

Real-time decoding of quantum error correction (QEC) is essential for enabling fault-tolerant quantum computation. A practical decoder must operate with high accuracy at low latency, while remaining robust to spatial and temporal variations…

We consider the design and analysis of coding schemes for the binary input two way relay channel with erasure noise. We are particularly interested in reliable physical layer network coding in which the relay performs perfect error…

Decoding low-density parity-check codes is critical in many current technologies, such as fifth-generation (5G) wireless networks and satellite communications. The belief propagation algorithm allows for fast decoding due to the low density…

Fault-tolerant quantum computation (FTQC) is expected to address a wide range of computational problems. To realize large-scale FTQC, it is essential to encode logical qubits using quantum error-correcting codes. High-rate concatenated…

Quantum communication relies on the existence of entanglement between two nodes of a network. However, due to its fragile nature, it is nearly impossible to establish entanglement at large distances through the direct transmission of…

Quantum error-correcting codes (QECCs) are necessary for fault-tolerant quantum computation. Surface codes are a class of topological QECCs that have attracted significant attention due to their exceptional error-correcting capabilities and…