Related papers: A matching decoder for bivariate bicycle codes
Product codes (PCs) protect a two-dimensional array of bits using short component codes. Assuming transmission over the binary symmetric channel, the decoding is commonly performed by iteratively applying bounded-distance decoding to the…
Many quantum technologies are now reaching a high level of maturity and control, and it is likely that the first demonstrations of suppression of naturally occurring quantum noise using small topological error correcting codes will soon be…
Cyclic codes are an interesting subclass of linear codes and have been used in consumer electronics, data transmission technologies, broadcast systems, and computer applications due to their efficient encoding and decoding algorithms. In…
Generalized Bicycle (GB) codes offer a compelling alternative to surface codes for quantum error correction. This paper focuses on (2,2)-Generalized Bicycle codes, constructed from pairs of binary circulant matrices with two non-zero…
Hypergraph product (HGP) codes are one of the most popular family of quantum low-density parity-check (LDPC) codes. Circuit-level simulations show that they can achieve the same logical error rate as surface codes with a reduced qubit…
Reed-Muller (RM) codes exhibit good performance under maximum-likelihood (ML) decoding due to their highly-symmetric structure. In this paper, we explore the question of whether the code symmetry of RM codes can also be exploited to achieve…
Topological color codes defined by the 4.8.8 semiregular lattice feature geometrically local check operators and admit transversal implementation of the entire Clifford group, making them promising candidates for fault-tolerant quantum…
A promising approach to overcome decoherence in quantum computing schemes is to perform active quantum error correction using topology. Topological subsystem codes incorporate both the benefits of topological and subsystem codes, allowing…
Quantum error correction is expected to be essential in large-scale quantum technologies. However, the substantial overhead of qubits it requires is thought to greatly limit its utility in smaller, near-term devices. Here we introduce a new…
flip is an extremely simple and maximally local classical decoder which has been used to great effect in certain classes of classical codes. When applied to quantum codes there exist constant-weight errors (such as half of a stabiliser)…
Providing closed-form estimates of the decoding failure rate of iterative decoders for low- and moderate-density binary parity-check codes has attracted significant interest in the research community. Recently, interest in this topic has…
Errors in surface code have typically been decoded by Minimum Weight Perfect Matching (MWPM) based method. Recently, neural-network-based Machine Learning (ML) techniques have been employed for this purpose. Here we propose a two-level (low…
Due to the high error rate of qubits, detecting and correcting errors is essential for achieving fault-tolerant quantum computing (FTQC). Quantum low-density parity-check (QLDPC) codes are one of the most promising quantum error correction…
Kitaev's toric code is one of the most prominent models for fault-tolerant quantum computation, currently regarded as the leading solution for connectivity constrained quantum technologies. Significant effort has been recently devoted to…
Cyclic codes are a subclass of linear codes and have applications in consumer electronics, data storage systems, and communication systems as they have efficient encoding and decoding algorithms. In this paper, almost perfect nonlinear…
Bias-tailoring allows quantum error correction codes to exploit qubit noise asymmetry. Recently, it was shown that a modified form of the surface code, the XZZX code, exhibits considerably improved performance under biased noise. In this…
Modern approaches for fast retrieval of similar vectors on billion-scaled datasets rely on compressed-domain approaches such as binary sketches or product quantization. These methods minimize a certain loss, typically the mean squared error…
Quantum low-density parity-check (qLDPC) codes offer a promising route to scalable fault-tolerant quantum computation with constant overhead. Recent advancements have shown that qLDPC codes can outperform the quantum memory capability of…
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…
We introduce a new type of sparse CSS quantum error correcting code based on the homology of hypermaps. Sparse quantum error correcting codes are of interest in the building of quantum computers due to their ease of implementation and the…