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The implementation of practical error correction protocols is essential for deployment of quantum information technologies. Ways of exploiting high-spin nuclei, which have multi-level quantum resources, have attracted interest in this…
We construct explicitly two infinite families of genuine nonadditive 1-error correcting quantum codes and prove that their coding subspaces are 50% larger than those of the optimal stabilizer codes of the same parameters via the linear…
Error correcting codes protect quantum information and form the basis of fault tolerant quantum computing. Leading proposals for fault-tolerant quantum computation require codes with an exceedingly rare property, a transverse non-Clifford…
Three-dimensional (3D) topological codes offer the advantage of supporting fault-tolerant implementations of non-Clifford gates, yet their performance against realistic noise remains largely unexplored. In this work, we focus on the…
To equip DNA-based data storage with random-access capabilities, Yazdi et al. (2018) prepended DNA strands with specially chosen address sequences called primers and provided certain design criteria for these primers. We provide explicit…
Many-hypercube codes, concatenated ${[[n,n-2,2]]}$ quantum error-detecting codes ($n$ is even), have recently been proposed as high-rate quantum codes suitable for fault-tolerant quantum computing. While the original many-hypercube codes…
Quantum error correction is widely thought to be the key to fault-tolerant quantum computation. However, determining the most suited encoding for unknown error channels or specific laboratory setups is highly challenging. Here, we present a…
Quantum error correction is an essential ingredient for universal quantum computing. Despite tremendous experimental efforts in the study of quantum error correction, to date, there has been no demonstration in the realisation of universal…
Background The theoretical requirements for a genetic code were well defined and modeled by George Gamow and Francis Crick in the 50-es. Their models failed. However the valid Genetic Code, provided by Nirenberg and Matthaei in 1961,…
We study coded distributed matrix multiplication from an approximate recovery viewpoint. We consider a system of $P$ computation nodes where each node stores $1/m$ of each multiplicand via linear encoding. Our main result shows that 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…
Determining the full complement of protein-coding genes is a key goal of genome annotation. The most powerful approach for confirming protein coding potential is the detection of cellular protein expression through peptide mass spectrometry…
Quantum error correction will be a necessary component towards realizing scalable quantum computers with physical qubits. Theoretically, it is possible to perform arbitrarily long computations if the error rate is below a threshold value.…
To synthesize peptides alongside the RNAs making the so-called RNA world, some genetic coding involving RNA had to develop. Herein, it is proposed that the first real-coding setup was a direct one, made up of continuous poly-tRNA-like…
The surface code scheme for quantum computation features a 2d array of nearest-neighbor coupled qubits yet claims a threshold error rate approaching 1% (NJoP 9:199, 2007). This result was obtained for the toric code, from which the surface…
We give new constructions of two classes of algebraic code families which are efficiently list decodable with small output list size from a fraction $1-R-\epsilon$ of adversarial errors where $R$ is the rate of the code, for any desired…
Fault-tolerant quantum computing requires a universal gate set, but the necessary non-Clifford gates represent a significant resource cost for most quantum error correction architectures. Magic state cultivation offers an efficient…
Quantum error detection (QED) offers a promising pathway to fault tolerance in near-term quantum devices by balancing error suppression with minimal resource overhead. However, its practical utility hinges on optimizing design…
Introduced in [CG24], pseudorandom error-correcting codes (PRCs) are a new cryptographic primitive with applications in watermarking generative AI models. These are codes where a collection of polynomially many codewords is computationally…
DNA, with remarkable properties of high density, durability, and replicability, is one of the most appealing storage media. Emerging DNA storage technologies use composite DNA letters, where information is represented by probability…