20 papers · ranked by Valyu relevance
Victor V. Albert, Philippe Faist
Barcode scans, clear phone calls, reliable data storage, satellite communication, and large-scale quantum computation are all made possible by error correction. We present a handbook version of The Error Correction Zoo, a curated reference of methods for protecting classical or quantum information from errors during…
Zhengzhong Yi, Zhipeng Liang, Yulin Wu, Xuan Wang + 1 more
Inspired by classical polar codes, whose coding rate can asymptotically achieve the Shannon capacity, researchers are trying to find their analogs in the quantum information field, which are called quantum polar codes. However, no one has designed a quantum polar coding scheme that applies to quantum computing yet.…
S. Andrew Lanham, Travis C. Cuvelier, Corey Ostrove, Brian R. La Cour + 2 more
'Brian R. La Cour' 'Granville Ott' 'Robert W. Heath'] Abstract—In this work, we develop a space-time block code for noncoherent communication using techniques from the field of quantum error correction. We decompose the multiple-input multiple-output (MIMO) channel into operators from quantum mechanics, and design a…
Alex Rigby, J.C. Olivier, Peter Jarvis
For a number of quantum channels of interest, phase-flip errors occur far more frequently than bit-flip errors. When transmitting across these asymmetric channels, the decoding error rate can be reduced by tailoring the code used to the channel. However, analyzing the performance of stabilizer codes on these channels…
Pavithran Iyer, David Poulin
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 decoding problem consists of determining the most likely recovery given the syndrome.…
Francisco Revson F. Pereira, Stefano Mancini, Giuliano G. La Guardia
The Lindblad master equation describes the evolution of a large variety of open quantum systems. An important property of some open quantum systems is the existence of decoherence-free subspaces. A quantum state from a decoherence-free subspace will evolve unitarily. However, there is no procedural and optimal method…
Francisco Revson F. Pereira, Stefano Mancini, Giuliano G. La Guardia
The Lindblad master equation describes the evolution of a large variety of open quantum systems. An important property of some open quantum systems is the existence of decoherence-free subspaces. A quantum state from a decoherence-free subspace will evolve unitarily. However, there is no procedural and optimal method…
Zhipeng Liang, Zicheng Wang, Zhengzhong Yi, Fusheng Yang + 2 more
The code distance is a critical parameter of quantum stabilizer codes (QSCs), and determining it-whether exactly or approximately-is known to be an NP-complete problem. However, its upper bound can be determined efficiently by some methods such as the Monte Carlo method. Leveraging the Monte Carlo method, we propose an…
Anatoly Dymarsky, Alfred D. Shapere
There is a rich connection between classical error-correcting codes, Euclidean lattices, and chiral conformal field theories. Here we show that quantum errorcorrecting codes, those of the stabilizer type, are related to Lorentzian lattices and non-chiral CFTs. More specifically, real self-dual stabilizer codes can be…
Fang Zhang, Jianxin Chen, Giuliano Benenti
Error correction is an essential part of the theory of quantum computation. However, new quantum computation students may find the theories of error correction and fault tolerance daunting, or they may be stuck with theoretical/outdated schemes (such as the one in the original proof of the threshold theorem by Aharonov…
Yuan Li, Ying Guo, Osamu Hirota
Motivated by a family of binary cocyclic block matrices over GF(2), we proposed a construction method to gain the stabilizer of long-length quantum error-correction codes (QECCs). Stabilizer quantum codes (SQCs) can be obtained by the different rows of the yielded circulant permutation matrices; hence, the quantum…
Simeon Ball, Edgar Moreno, Robin Simoens
We prove that the natural isomorphism F2 h ∼= F h 2 induces a bijection between stabiliser codes on n quqits with local dimension q = 2h and binary stabiliser codes on hn qubits. This allows us to describe these codes geometrically: a stabiliser code over a field of even order corresponds to a so-called quantum set of…
Alex Rigby, J.C. Olivier, Peter Jarvis
Quantum low-density parity-check codes can be decoded using a syndrome based GF(4) belief propagation decoder. However, the performance of this decoder is limited both by unavoidable 4-cycles in the code's factor graph and the degenerate nature of quantum errors. For the subclass of CSS codes, the number of 4-cycles…
Anthony Beucher, Irene Miguel-Escalada, Diego Balboa, Matías G. De Vas + 9 more
The biological purpose and disease relevance of long noncoding RNAs (lncRNAs) is poorly understood. We examined HASTER, a lncRNA antisense to HNF1A. Haploinsufficient mutations in HNF1A, encoding a homeodomain transcription factor, cause diabetes mellitus. Using mouse and human models, we show that HASTER maintains…
Authors not listed
The Hidden Subgroup Problem (HSP) unifies several landmark quantum algorithms, yet systematic exploration of its variants and modern applications has slowed. This paper revives HSP-based algorithm design by examining new group structures with direct relevance to post-quantum cryptography, lattice problems, and…
Julie D. Thompson, Raymond Ripp, Claudine Mayer, Olivier Poch + 1 more
The X circular code is a set of 20 trinucleotides (codons) that has been identified in the protein-coding genes of most organisms (bacteria, archaea, eukaryotes, plasmids, viruses). It has been shown previously that the X circular code has the important mathematical property of being an error-correcting code. Thus…
Rodrick Wallace
The living state is cognitive at every scale and level of organization. Since it is possible to associate a broad class of cognitive processes with ‘dual’ information sources, many pathologies can be addressed using statistical models based on the Shannon Coding, the Shannon-McMillan Source Coding, the Rate Distortion…
W. Jeffrey Johnston, Stephanie E. Palmer, David J. Freedman
Neuronal activity in the brain is variable, yet both perception and behavior are generally reliable. How does the brain achieve this? Here, we show that the conjunctive coding of multiple stimulus features, commonly known as nonlinear mixed selectivity, may be used by the brain to support reliable information…
Authors not listed
Sequence-defined oligomers offer programmable molecular architectures with potential in data storage, authentication, and anticounterfeiting. However, their deployment in real-world materials has been constrained by their low scale, limited thermal resilience and the need for specialized analytical methods. Here we…
Michael Yarus
A near-universal Standard Genetic Code (SGC) implies a single origin for Earthly life. To study this unique event, I compute paths to the SGC, comparing different plausible histories. Notably, SGC-like coding emerges from traditional evolutionary mechanisms, and a superior path can be identified. To objectively measure…