Bounds on Autonomous Quantum Error Correction

Quantum computing offers unprecedented speed and power for solving complex problems, but its susceptibility to errors makes error-correction codes crucial. An important metric for evaluating the performance of error-correction codes is the code distance, which measures the number of errors a code can correct. Current qubit-plane architectures are implemented using the same code distance. However, a larger code distance reduces the logical error rate but increases resources. In fact, distance-5 code uses more resources but offers higher resilience to logical errors compared to distance-3 code. We propose a qubit-plane architecture for rotated and unrotated surface codes called Qentaurus that combines various code distances of logical qubits for robust error correction while maintaining qubit efficiency. Qentaurus is designed to be highly scalable regarding computation, layout, and code distance. We performed a case study using Qentaurus with distance-3 and -7 codes to evaluate the performance. Moreover, we additionally developed a qubit placement scheme that considers the critical path of the quantum circuit to reduce the logical error rate and gate count. Our main experimental results demonstrated that Qentaurus considerably reduces the overall logical error rate (by 15.76% on average and up to 25.25%) than that of the Distance-3 Checkerboard architecture. After additionally implementing the qubit placement scheme, the average reduction increases to 13.44% (up to 39.07%). Notably, the Qentaurus-37 maintains logical error rates comparable to those of the Distance-5 Checkerboard, achieving considerable qubit efficiency. The Distance-5 Checkerboard demands 227.7% more physical qubits than that required by the Distance-3 Checkerboard, while Qentaurus-37 utilizes just 131.2% of the physical qubits required by Distance-3 the Checkerboard, marking a substantial reduction of 96.5% in the resource gap. The overall gate count is reduced by an average of 1.74% with Qentaurus alone and by 3.33% on average with the qubit placement scheme. We believe that the proposed Qentaurus and qubit placement scheme have the potential to significantly improve the error-correction performance of large-scale quantum computers in practical applications.

Quantum error correction enables the preservation of logical qubits with a lower logical error rate than the physical error rate, with performance depending on the decoding method. Traditional decoding approaches rely on the binarization (“hardening”) of readout data, thereby ignoring valuable information embedded in the analog (“soft”) readout signal. We present experimental results showcasing the advantages of incorporating soft information into the decoding process of a distance-3 (d=3) bit-flip surface code with flux-tunable transmons. We encode each of the 16 computational states that make up the logical state |0L⟩, and protect them against bit-flip errors by performing repeated Z-basis stabilizer measurements. To infer the logical fidelity for the |0L⟩ state, we average across the 16 computational states and employ two decoding strategies: minimum-weight perfect matching and a recurrent neural network. Our results show a reduction of up to 6.8% in the extracted logical error rate with the use of soft information. Decoding with soft information is widely applicable, independent of the physical qubit platform, and could allow for shorter readout durations, further minimizing logical error rates. Published by the American Physical Society 2024

Fault-tolerant quantum computation critically depends on the ability to detect and correct physical qubit errors faster than they accumulate. The surface code (SC) has emerged as the most experimentally promising quantum error correction (QEC) framework due to its high threshold and local stabilizer structure, yet its practical performance is bottlenecked by decoder efficiency. Traditional decoding approaches such as minimum-weight perfect matching (MWPM) achieve near-optimal accuracy under independent noise but struggle with correlated errors, circuit-level noise, and real-time latency constraints. This paper investigates how neural network (NN)-based decoders reduce logical error rates in SC quantum systems by learning complex syndrome-to-correction mappings from data. We propose a hybrid convolutional-recurrent neural architecture that processes stabilizer measurement syndromes across both spatial and temporal dimensions, enabling the decoder to capture correlated error patterns inherent in realistic hardware. Systematic simulations under depolarizing, biased, and circuit-level noise models demonstrate that the proposed neural decoder achieves a logical error rate reduction of up to 41.3% compared to MWPM at a physical error rate of p = 0.008, while maintaining sub-millisecond decoding latency compatible with superconducting qubit cycle times. These results establish that data-driven neural decoders represent a scalable and hardware-compatible pathway toward achieving the logical error rates required for practical fault-tolerant quantum computing.

BackgroundCannabis is the third most commonly used drug worldwide, with studies suggesting a deleterious effect on some aspects of performance monitoring. It is unknown, however, whether diminished error awareness influences adaptive behaviour in cannabis users. Therefore, this study examined the effect of error awareness on learning from errors in cannabis users.MethodsThirty-six chronic cannabis users (Mage = 23.81 years; female, 36%) and 34 controls (Mage = 21.53 years; female, 76%) completed a Go/No-Go task that allowed participants to learn from errors and adapt their behaviour. Multilevel models were specified to determine whether the effect of error awareness on learning from errors differs between cannabis users and controls, and whether cannabis-use measures predict error correction while accounting for error awareness.ResultsWhile error awareness and correction rates did not differ between the groups, there was a significant effect of age of use onset on error correction in cannabis users. Further, the effect of error awareness was dependent on age of onset, and cannabis use-related frequency and harm. That is, cannabis users reporting an earlier age of regular use or scoring higher on the cannabis use index were less likely to perform correctly following an aware error.ConclusionIt appears overall cannabis use might not be tightly coupled to behavioural indices of performance monitoring. There is evidence, however, that aspects of cannabis use predict impairments in learning from errors that may be associated with treatment outcomes.

Imperfect measurements are a prevalent source of error across quantum computing platforms, significantly degrading the logical error rates achievable on current hardware. To mitigate this issue, rich measurement data referred to as soft information has been proposed to efficiently identify and correct measurement errors as they occur. In this work, we model soft information decoding across a variety of physical qubit platforms and decoders and showcase how soft information can make error correction viable at lower code distances and higher physical error rates than is otherwise possible. We simulate the effects of soft information decoding on quantum memories for surface codes and bivariate bicycle codes, and evaluate the error suppression performance of soft decoders against traditional decoders. Our simulations show that soft information decoding on near-term devices can provide up to 11% higher error suppression on superconducting qubits and up to 20% stronger error suppression on neutral atom qubits. These accuracy gains correspond to 13% and 33% reductions in the physical qubit footprint of superconducting and neutral atom devices respectively when operating at a logical error rate of 10 −6 , showcasing that soft information is a powerful tool for reducing the cost and complexity of large-scale fault-tolerant quantum computers.

Grammatical errors are one of the most common types of errors in English learning and writing. Intelligent detection and correction of English grammatical errors can effectively help English learners improve their learning efficiency. The research is based on the BLSTM bi-directional and long-short-term memory neural network to construct a sequence labeling model to detect and correct English grammatical errors. The results show that the sequence tagging model based on the BLSTM bi-directional and long-short-term memory neural network has an accuracy of 96.88% for the part-of-speech tagging of special corpora containing grammatical errors, the accuracy rate of error correction is 33.58%, the recall rate is 44.95%, F-measure index value is 38.26%, which is 4.85% higher than the UIUC model and 4.92% higher than the Corpus GEC model. It can automatically detect and correct text grammatical errors with good effect, which provides a new idea for the development of intelligent English grammatical error detection and correction technology.

Codes for rank modulation have been recently proposed as a means of protecting flash memory devices from errors. We study basic coding theoretic problems for such codes, representing them as subsets of the set of permutations of $n$ elements equipped with the Kendall tau distance. We derive several lower and upper bounds on the size of codes. These bounds enable us to establish the exact scaling of the size of optimal codes for large values of $n$. We also show the existence of codes whose size is within a constant factor of the sphere packing bound for any fixed number of errors.

Soft errors hamper reliability of modern electronic circuits. In critical application areas, demand of safety against soft errors is increasing. Several methods have been developed to provide such error free environment in modern systems. The use of Golay code, and BCH codes are some of the top most widely used techniques. Nonetheless, still no methods have claimed that it has 100% correction rate. In this paper, a new Successive Parity Generation (SPG) based approach is proposed to tolerate such soft errors. After occurrence of bit errors in data, the proposed method corrects all the bit errors completely. It calculates parity at receiver end and successively detects errors and correct the erroneous data by comparing sender and receiver parity bits. The proposed method can detect and correct 100% error for any size of codeword with a moderate overhead. Experimental studies show that it outperforms existing methods with respect to error correction rate, time and information overhead.

BackgroundMany neurodegenerative disorders are characterised by changes in specific eye movement (EM) outcomes. Individuals with Alzheimer’s disease (AD) make more antisaccade errors and correct a lower proportion of those errors compared to controls. EM impairments occur at an early stage of neuropathological changes and have, therefore, been discussed as a potential biomarker. Despite high test‐retest correlations for measures of EM performance and an estimated heritability of >40% for antisaccade performance, genetic association studies identified only a few single‐nucleotide polymorphisms (SNPs) related to EM performance. Polygenic risk scores (PRSs) are advantageous as they summarize the effects of many SNPs into a single score. Therefore, we assessed whether higher genetic risk for AD in healthy participants was associated with higher antisaccade error rate and lower correction rate of antisaccade errors.MethodThe analyses were based on data of the first 2,000 participants (aged 30‐95) of the Rhineland Study, a community‐based prospective cohort study in Bonn, Germany. Genotyping was performed on Omni 2.5 exome arrays. We created PRS for AD by including all SNPs that reached genome‐wide significance at a threshold of p=5x10‐7in stage one of the GWAS of the “IGAP consortium”. Missing SNPs were imputed using the 1000 Genomes reference panel. We examined the association between genetic risk for AD and antisaccade error rate using multivariable regression with PRS as predictor and antisaccade error rate as outcome variables. For antisaccade correction rate we used a one‐inflated beta regression model as the residuals were severely skewed. Ancestry, age, age2, sex, visual acuity and education were added as covariates in both regression models.ResultPolygenic risk for AD was associated with neither antisaccade error rate nor the proportion of uncorrected errors in those who did not correct all of their errors. However, a higher PRS for AD was associated with a lower odds of correcting all mistakes (odds ratio=0.85 (95%‐CI:0.73‐1.00) per one standard deviation increase in PRS).ConclusionPolygenic risk for AD was associated with error correction rate in healthy individuals. Our findings suggest that eye movement performance may be a potential biomarker for early‐stage AD‐related neuropathological changes in the general population.

This paper considers a novel error-correcting scheme exploiting chaotic dynamics for noncoherent chaos communication. In our proposed system, two successive chaotic sequences are generated from the same chaotic map; the second sequence is generated with an initial value which is the last value of the first sequence. In this case, successive chaotic sequences having the same chaotic dynamics are created. This feature gives the receiver additional information to correctly recover the information data and thus improves the bit error performance of the receiver. Further, enhanced efficiency also comes from operating on successively modulated data; by involving less redundancy in the error correction system, it can be designed with high coding rate. In this paper, we analyze the scheme's capability, by examining computational times and accuracy rates of error correction, bounds on its capability.

High precision of task performance is required in almost all activities of humans and non-human subjects – the hallmark of the functioning of the error monitoring and processing system (EMPS). In many cases, however, task precision is affected by the level of error commission, which decreases the quality of work or task performance. But error commission is an integral component of the EMPS. Previously we have estimated the physiological range of error commission to be around 5%. This suggests that above the physiological range, error commission is a negative coupling factor in the EMPS. However, even at the physiological range of error commission, the rate of error detection and concomitant correction, which are required to improve task precision, differs in many subjects. In conditions of correct performance of task, precision is promoted, and thus, represents a positive coupling factor in the EMPS. Therefore, error commission, detection and correction represent integral components required for high precision task performance. Been the main energy substrate for neural activity, glucose modulates several domains of EMPS. Interestingly, the main components of EMPS functioning – error commission, correction and detection are associated with changes in glucoallostasis. Here we propose the high precision functioning of EMPS involves coupling at different levels of error commission, correction and detection. Further we suggest that this multilevel coupling modulates neural plasticity through changes in glucoallostasis. This work provides a conceptual background to the modeling of high precision task performance in human and non-human subjects.

Recent developments in cognitive neuroscience, particularly predictive processing models, demonstrate that human perception operates through active inference rather than passive observation (Clark, 2016; Friston, 2010). This finding, combined with previous research on heuristics and biases, challenges the empirical viability of the traditionally conceived version of individual-level objectivity. (Kahneman, 2011; Hohwy, 2013). Simultaneously, digital systems exhibit measurable tendencies toward homophily reinforcement and selective exposure amplification that worsen the information environment (Pariser, 2011; Bakshy et al., 2015). Therefore, this paper develops a framework of strong institutional objectivity that synthesizes insights from predictive processing, social epistemology, and power analysis to reconceptualize objectivity as an emergent institutional property rather than an individual action.. Through comparative case analysis of scientific reform initiatives and algorithmic mediation systems, I identify specific institutional design features that demonstrably improve error detection and correction rates while addressing structural exclusions that compromise knowledge production. The analysis yields testable propositions about the interaction between procedural controls and participation structures in determining epistemic outcomes, providing both a theoretical synthesis and an empirically grounded model for designing knowledge systems that achieve reliability through institutional mechanisms.

We have developed highly efficient parallel solutions for three practical, full-scale scientific problems: wave mechanics, fluid dynamics, and structural analysis. Several algorithmic techniques are used to keep communication and serial overhead small as both problem size and number of processors are varied. A new parameter, operation efficiency, is introduced that quantifies the tradeoff between communication and redundant computation. A 1024-processor MIMD ensemble is measured to be 502 to 637 times as fast as a single processor when problem size for the ensemble is fixed, and 1009 to 1020 times as fast as a single processor when problem size per processor is fixed. The latter measure, denoted scaled speedup, is developed and contrasted with the traditional measure of parallel speedup. The scaled-problem paradigm better reveals the capabilities of large ensembles, and permits detection of subtle hardware-induced load imbalances (such as error correction and data-dependent MFLOPS rates) that may become increasingly important as parallel processors increase in node count. Sustained performance for the applications is 70 to 130 MFLOPS, validating the massively parallel ensemble approach as a practical alternative to more conventional processing methods. The techniques presented appear extensible to even higher levels of parallelism than the 1024-processor level explored here.

The increasing demand for high-density and high-speed digital optical recording systems has made the development of advanced coding and signal processing techniques for fast and reliable data recovery increasingly important. In recent years, the parity-check (PC)-code-based reception technique has been widely studied for magnetic recording systems, and it is projected to be highly promising for high-density optical recording. The PC code is an inner error correction code (ECC), which can detect dominant short error events of the system, using only a few parity bits. This reduces the loss in error correction capability of the outer ECC due to random short errors and results in a simple and efficient solution to improve the overall performance. This thesis is dedicated to the design and analysis of PCcode- based recording systems to achieve higher recording capacity with low implementation complexity, for high-density blue laser disc systems. In particular, most of the key components of the PC-code-based optical recording system have been designed and optimized for different recording densities, and different proportions of white noise and media noise. During the development of advanced coding and detection techniques, it becomes necessary to investigate the system’s performance with different coding schemes and recording densities. In Chapter 2 of the thesis, we propose a generalized Braat-Hopkins model for optical recording channels, which provides a fair basis for the performance comparison of detection schemes over different coding schemes and recording densities, for channels with additive, white Gaussian noise (AWGN) and media noise. Various basic issues associated with the PC-code-based systems are investigated in Chapter 3. These include bounds for bit error rates and error event probabilities, the dominant error events at channel detector output, different PC codes, simple and efficient post-processors, the impact of error events that are split across data block boundaries and the corresponding remedy, as well as the effects of code rates and recording densities. Simulation results show that a 4-bit PC code achieves the best performance. The corresponding bit error rates (BERs) are very close to the performance bounds, at both nominal and high densities. Constrained codes, which serve as a key component in the read-write channel of data storage systems, are desired to have a high code rate with low-complexity encoder/decoder. In Chapter 4, we investigate the design of certain capacity-approaching constrained codes for optical recording systems. In particular, we derive analytically the relationship between the number of encoder states and the maximum size of these codes. We identify the minimum number of encoder states that maximizes the code rate, for any desired codeword length. The design of constrained PC codes is key to the development of PCcode- based systems, and the systematic design of efficient constrained PC codes remains a challenging problem. In Chapter 5, we propose a general and systematic code design technique for constructing capacity-approaching constrained PC codes, which can detect any type of error events of the system, with the minimum code rate loss. Compared to the rate 2/3 code without parity, the newly designed constrained 4-bit PC code achieves a performance gain of 2 dB at nominal density, and 1.5 dB at high density, at BER = 10-5. As the dominant noise for high-density optical recording systems, media noise severely degrades the performance of channel detectors and postprocessors that are designed for AWGN. In Chapter 6, we propose two novel modifications to the bit detector to combat media noise. We further develop a data-dependent post-processing scheme for error correction. Compared to the system designed without considering media noise and without PC codes, the overall performance gain of the developed scheme can be more than 11 dB at high media noise levels. In data storage systems, the ECC failure rate (EFR) serves as the ultimate measure of the data recovery performance. In Chapter 7, we develop semi-analytical approaches for estimating the EFR, and analyze EFRs for the developed PC-code-based systems, for the cases without and with interleaving. Our analysis shows that with the optimum interleaving degrees, compared to the rate 9/13 code without parity, the 2-bit PC code achieves a gain of around 0.5 dB, and the 4-bit PC code gains 0.6 dB, at high record ing density and EFR = 10-16. The thesis concludes in Chapter 8 with some suggestions for further work.

Congenital heart defects (CHDs) remain a leading cause of infant morbidity and mortality worldwide, with current treatments largely focused on symptomatic management rather than addressing underlying genetic causes. This study evaluates the effectiveness, therapeutic potential, and clinical feasibility of CRISPR-based gene-editing interventions in the personalized treatment of CHDs. Using a quantitative research design, data were collected from clinical trials, laboratory experiments, and genomic datasets, with stratified sampling to ensure representation across different CHD types and genetic mutations. Statistical analyses assessed gene correction rates, improvements in cardiac function, survival, symptom reduction, and quality of life, alongside safety metrics including adverse effects, off-target mutations, and immune responses. Results indicate that advanced CRISPR techniques such as base editing and prime editing—achieved high mutation correction rates (72%–88%) with low off-target effects (1.5%–6%) and meaningful improvements in cardiac function (60%–75%). Personalized approaches, including patient-specific guide RNAs, iPSC-based ex vivo editing, genomic profiling-guided prime editing, and AI-assisted targeting, led to increased survival (30%–40%), reduced symptoms (55%–65%), decreased hospital readmissions, and enhanced quality of life (65%–75%), with all findings statistically significant (p < 0.05). Safety evaluation demonstrated acceptable adverse effect rates (6%–14%) and moderate immune responses (4%–9%), while ethical compliance and clinical feasibility scores were high (7.0–9.0 and 6.5–8.5, respectively). These findings suggest that CRISPR-based therapies are both effective and clinically feasible for personalized CHD treatment, supporting a shift from symptom-based interventions to curative, gene-targeted strategies. Future research should focus on optimizing delivery systems, ensuring long-term safety, and developing scalable clinical protocols to advance precision medicine for CHDs.