Decoding Algorithm Research Articles

Stopping Sets of Algebraic Geometry Codes over Hyperelliptic Curves of Genus Two

Stopping sets are useful for analyzing the performance of a linear code under an iterative decoding algorithm over an erasure channel. In this paper, we consider stopping sets of one-point algebraic geometry codes defined by a hyperelliptic curve of genus g=2 defined by the plane model y2=f(x), where the degree of f(x) was 5. We completely classify the stopping sets of the one-point algebraic geometric codes C=CΩ(D,mP∞) defined by a hyperelliptic curve of genus 2 with m≤4. For m=3, we proved in detail that all sets S⊆{1,2,⋯,n} of a size greater than 3 are stopping sets and we give an example of sets of size 2,3 that are not.

Few-shot Algorithms for Consistent Neural Decoding (FALCON) Benchmark.

Intracortical brain-computer interfaces (iBCIs) can restore movement and communication abilities to individuals with paralysis by decoding their intended behavior from neural activity recorded with an implanted device. While this activity yields high-performance decoding over short timescales, neural data are often nonstationary, which can lead to decoder failure if not accounted for. To maintain performance, users must frequently recalibrate decoders, which requires the arduous collection of new neural and behavioral data. Aiming to reduce this burden, several approaches have been developed that either limit recalibration data requirements (few-shot approaches) or eliminate explicit recalibration entirely (zero-shot approaches). However, progress is limited by a lack of standardized datasets and comparison metrics, causing methods to be compared in an ad hoc manner. Here we introduce the FALCON benchmark suite (Few-shot Algorithms for COnsistent Neural decoding) to standardize evaluation of iBCI robustness. FALCON curates five datasets of neural and behavioral data that span movement and communication tasks to focus on behaviors of interest to modern-day iBCIs. Each dataset includes calibration data, optional few-shot recalibration data, and private evaluation data. We implement a flexible evaluation platform which only requires user-submitted code to return behavioral predictions on unseen data. We also seed the benchmark by applying baseline methods spanning several classes of possible approaches. FALCON aims to provide rigorous selection criteria for robust iBCI decoders, easing their translation to real-world devices.

Hardness results for decoding the surface code with Pauli noise

Real quantum computers will be subject to complicated, qubit-dependent noise, instead of simple noise such as depolarizing noise with the same strength for all qubits. We can do quantum error correction more effectively if our decoding algorithms take into account this prior information about the specific noise present. This motivates us to consider the complexity of surface code decoding where the input to the decoding problem is not only the syndrome-measurement results, but also a noise model in the form of probabilities of single-qubit Pauli errors for every qubit.In this setting, we show that quantum maximum likelihood decoding (QMLD) and degenerate quantum maximum likelihood decoding (DQMLD) for the surface code are NP-hard and #P-hard, respectively. We reduce directly from SAT for QMLD, and from #SAT for DQMLD, by showing how to transform a boolean formula into a qubit-dependent Pauli noise model and set of syndromes that encode the satisfiability properties of the formula. We also give hardness of approximation results for QMLD and DQMLD. These are worst-case hardness results that do not contradict the empirical fact that many efficient surface code decoders are correct in the average case (i.e., for most sets of syndromes and for most reasonable noise models). These hardness results are nicely analogous with the known hardness results for QMLD and DQMLD for arbitrary stabilizer codes with independent X and Z noise.

Two-Phase Globally Coupled Low-Density Parity Check Decoding Aided with Early Termination and Forced Convergence.

To enhance the decoding efficiency of Globally Coupled (GC) LDPC codes, we incorporated Early Termination (ET) and Forced Convergence (FC) into the local/global two-phase decoding algorithm to expedite the decoding process. The two-phase decoding scheme integrates the ET technique to halt unnecessary iterations in the local decoding phase while employing the FC technique to accelerate convergence in the global phase decoding. The application of ET technology in the local decoding of GC-LDPC codes will not cause performance loss as in traditional block codes and will cause considerable complexity gains. For a longer code length and larger convergence differences between nodes' global codes, the FC technique operates more efficiently in global code than local code. Two variants are proposed for the ET scheme in the local decoding, namely ET-1 and ET-2. The initial variant, ET-1, predicts whether local decoding can be successful according to data characteristics and stop the local decoding iteration that is not expected to be successful in time. In the case of ET-2, the saved local iterations are transformed to global decoding equally. The results show that ET-1 saves considerable decoding time complexity and ET-2 improves the performance of the GC-LDPC code with the same decoding time complexity. The combined approach of ET-1 with FC reduces the decoding time complexity up to 42% at a low Signal Noise Rate region while maintaining its performance; ET-2-FC two-phase decoding saves approximately 25% decoding time complexity while improving the BER by about 0.18 dB and FER by about 0.23 dB.

Distinct Neuron Types Contribute to Hybrid Auditory Spatial Coding.

Neural decoding is a tool for understanding how activities from a population of neurons inside the brain relate to the outside world and for engineering applications such as brain-machine interfaces. However, neural decoding studies mainly focused on different decoding algorithms rather than different neuron types which could use different coding strategies. In this study, we used two-photon calcium imaging to assess three auditory spatial decoders (space map, opponent channel, and population pattern) in excitatory and inhibitory neurons in the dorsal inferior colliculus of male and female mice. Our findings revealed a clustering of excitatory neurons that prefer similar interaural level difference (ILD), the primary spatial cues in mice, while inhibitory neurons showed random local ILD organization. We found that inhibitory neurons displayed lower decoding variability under the opponent channel decoder, while excitatory neurons achieved higher decoding accuracy under the space map and population pattern decoders. Further analysis revealed that the inhibitory neurons' preference for ILD off the midline and the excitatory neurons' heterogeneous ILD tuning account for their decoding differences. Additionally, we discovered a sharper ILD tuning in the inhibitory neurons. Our computational model, linking this to increased presynaptic inhibitory inputs, was corroborated using monaural and binaural stimuli. Overall, this study provides experimental and computational insight into how excitatory and inhibitory neurons uniquely contribute to the coding of sound locations.

Decoding LDPC Codes with a Regular Check Matrix Structure Using the Bit Flip Method

Problem statement: low-density LDPC codes have become very popular in modern communication systems, which make it possible to implement decoders for them in practice. In conditions of severe limitations of equipment performance, the task of searching and researching the characteristics of decoding algorithms for these codes is urgent. The aim of the work is to find a simplified algorithm for decoding LDPC codes and to study the noise immunity of the proposed algorithm. The methods used: to solve this problem computer simulation is used to compare the noise immunity of known decoding algorithms and the proposed algorithm. Scientific novelty: the noise immunity characteristics of the proposed Bit Flip algorithm for decoding LDPC code with a regular structure of the check matrix using gradient descent and the procedure for escaping the local minimum are investigated. Result: a specific variant of the Bit Flip algorithm for LDPC code with a regular structure check matrix using gradient descent and a procedure for escaping the local minimum is proposed. The results of computer simulation are presented. Theoretical significance: the characteristics of noise immunity for the proposed variant of the LDPC code decoding algorithm with a regular structure of the check matrix are investigated. Practical significance: when using the proposed LDPC code decoding algorithm in the receiver, it is possible to calculate the parameters of the communication system based on the available dependencies of the error coefficient on the signal-to-noise ratio.

Tensor-Network Decoding Beyond 2D

Decoding algorithms based on approximate tensor-network (TN) contraction have proven tremendously successful in decoding two-dimensional (2D) local quantum codes such as toric or surface codes and color codes, effectively achieving optimal decoding accuracy. In this work, we introduce several techniques to generalize TN decoding to higher dimensions so that it can be applied to three-dimensional (3D) codes as well as 2D codes with noisy syndrome measurements (phenomenological noise or circuit-level noise). The 3D case is significantly more challenging than 2D, as the involved approximate tensor contraction is dramatically less well behaved than its 2D counterpart. Nonetheless, we numerically demonstrate that the decoding accuracy of our approach outperforms state-of-the-art decoders on the 3D surface code, both in the point and loop sectors, as well as for depolarizing noise. Our techniques could prove useful in near-term experimental demonstrations of quantum error correction, when decoding is to be performed off line and accuracy is of the utmost importance. To this end, we show how TN decoding can be applied to circuit-level noise and demonstrate that it outperforms the matching decoder on the rotated surface code. Published by the American Physical Society 2024

A new approach for neural decoding by inspiring of hyperdimensional computing for implantable intra-cortical BMIs

In the field of Brain Machine Interface (BMI), the process of translating motor intention into a machine command is denoted as decoding. However, despite recent advancements, decoding remains a formidable challenge within BMI. The utilization of current decoding algorithms in the field of BMI often involves computational complexity and requires the use of computers. This is primarily due to the reliance on mathematical models to address the decoding issue and perform subsequent output calculations. Unfortunately, computers are not feasible for implantable BMI systems due to their size and power consumption. To address this predicament, this study proposes a pioneering approach inspired by hyperdimensional computing. This approach first involves identifying the pattern of each stimulus by considering the normal firing rate distribution of each neuron. Subsequently, the newly observed firing pattern for each input is compared with the patterns detected at each moment for each neuron. The algorithm, which shares similarities with hyperdimensional computing, identifies the most similar pattern as the final output. This approach reduces the dependence on mathematical models. The efficacy of this method is assessed through the utilization of an authentic dataset acquired from the Frontal Eye Field (FEF) of two male rhesus monkeys. The output space encompasses eight possible angles. The results demonstrate an accuracy rate of 51.5% while exhibiting significantly low computational complexity, involving a mere 2050 adder operators. Furthermore, the proposed algorithm is implemented on a field-programmable gate array (FPGA) and as an ASIC designe in a standard CMOS 180 nm technology, underscoring its suitability for real-time implantable BMI applications. The implementation required only 2.3 Kbytes of RAM, occupied an area of 2.2 mm2, and consumed 9.32 µW at a 1.8 V power supply. Consequently, the proposed solution represents an accurate, low computational complexity, hardware-friendly, and real-time approach.

Assessing the impact of degree of fusion and muscle fibre twitch shape variation on the accuracy of motor unit discharge time identification from ultrasound images

ObjectiveUltrasound (US) images during a muscle contraction can be decoded into individual motor unit (MU) activity, i.e., trains of neural discharges from the spinal cord. However, current decoding algorithms assume a stationary mixing matrix, i.e. equal mechanical twitches at each discharge. This study aimed to investigate the accuracy of these approaches in non-ideal conditions when the mechanical twitches in response to neural discharges vary over time and are partially fused in tetanic contractions. MethodsWe performed an in silico experiment to study the decomposition accuracy for changes in simulation parameters, including the twitch waveforms, spatial territories, and motoneuron-driven activity. Then, we explored the consistency of the in silico findings with an in vivo experiment on the tibialis anterior muscle at varying contraction forces. ResultsA large population of MU spike trains across different excitatory drives, and noise levels could be identified. The identified MUs with varying twitch waveforms resulted in varying amplitudes of the estimated sources correlated with the ground truth twitch amplitudes. The identified spike trains had a wide range of firing rates, and the later recruited MUs with larger twitch amplitudes were easier to identify than those with small amplitudes. Finally, the in silico and in vivo results were consistent, and the method could identify MU spike trains in US images at least up to 40% of the maximal voluntary contraction force. ConclusionThe decoding method was accurate irrespective of the varying twitch-like shapes or the degree of twitch fusion, indicating robustness, important for neural interfacing applications.

Real-Time Decoding of Snapshot Compressive Imaging Using Tensor FISTA-Net.

Snapshot compressive imaging (SCI) cameras compress high-speed videos or hyperspectral images into measurement frames. However, decoding the data frames from measurement frames is compute-intensive. Existing state-of-the-art decoding algorithms suffer from low decoding quality or heavy running time or both, which are not practical for real-time applications. In this article, we exploit the powerful learning ability of deep neural networks (DNN) and propose a novel tensor fast iterative shrinkage-thresholding algorithm net (Tensor FISTA-Net) as a real-time decoder for SCI cameras. Since SCI cameras have an accurate physical model, we can trade training time for the decoding time by generating abundant synthetic data and training a decoder on the cloud. Tensor FISTA-Net not only learns a sparse representation of the frames through convolution layers but also reduces the decoding time and memory consumption significantly through tensor operations, which makes Tensor FISTA-Net an appropriate approach for a real-time decoder. Our proposed Tensor FISTA-Net obtains an average PSNR improvement of 0.79-2.84 dB (video images) and 2.61-4.43 dB (hyperspectral images) over the state-of-the-art algorithms, along with more clear and detailed visual results on real SCI datasets, Hammer and Wheel, respectively. Our Tensor FISTA-Net reaches 45 frames per second in video datasets and 70 frames per second in hyperspectral datasets, meeting the real-time requirement. Besides, the trained model occupies only a 12 -MB memory footprint, making it applicable to real-time Internet of Things (IoT) applications.

Iterative decoding algorithm for LDPC-RS product codes based on joint check

Iterative decoding algorithm for LDPC-RS product codes based on joint check

Open-AI model Efficient Memory Reduce Management for the Large Language Models (LLMs) Serving with Paged Attention of sharing the KV Cashes

Abstract: High throughput serving of large language models (LLMs) requires batching sufficiently many requests at a time. However, existing systems struggle because the key-value cache (KV cache) memory for each request is huge and grows and shrinks dynamically. When managed inefficiently, this memory can be significantly wasted by fragmentation and redundant duplication, limiting the batch size. To address this problem we proposed a Paged Attention. An alternative algorithm inspired by the classical virtual memory and paging techniques in operating systems. An LLM serving system that achieves (1) near-zero waste in KV cache memory and (2) flexible sharing of KV cache within and across requests to further reduce memory usage. Our evaluations show that LLM improves the throughput of popular LLMs by 2-4× with the same level of latency compared to the state-of-the-art systems, such as Faster Transformer and Orca. The improvement is more pronounced with longer sequences, larger models, and more complex decoding algorithms

A deep transfer learning approach for cross-subject recognition of mental tasks based on functional near-infrared spectroscopy

In the field of brain-computer interfaces (BCIs) based on functional near-infrared spectroscopy (fNIRS), traditional subject-specific decoding methods suffer from the limitations of long calibration time and low cross-subject generalizability, which restricts the promotion and application of BCI systems in daily life and clinic. To address the above dilemma, this study proposes a novel deep transfer learning approach that combines the revised inception-residual network (rIRN) model and the model-based transfer learning (TL) strategy, referred to as TL-rIRN. This study performed cross-subject recognition experiments on mental arithmetic (MA) and mental singing (MS) tasks to validate the effectiveness and superiority of the TL-rIRN approach. The results show that the TL-rIRN significantly shortens the calibration time, reduces the training time of the target model and the consumption of computational resources, and dramatically enhances the cross-subject decoding performance compared to subject-specific decoding methods and other deep transfer learning methods. To sum up, this study provides a basis for the selection of cross-subject, cross-task, and real-time decoding algorithms for fNIRS-BCI systems, which has potential applications in constructing a convenient and universal BCI system.

Wearable high-density EMG sleeve for complex hand gesture classification and continuous joint angle estimation

High-density electromyography (HD-EMG) can provide a natural interface to enhance human–computer interaction (HCI). This study aims to demonstrate the capability of a novel HD-EMG forearm sleeve equipped with up to 150 electrodes to capture high-resolution muscle activity, decode complex hand gestures, and estimate continuous hand position via joint angle predictions. Ten able-bodied participants performed 37 hand movements and grasps while EMG was recorded using the HD-EMG sleeve. Simultaneously, an 18-sensor motion capture glove calculated 23 joint angles from the hand and fingers across all movements for training regression models. For classifying across the 37 gestures, our decoding algorithm was able to differentiate between sequential movements with 97.3±0.3%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$97.3 \\pm 0.3\\%$$\\end{document} accuracy calculated on a 100 ms bin-by-bin basis. In a separate mixed dataset consisting of 19 movements randomly interspersed, decoding performance achieved an average bin-wise accuracy of 92.8±0.8%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$92.8 \\pm 0.8\\%$$\\end{document}. When evaluating decoders for use in real-time scenarios, we found that decoders can reliably decode both movements and movement transitions, achieving an average accuracy of 93.3±0.9%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$93.3 \\pm 0.9\\%$$\\end{document} on the sequential set and 88.5±0.9%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$88.5 \\pm 0.9\\%$$\\end{document} on the mixed set. Furthermore, we estimated continuous joint angles from the EMG sleeve data, achieving a R2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$R^2$$\\end{document} of 0.884±0.003\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$0.884 \\pm 0.003$$\\end{document} in the sequential set and 0.750±0.008\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$0.750 \\pm 0.008$$\\end{document} in the mixed set. Median absolute error (MAE) was kept below 10° across all joints, with a grand average MAE of 1.8±0.04∘\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1.8 \\pm 0.04^\\circ$$\\end{document} and 3.4±0.07∘\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$3.4 \\pm 0.07^\\circ$$\\end{document} for the sequential and mixed datasets, respectively. We also assessed two algorithm modifications to address specific challenges for EMG-driven HCI applications. To minimize decoder latency, we used a method that accounts for reaction time by dynamically shifting cue labels in time. To reduce training requirements, we show that pretraining models with historical data provided an increase in decoding performance compared with models that were not pretrained when reducing the in-session training data to only one attempt of each movement. The HD-EMG sleeve, combined with sophisticated machine learning algorithms, can be a powerful tool for hand gesture recognition and joint angle estimation. This technology holds significant promise for applications in HCI, such as prosthetics, assistive technology, rehabilitation, and human–robot collaboration.

Highly reliable DHR-based polar compilation code communication method

The advent of fifth-generation mobile communication technology, 5G, has raised the bar for data transmission rates, information security, and reliability. Polar codes, the channel coding scheme in the 5G communication standard, encounter issues of singularity, limitations, and passivity in the face of unknown attacks. Therefore, this study introduces a highly reliable DHR-based polar coding communication approach. Drawing parallels between cyber attacks and channel noise, the method incorporates reconfigurable executors, decoding decisions, strategy scheduling, and other mechanisms to enable active defense. The True Relatively Axiom (TRA) is employed to theoretically validate the method’s heterogeneity, redundancy, and dynamics. Comparative simulation experiments with traditional polar decoding algorithms, such as SCL, SC, BP, SCAN, and SSC decoding algorithms, demonstrate that the proposed method not only improves secure transmission efficiency but also guarantees secure and reliable transmission across various attack scenarios. Our code is available at https://github.com/yuluzi/my-code.git.

English-Chinese Translation Quality Assessment Based on Phrase Statistical Machine Translation Decoding Algorithm

Machine learning translation is the automated process of translating text from one language to another using computational algorithms and statistical models. neural network-based approaches, particularly using models like sequence-to-sequence (Seq2Seq) with attention mechanisms, have shown remarkable performance improvements in translation quality. This paper proposes a Statistical Stochastic Gradient Machine Translation Decoding (SSGM-TD) algorithm for the English–Chinese translation for the quality assessment. The proposed SSGM-TD model uses statistical analysis for the estimation and evaluation of the features for the computation of variables. The proposed SSGM – TD model estimates the stochastic gradient with the regression analysis for the feature estimation. The developed SSGM-TD model is implemented with the machine learning model for the automated translation of the English–Chinese languages. The simulation analysis is performed for the evaluation of the quality assessment in the translation process. The detailed evaluation is conducted using various metrics, including BLEU and METEOR scores, offering quantitative insights into the algorithm's performance. The classification process of the SSGM-TD algorithm is examined, revealing its proficiency in correctly classifying positive and negative instances. Precision, recall, and F1 score metrics provide a significant evaluation of the algorithm's classification capabilities. The decoding results and quality assessments are presented with providing a comprehensive view of the algorithm's strengths and potential areas for improvement. The quality assessments incorporate both quantitative metrics and human evaluations, ensuring a holistic understanding of the algorithm's translation capabilities. The consistency between automated metrics and human assessments underscores the algorithm's commendable performance in maintaining semantic accuracy and linguistic coherence.

Facilitating practical fault-tolerant quantum computing based on color codes

Color codes are a promising topological code for fault-tolerant quantum computing. Insufficient research on color codes has delayed their practical application. In this work, we address several key issues to facilitate practical fault-tolerant quantum computing based on color codes. First, by introducing decoding graphs with error-rate-related weights, we obtain the threshold of 0.47% of the 6.6.6 triangular color code under the standard circuit-level noise model, narrowing the gap to that of the surface code. Second, our work first investigates the circuit-level decoding of color code lattice surgery, then gives an efficient decoding algorithm, which is crucial to perform logical operations in a quantum computer with two-dimensional architectures. Last, a state injection protocol of the triangular color code is proposed, reducing the output magic state error rate in one round of 15 to 1 distillation by two orders of magnitude compared to a previous rough protocol. We also prove that our protocol offers the lowest logical error rates for state injection among all possible codes. Published by the American Physical Society 2024

Multiplexed detection platform implemented with magnetic encoding and deep learning-based decoding for quantitative analysis of exosomes from cancers

Although a number of biosensing technologies have been reported for the detection of cancer-derived exosomes used as early diagnosis markers for cancers, it is necessary to identify them with various biomarkers to distinguish the stages and types of cancers owing to the extreme heterogeneity of cancer. Here, we developed a new multiplexed assay platform for the detection of exosomes using magnetic encoded microparticles (MEMPs), which can recognize multiple proteins expressed on exosomes, and a deep learning-based decoding algorithm. This platform, in which the accuracy of the decoding algorithm was evaluated to be 93 %, was applied to detect exosomes from four types of cancer cell lines and plasma from patients with cancer using three cancer biomarkers: PD-L1 (Programmed Death-Ligand 1), EpCAM (Epithelial cell adhesion molecule), and EGFR (Epidermal growth factor receptor). The limit of detections (LODs) of this platform when applied to the detection of exosomes from MDA-MB-231 cell line were calculated as 4.03 × 106 mL−1 for PD-L1, 1.00 ×107 mL−1 for EpCAM, and 7.17×106 mL−1 for EGFR, respectively. In a clinical study, four types of samples from patients with cancer (n = 92) showed higher signals than those of healthy controls (n = 18). Based on these results, we confirmed that this platform can distinguish patients with cancer from healthy individuals.

Analog Information Decoding of Bosonic Quantum Low-Density Parity-Check Codes

Quantum error correction is crucial for scalable quantum information-processing applications. Traditional discrete-variable quantum codes that use multiple two-level systems to encode logical information can be hardware intensive. An alternative approach is provided by bosonic codes, which use the infinite-dimensional Hilbert space of harmonic oscillators to encode quantum information. Two promising features of bosonic codes are that syndrome measurements are natively analog and that they can be concatenated with discrete-variable codes. In this work, we propose novel decoding methods that explicitly exploit the analog syndrome information obtained from the bosonic qubit readout in a concatenated architecture. Our methods are versatile and can be generally applied to any bosonic code concatenated with a quantum low-density parity-check (QLDPC) code. Furthermore, we introduce the concept of quasi-single shot protocols as a novel approach that significantly reduces the number of repeated syndrome measurements required when decoding under phenomenological noise. To realize the protocol, we present the first implementation of time-domain decoding with the overlapping window method for general QLDPC codes and a novel analog single-shot decoding method. Our results lay the foundation for general decoding algorithms using analog information and demonstrate promising results in the direction of fault-tolerant quantum computation with concatenated bosonic-QLDPC codes. Published by the American Physical Society 2024

Diagnostics of Mixed-State Topological Order and Breakdown of Quantum Memory

Topological quantum memory can protect information against local errors up to finite error thresholds. Such thresholds are usually determined based on the success of decoding algorithms rather than the intrinsic properties of the mixed states describing corrupted memories. Here we provide an intrinsic characterization of the breakdown of topological quantum memory, which both gives a bound on the performance of decoding algorithms and provides examples of topologically distinct mixed states. We employ three information-theoretical quantities that can be regarded as generalizations of the diagnostics of ground-state topological order, and serve as a definition for topological order in error-corrupted mixed states. We consider the topological contribution to entanglement negativity and two other metrics based on quantum relative entropy and coherent information. In the concrete example of the two-dimensional (2D) Toric code with local bit-flip and phase errors, we map three quantities to observables in 2D classical spin models and analytically show they all undergo a transition at the same error threshold. This threshold is an upper bound on that achieved in any decoding algorithm and is indeed saturated by that in the optimal decoding algorithm for the Toric code. Published by the American Physical Society 2024