Error Correction Scheme Research Articles

Fault-tolerant double-circular connectivity pattern for quantum stabilizer codes

Recently, the circular connectivity pattern has been presented for a class of stabilizer quantum error correction codes. The circular connectivity pattern for such a class of stabilizer codes can be implemented in a resource-efficient manner using a single ancilla and native two-qubit Controlled-Not-Swap gates (CNS) gates, which may be interesting for demonstrating error-correction codes with superconducting quantum processors. However, one concern is that this scheme is not fault-tolerant. And it might not apply to the Calderbank-Shor-Steane (CSS) codes. In this paper, we present a fault-tolerant version of the circular connectivity pattern, named the double-circular connectivity pattern. This pattern is an implementation for syndrome-measurement circuits with a flagged error correction scheme for stabilizer codes. We illustrate that this pattern is available for Steane code (a CSS code), Laflamme’s five-qubit code, and Shor’s nine-qubit code. For Laflamme’s five-qubit code and Shor’s nine-qubit code, the pattern has the property that it uses only native two-qubit CNS gates, which are more efficient in the superconducting quantum platform.

Characterizing randomness in parameterized quantum circuits through expressibility and average entanglement

Abstract While scalable error correction schemes and fault tolerant quantum computing seem not to be universally accessible in the near sight, the efforts of many researchers have been directed to the exploration of the contemporary available quantum hardware. Due to these limitations, the depth and dimension of the possible quantum circuits are restricted. This motivates the study of circuits with parameterized operations that can be classically optimized in hybrid methods as variational quantum algorithms, enabling the reduction of circuit depth and size. The characteristics of these Parameterized Quantum Circuits (PQCs) are still not fully understood outside the scope of their principal application, motivating the study of their intrinsic properties. In this work, we analyse the generation of random states in PQCs under restrictions on the qubits connectivities, justified by different quantum computer architectures. We apply the expressibility quantifier and the average entanglement as diagnostics for the characteristics of the generated states and classify the circuits depending on the topology of the quantum computer where they can be implemented. As a function of the number of layers and qubits, circuits following a Ring topology will have the highest entanglement and expressibility values, followed by Linear/All-to-all almost together and the Star topology. In addition to the characterization of the differences between the entanglement and expressibility of these circuits, we also place a connection between how steep is the increase on the uniformity of the distribution of the generated states and the generation of entanglement. Circuits generating average and standard deviation for entanglement closer to values obtained with the truly uniformly random ensemble of unitaries present a steeper evolution when compared to others.

Plaintext-based Side-channel Collision Attack

Side-channel Collision Attacks (SCCA) is a classical method that exploits information dependency leaked during cryptographic operations. Unlike collision attacks that seek instances where two different inputs to a cryptographic algorithm yield identical outputs, SCCAs specifically target the internal state, where identical outputs are more likely. Although SCCA does not rely on the pre-assumption of the leakage model, it explicitly operates on precise trace segments reflecting the target operation, which is challenging to perform when the leakage measurements are noisy. Besides, its attack performance may vary dramatically, as it relies on selecting a reference byte (and its corresponding leakages) to “collide” other bytes. A poor selection would lead to many bytes unrecoverable. These two facts make its real-world application problematic. This paper addresses these challenges by introducing a novel plaintext-based SCCA. We leverage the bijective relationship between plaintext and secret data, using plaintext as labels to train profiling models to depict leakages from varying operations. By comparing the leakage representations produced by the profiling model instead of the leakage segmentation itself, all secret key differences can be revealed simultaneously without processing leakage traces. Furthermore, we propose a novel error correction scheme to rectify false predictions further. Experimental results show that our approach significantly surpasses the state-of-the-art SCCA in both attack performance and computational complexity (e.g., training time reduced from approximately three hours to five minutes). These findings underscore our method's effectiveness and practicality in real-world attack scenarios.

Autonomous stabilization with programmable stabilized state

Reservoir engineering is a powerful technique to autonomously stabilize a quantum state. Traditional schemes involving multi-body states typically function for discrete entangled states. In this work, we enhance the stabilization capability to a continuous manifold of states with programmable stabilized state selection using multiple continuous tuning parameters. We experimentally achieve 84.6% and 82.5% stabilization fidelity for the odd and even-parity Bell states as two special points in the manifold. We also perform fast dissipative switching between these opposite parity states within 1.8 μs and 0.9 μs by sequentially applying different stabilization drives. Our result is a precursor for new reservoir engineering-based error correction schemes.

IEDCL: Streamlined, False-Error-Free Error Detection and Correction Scheme in a Near-Threshold Enabled 32-bit Processor

iEDCL: Streamlined, False-Error-Free Error Detection and Correction Scheme in a Near-Threshold Enabled 32-bit Processor

Bases for optimising stabiliser decompositions of quantum states

Stabiliser states play a central role in the theory of quantum computation. For example, they are used to encode computational basis states in the most common quantum error correction schemes. Arbitrary quantum states admit many stabiliser decompositions: ways of being expressed as a superposition of stabiliser states. Understanding the structure of stabiliser decompositions has significant applications in verifying and simulating near-term quantum computers. We introduce and study the vector space of linear dependencies of n-qubit stabiliser states. These spaces have canonical bases containing vectors whose size grows exponentially in n. We construct elegant bases of linear dependencies of constant size three. Critically, our sparse bases can be computed without first compiling a dictionary of all n-qubit stabiliser states. We utilise them to explicitly compute the stabiliser extent of states of more qubits than is feasible with existing techniques. Finally, we delineate future applications to improving theoretical bounds on the stabiliser rank of magic states.

Single-step parity check gate set for quantum error correction

A key requirement for an effective quantum error correction (QEC) scheme is that the physical qubits have error rates below a certain threshold. The value of this threshold depends on the details of the specific QEC scheme, and its hardware-level implementation. This is especially important with parity-check circuits, which are the fundamental building blocks of QEC codes. The standard way of constructing the parity check circuit is using a universal set of gates, namely sequential CNOT gates, single-qubit rotations and measurements. We exploit the insight that a QEC code does not require universal logic gates, but can be simplified to perform the sole task of error detection and correction. By building gates that are fundamental to QEC, we can boost the threshold and ease the experimental demands on the physical hardware. We present a rigorous formalism for constructing and verifying the error behavior of these gates, linking the physical measurement of a process matrix to the abstract error models commonly used in QEC analysis. This allows experimentalists to directly map the gates used in their systems to thresholds derived for a broad-class of QEC codes. We give an example of these new constructions using the model system of two nuclear spins, coupled to an electron spin, showing the potential benefits of redesigning fundamental gate sets using QEC primitives, rather than traditional gate sets reliant on simple single and two-qubit gates.

Analyzing learner language: the case of the Hebrew Learner Essay Corpus

AbstractWe present the Hebrew Learner Essay Corpus (HELEECS): an annotated corpus of Hebrew language argumentative essays authored by prospective higher-education students. The corpus includes essays by two main populations: (1) essays by native speakers of Hebrew, written as part of the psychometric exam that is used to assess their future success in academic studies; (2) essays by non-native speakers of Hebrew, with three different native languages (Arabic, French, and Russian), that were written as part of a language aptitude test. The corpus is uniformly encoded and stored. The non-native essays were annotated with target hypotheses (i.e., hypothesized intended formulations in standard written Hebrew). The corpus is available for research purposes upon request. We describe the corpus and the error correction and annotation schemes used in its analysis. In addition to introducing this new resource, we discuss the challenges of identifying and analyzing non-native language use. Among these challenges are determining whether the language used in a particular utterance is native-like, and determining the target hypothesis when language use is non-native-like. We propose various ways for dealing with these challenges.

Efficient Pipeline Conflict Resolution for Layered QC-LDPC Decoders in OFDM-PON

Efficient Pipeline Conflict Resolution for Layered QC-LDPC Decoders in OFDM-PON

Explicit error-correction scheme and code distance for bosonic codes with rotational symmetry

Explicit error-correction scheme and code distance for bosonic codes with rotational symmetry

Parallel Flagged Fault‐tolerant Error Correction for Stabilizer Codes of Distance 5

AbstractFlagged fault‐tolerant error correction schemes have attracted a lot of attention for their low qubit overhead, but usually require a high circuit depth. One way to reduce the depth is to develop parallel flagged syndrome extraction circuits. This study investigates parallel syndrome extraction circuits for Calderbank‐Shor‐Steane codes with distance 5. A simple algorithm for finding parallel flagged syndrome extraction circuits is provided. Using this algorithm, the parallel flagged circuits of the [[17,1,5]] and [[19,1,5]] color codes are constructed precisely. The error pseudo‐thresholds for code schemes are also precisely simulated and calculated. The parallel scheme in this study, based on the [[17,1,5]] and [[19,1,5]] color codes, outperforms traditional flagged schemes, particularly when the idle location error rate is high.

Evaluating the Effects of Reducing Voltage Margins for Energy-Efficient Operation of MPSoCs

Voltage margins, or guardbands, are imposed on DVFS systems to account for process, voltage, and temperature variability effects. While necessary to assure correctness, guardbands reduce energy efficiency, a crucial requirement for embedded systems. The literature shows that error detection techniques can be used to maintain the system’s reliability while reducing or eliminating the guardbands. This letter assesses the practically available margins of a commercial RISC-V MPSoC while violating its guardband limits. The primary motivation of this work is to support the development of an efficient system leveraging the redundancy of multicore architectures for an error detection and correction scheme capable of mitigating the errors caused by aggressive voltage margin reduction. For an equivalent performance, we achieved up to 27% energy reduction while violating the manufacturer’s defined guardband, leaving reasonable energy margins for further development.

Measurement Error in Thermoelectric Generator Induced by Temperature Fluctuation

The thermal-electric conversion efficiency is a crucial metric for evaluating the performance of a thermoelectric generator (TEG). However, accurate measurement of this efficiency remains a significant challenge due to various factors that impact heat flow measurements. We have observed that temperature fluctuations during temperature control are the primary factor contributing to measurement errors in heat flow under vacuum conditions. To address this issue, we have developed a time-dependent theoretical model for the thermal-electric coupling of a TEG measurement system based on Fourier’s theory of heat conduction. This model allows us to investigate the effects of both temperature fluctuation and structural parameters on the measurement error of TEG performance. Furthermore, we have proposed an error correction scheme for TEG performance based on our theoretical and experimental findings. These insights provide a theoretical framework and technical guidance for more precise measurements of TEG performance.

Comparison Of Two Encoding Methods in RAID6 Storage Architecture and Analysis of Improvement of EVENODD Encodings

This paper provides a comparative analysis of two widely used error correction codes: RS (Reed-Solomon) and EVENODD. The analysis covers principles, algebraic forms, computational complexities, minimum Hamming distances, decoding processes, and specific application scenarios. RS encoding is known for its versatility, allowing for the flexible addition of parity symbols. However, it comes with a high computational cost due to polynomial evaluations. On the other hand, EVENODD encoding offers simplicity and computational efficiency through mere XOR operations but has limitations on the number of parity symbols it can generate. The paper explores the algebraic representations of both codes, discusses their minimum Hamming distances, and evaluates their decoding processes. Additionally, it analyzes the computational requirements of EVENODD under small write operations and provides a comprehensive comparison of the computational complexities of RS and EVENODD, aiding practitioners in choosing the most suitable error correction scheme for specific applications. A seeming limitation in our building process is because of the number of information disks must fall into a prime number. Nevertheless, if the preferred quantity of data sectors isn't a prime number, we can easily posit the existence of additional disks filled entirely with zeros, and this won't impact the encoding and decoding procedures.

Special features of the Weyl–Heisenberg Bell basis imply unusual entanglement structure of Bell-diagonal states

Abstract Bell states are of crucial importance for entanglement based methods in quantum information science. Typically, a standard construction of a complete orthonormal Bell-basis by Weyl–Heisenberg operators is considered. We show that the group structure of these operators has strong implication on error correction schemes and on the entanglement structure within Bell-diagonal states. In particular, it implies an equivalence between a Pauli channel and a twirl channel. Interestingly, other complete orthonormal Bell-bases do break the equivalence and lead to a completely different entanglement structure, for instance in the share of positive partial transposition (PPT)-entangled states. In detail, we find that the standard Bell basis has the highest observed share on PPT-states and PPT-entangled states compared to other Bell bases. In summary, our findings show that the standard Bell basis construction exploits a very special structure with strong implications to quantum information theoretic protocols if a deviation is considered.

Design of Autoconfigurable Random Access NOMA for URLLC Industrial IoT Networking

Low power devices are massively deployed to facilitate real time sensing and data transmission requested in low power wide-area network (LPWAN). However, the dominating signaling, i.e. continuous phase modulation (CPM), barely gains attention in the context of supporting massive connectivity, not to mention ultra-reliable low-latency communications (URLLC), a primary concern in industrial network automation. To this end, auto-configurable nonorthogonal multiple access (AC-NOMA) based on CPM signaling is proposed. The term auto-configuration is used since each device selects a setup from a pool of configurations whenever connecting to the access point in a random and distributive way. It is proven, using ideal power allocation and phase shaping technique, AC-NOMA offers drastically improved user load and near capacity performance even in finite blocklength regime. Moreover, to enable massive yet sporadic access, slotted ALOHA is combined with AC-NOMA. It is proven that the resultant scheme outperforms power-domain NOMA in terms of throughput even with reduced transmit power and simple forward error correction schemes such as repetition and convolutional coding. The throughput is further improved using semi AC-NOMA with slightly increased latency. It is demonstrated that both designs can support very high user load while enabling URLLC in finite blocklength regime, where the packet size is merely 256 bits while the error rate is <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$10^{-5}$</tex-math></inline-formula> , which are also desirable in a number of applications including satellite communications, visible light communications, etc.

Two RRNS-Based Error Correction Schemes for DNA Storage Channels

Two RRNS-Based Error Correction Schemes for DNA Storage Channels

Optimizing Communication Systems with Applied Nonlinear Analysis Techniques

The introduction of applied nonlinear analytic techniques is a disruptive force in the field of modern communication systems, revolutionising the methodology for system optimisation. This investigation into nonlinear approaches provides a deep grasp of the complex dynamics in communication networks and opens a realm beyond the confines of conventional linear models. This paper has become a beacon, illuminating the potential of nonlinear optimisation to tackle issues inherent in linear frameworks by exploring the intricacies of nonlinear systems. Nonlinear analytic integration has impacted concrete implementations in various communication domains, surpassing theoretical limitations. The application of nonlinear optimisation has produced robust error correction schemes, optimised signal processing algorithms, and adaptive modulation techniques that can dynamically adapt to the unpredictable network landscape. These innovations span wireless and optical communication, error correction coding, and adaptive modulation techniques. But there are obstacles on this journey of transformation. Implementation challenges in real-time and computational complexity still exist. However, communication systems strengthened by nonlinear analysis have a bright future ahead of them. With new technologies like artificial intelligence (AI) and machine learning positioned to be powerful partners that may accelerate and simplify nonlinear optimisation, the field of communication systems seems set for a period of intelligent, responsive, and adaptive networks. In conclusion, a new age for communication systems is being heralded by the integration of applied nonlinear analytic techniques, which promises resilience, efficiency, and adaptability. With new technologies and methods emerging to overcome obstacles, it seems that communication systems will continue to evolve in the future, ushering in a new era of network architecture.

Deep learning for enhanced free-space optical communications

Atmospheric effects, such as turbulence and background thermal noise, inhibit the propagation of light used in ON–OFF keying (OOK) free-space optical (FSO) communication. Here we present and experimentally validate a convolutional neural network (CNN) to reduce the bit error rate of FSO communication in post-processing that is significantly simpler and cheaper than existing solutions based on advanced optics. Our approach consists of two neural networks, the first determining the presence of bit sequences in thermal noise and turbulence and the second demodulating the bit sequences. All data used for training and testing our network is obtained experimentally by generating OOK bit streams, combining these with thermal light, and passing the resultant light through a turbulent water tank which we have verified mimics turbulence in the air to a high degree of accuracy. Our CNN improves detection accuracy over threshold classification schemes and has the capability to be integrated with current demodulation and error correction schemes.

Efficient learning-driven data transmission algorithm for cloud-to-thing continuum

In the cloud-to-thing continuum paradigm, the efficient transmission of learning-driven data is critical for facilitating real-time decision-making and continuous learning processes. Fountain codes have gained popularity as Forward Error Correction (FEC) schemes in application layer networking due to their ability to recover lost data packets. Gaussian Elimination (GE) algorithms, which form the core of Fountain codes, can be optimized to improve transmission efficiency. We introduces techniques that leverage GE algorithms to enhance the transmission of learning-driven data within the cloud-to-thing continuum. A fast matrix element architecture is developed to improve computational speed. Additionally, a pipelined normalization component based on binary trees is introduced to enable parallel processing. A pipelined elimination component utilizing binary trees is also presented to further boost transmission speeds and efficiency. These techniques are implemented using Field Programmable Gate Array (FPGA) technology. Their performance is evaluated against existing methods, demonstrating significant gains in transmission efficiency. By effectively managing increasing Internet traffic loads and optimizing the flow of learning-driven data, these approaches facilitate more efficient communication between cloud-based AI systems and edge devices. Ultimately, this research supports enhanced real-time decision-making and continuous learning processes across the full cloud-to-thing continuum.