Error Rate Threshold Research Articles

Breakdown of surface-code error correction due to coupling to a bosonic bath

We consider a surface code suffering decoherence due to coupling to a bath of bosonic modes at finite temperature and study the time available before the unavoidable breakdown of error correction occurs as a function of coupling and bath parameters. We derive an exact expression for the error rate on each individual qubit of the code, taking spatial and temporal correlations between the errors into account. We investigate numerically how different kinds of spatial correlations between errors in the surface code affect its threshold error rate. This allows us to derive the maximal duration of each quantum error correction period by studying when the single-qubit error rate reaches the corresponding threshold. At the time when error correction breaks down, the error rate in the code can be dominated by the direct coupling of each qubit to the bath, by mediated subluminal interactions, or by mediated superluminal interactions. For a 2D Ohmic bath, the time available per quantum error correction period vanishes in the thermodynamic limit of a large code size $L$ due to induced superluminal interactions, though it does so only like $1/\sqrt{\log L}$. For all other bath types considered, this time remains finite as $L\rightarrow\infty$.

Quantifying the effects of local many-qubit errors and nonlocal two-qubit errors on the surface code

Topological quantum error correction codes are known to be able to tolerate arbitrary local errors given sufficient qubits. This includes correlated errors involving many local qubits. In this work, we quantify this level of tolerance, numerically studying the effects of many-qubit errors on the performance of the surface code. We find that if increasingly large-area errors are at least moderately exponentially suppressed, arbitrarily reliable quantum computation can still be achieved with practical overhead. We furthermore quantify the effect of nonlocal two-qubit correlated errors, which would be expected in arrays of qubits coupled by a polynomially decaying interaction, and when using many-qubit coupling devices. We surprisingly find that the surface code is very robust to this class of errors, despite a provable lack of a threshold error rate when such errors are present.

Fault-tolerant thresholds for quantum error correction with the surface code

The surface code is a promising candidate for fault-tolerant quantum computation, achieving a high threshold error rate with nearest-neighbor gates in two spatial dimensions. Here, through a series of numerical simulations, we investigate how the precise value of the threshold depends on the noise model, measurement circuits, and decoding algorithm. We observe thresholds between 0.502(1)% and 1.140(1)% per gate, values which are generally lower than previous estimates.

Channel Aware Cooperative FEC/ARQ Mechanism Based on Kalman Filter Prediction for Wireless Sensor Networks

The QoS-Guarantee of data delivery over wireless link is a big challenge due to the unreliable and dynamic characteristics of wireless sensor networks. In this paper, a cooperative forward error correction (FEC)/automatic repeat request (ARQ) mechanism was proposed, in the hope that the data packets could be received on receiver node with high quality. The mechanism, based on Kalman filter, predicts the bit error rate and adjusts the channel state parameters according to the bit error rate threshold value. Both the mathematical analyses and NS simulation demonstrate that the proposed mechanism achieves better performance, in terms of throughput, delay, reliability and energy efficiency comparing with traditional FEC/ARQ, cooperative FEC and cooperative ARQ.

A Study of Error Correction Codes for PAM Signals in Data Center Applications

A study is presented through simulation and experiment on the proposed forward error correction (FEC) codes for data centers using higher order pulse amplitude modulation (PAM). The results highlight the tradeoffs in the adopted FEC approach for a fixed transmission link. Reed-Solomon (RS) and Bose-Chaudhuri-Hocquenghem (BCH) codes are considered in data center applications due to the low latency requirement budgeted for the encoding and decoding processes. Using Monte-Carlo and semi-analytical simulations, the signal to noise ratio requirement of PAM-N is obtained for a 500-m fiber transmission link at 100 Gb/s. For latency requirement under 100 ns, short-block RS codes offer possibly low complexity implementation with a pre-FEC bit error rate (BER) threshold at 8.8×10-5. On the other end, BCH codes provide higher coding gain up to 9.3 dB with a BER threshold at 2.5×10-3 at the expense of potentially longer decoding delay and complexity. An experimental investigation at 25 Gb/s for PAM-4 signal is performed to measure the actual net coding gain of the system. Results show that the performance of RS(578 514) code is within 1 dB of both BCH(3456 3084) and BCH(2464 2056) with 15% and 23% reduction in complexity, respectively.

Coping with qubit leakage in topological codes

Many physical systems considered promising qubit candidates are not, in fact, two-level systems. Such systems can leak out of the preferred computational states, leading to errors on any qubits that interact with leaked qubits. Without specific methods of dealing with leakage, long-lived leakage can lead to time-correlated errors. We study the impact of such time-correlated errors on topological quantum error correction codes, which are considered highly practical codes, using the repetition code as a representative case study. We show that, under physically reasonable assumptions, a threshold error rate still exists, however performance is significantly degraded. We then describe simple additional quantum circuitry that, when included in the error detection cycle, restores performance to acceptable levels.

Accurate simulations of planar topological codes cannot use cyclic boundaries

Cyclic boundaries are used in many branches of physics and mathematics, typically to assist the approximation of a large space. We show that when determining the performance of planar, fault-tolerant, topological quantum error correction, using cyclic boundaries leads to a significant underestimate of the logical error rate. We present cyclic and noncyclic surface code simulations exhibiting this discrepancy and analytic formulas precisely reproducing the observed behavior in the limit of low physical error. These asymptotic formulas are then used to prove that the underestimate is exponentially large in the code distance $d$ at any fixed physical error rate $p$ below the threshold error rate ${p}_{\mathrm{th}}$.

MIMO Exploitation of 3D Multipath Statistics in a Heterogeneous LTE-Advanced Network

This paper analyses the impact of 3D multipath in an LTE-Advanced heterogeneous network. The impact of the base station array configuration is considered in both the azimuth and elevation planes. Spatial and temporal multipath statistics are generated for example macro- and picocellular base stations, and these are combined with appropriately oriented complex polarimetric antenna patterns. The resulting wideband channels are then passed to an LTE-Advanced physical layer simulator. The optimal spatial multiplexing mode is determined by computing the throughput using the received bit mutual information rate for all modulation and coding schemes. The fastest link speed for each user is identified given a packet error rate threshold of 10%. Results show that RMS angle spread statistics and the base station MIMO array configuration strongly influence user performance in an LTE-A network. The deployment of macrocellular vertical arrays is shown to significantly degrade network performance. In contrast, the elevation angle spread is found to be far greater in picocells, and this allows vertical arrays to be applied to produce compact high performance picobase stations.

High Threshold Error Correction for the Surface Code

An algorithm is presented for error correction in the surface code quantum memory. This is shown to correct depolarizing noise up to a threshold error rate of 18.5%, exceeding previous results and coming close to the upper bound of 18.9%. The time complexity of the algorithm is found to be polynomial with error suppression, allowing efficient error correction for codes of realistic sizes.

Simple regression models as a threshold for selecting AFLP loci with reduced error rates

BackgroundAmplified fragment length polymorphism is a popular DNA marker technique that has applications in multiple fields of study. Technological improvements and decreasing costs have dramatically increased the number of markers that can be generated in an amplified fragment length polymorphism experiment. As datasets increase in size, the number of genotyping errors also increases. Error within a DNA marker dataset can result in reduced statistical power, incorrect conclusions, and decreased reproducibility. It is essential that error within a dataset be recognized and reduced where possible, while still balancing the need for genomic diversity.ResultsUsing simple regression with a second-degree polynomial term, a model was fit to describe the relationship between locus-specific error rate and the frequency of present alleles. This model was then used to set a moving error rate threshold that varied based on the frequency of present alleles at a given locus. Loci with error rates greater than the threshold were removed from further analyses. This method of selecting loci is advantageous, as it accounts for differences in error rate between loci of varying frequencies of present alleles. An example using this method to select loci is demonstrated in an amplified fragment length polymorphism dataset generated from the North American prairie species big bluestem. Within this dataset the error rate was reduced from 12.5% to 8.8% by removal of loci with error rates greater than the defined threshold. By repeating the method on selected loci, the error rate was further reduced to 5.9%. This reduction in error resulted in a substantial increase in the amount of genetic variation attributable to regional and population variation.ConclusionsThis paper demonstrates a logical and computationally simple method for selecting loci with a reduced error rate. In the context of a genetic diversity study, this method resulted in an increased ability to detect differences between populations. Further application of this locus selection method, in addition to error-reducing methodological precautions, will result in amplified fragment length polymorphism datasets with reduced error rates. This reduction in error rate should result in greater power to detect differences and increased reproducibility.

Development of mechanisms of recognition of fragmented images differing in the degree of fragmentation in children of preschool and primary school ages

Recognition of fragmented images with an increasing number of fragments was studied in children of three age groups (five to six, seven to eight, and nine to ten years of age) to compare the behavioral and neurophysiological parameters of recognition in these groups. The most pronounced changes in effectiveness of recognition were observed when the five- to six-year-old and seven- to eight-year-old children were compared. In the former, recognition was not accompanied by any significant changes in the event-related potentials of the prefrontal cortex or by an increase in N250–400 (Ncl) in the extrastriate cortex (though it is an important characteristic of the process). However, the amplitude of the N170–200 component, which reflects analysis and encoding of sensory features, did increase at the age of five to six years. Immaturity of the prefrontal cortex is manifested in a deficiency of the control: these children respond hastily and make numerous mistakes. In seven- to eight-year-old children, recognition is accompanied by an increase in the amplitude of the N100 and N250 components in the prefrontal cortex, whereas the amplitude of the Ncl component increases in the extrastriate cortex. The error rate and recognition threshold are significantly lower in these children than at the age of five to six years. The role of prefrontal cortex is the most pronounced at the age of nine to ten years, which is manifested in the Ncl amplitude and the later phases corresponding to the cognitive recognition. Our results demonstrate qualitative differences in the mechanisms of recognition in children of the preschool and primary school age. At the age of five to six years, recognition is a result of integration of the sensory signs. Beginning from the age of seven to eight years, the prefrontal cortex plays an important role in recognition of the fragmentary images; this brain region is responsible for a search of possible analogues in memory and identification of an object.

LLR Approximation for Wireless Channels Based on Taylor Series and its Application to BICM With LDPC Codes

A new approach for the approximation of the channel log-likelihood ratio (LLR) for wireless channels based on Taylor series is proposed. The approximation is applied to uncorrelated flat fading channels with unknown channel state information at the receiver. It is shown that the proposed approximation greatly simplifies the calculation of channel LLRs, and yet provides results almost identical to those based on the exact calculation of channel LLRs. The results are obtained in the context of bit-interleaved coded modulation (BICM) schemes with low-density parity-check (LDPC) codes, and include threshold calculations and error rate performance of finite-length codes. Compared to the existing approximations, the proposed method is either significantly less complex, or considerably more accurate.

Towards Practical Classical Processing for the Surface Code

The surface code is unarguably the leading quantum error correction code for 2D nearest neighbor architectures, featuring a high threshold error rate of approximately 1%, low overhead implementations of the entire Clifford group, and flexible, arbitrarily long-range logical gates. These highly desirable features come at the cost of significant classical processing complexity. We show how to perform the processing associated with an n×n lattice of qubits, each being manipulated in a realistic, fault-tolerant manner, in O(n2) average time per round of error correction. We also describe how to parallelize the algorithm to achieve O(1) average processing per round, using only constant computing resources per unit area and local communication. Both of these complexities are optimal.

Deterministic secure quantum communication without unitary operation based on high-dimensional entanglement swapping

By analysis of the basic properties of entanglement swapping of high-dimensional Bell states, a universal and general deterministic secure quantum communication (DSQC) protocol is proposed, in which unitary operation is not required. By making use of the results of high-dimensional Bell measurement, the sender and the receiver can encode and decode the message respectively by performing the modular addition and subtraction. Two mutually complementary bases are constructed; and according to the property of mutual complement, a method for checking security of the high-dimensional quantum channel is put forward. Some common attack strategies are analyzed, and the corresponding error rates are calculated. Then the upper bound of the threshold of error rate is deduced.

Low Complexity Time-Concatenated Turbo Equalization for Block Transmission without Guard Interval: Part 2—Application to SC-FDMA

The primary objective of this paper is to apply the CHATUE algorithm, presented in the Part-1 paper of this article, to multi-user Single Carrier Frequency Division Multiple Access (SC-FDMA) Systems. The CHATUE algorithm connects turbo equalizers neighboring in time in the absence of Cyclic Prefix or Guard Interval, where the latest version of the reduced complexity equalization technique, Frequency Domain Soft Cancellation Minimum Mean Square Error turbo equalization is utilized not only to mitigate the inter-carrier interference but also to eliminate the inter-block interferences from the neighboring blocks. Furthermore, doped accumulator is combined with our proposed CHATUE-SC-FDMA system. Extrinsic Information Transfer analysis is used to demonstrate the improvement in convergence property as well as to analyze the bit error rate threshold. This paper provides in detail the time-concatenated turbo equalization algorithm for SC-FDMA, referred to as CHATUE-SC-FDMA, and evaluates its performances. When deriving the algorithm, we also propose, without imposing significant performance degradation, an approximation technique to eliminate the necessity of the covariance matrix inversion.

A Composed Protocol of Quantum Identity Authentication Plus Quantum Key Distribution Based on Squeezed States

It is established that a single quantum cryptography protocol usually cooperates with other cryptographic systems, such as an authentication system, in the real world. However, few protocols have been proposed on how to combine two or more quantum protocols. To fill this gap, we propose a composed quantum protocol, containing both quantum identity authentication and quantum key distribution, using squeezed states. Hence, not only the identity can be verified, but also a new private key can be generated by our new protocol. We also analyze the security under an optimal attack, and the efficiency, which is defined by the threshold of the tolerant error rate, using Gaussian error function.

SNVer: a statistical tool for variant calling in analysis of pooled or individual next-generation sequencing data

We develop a statistical tool SNVer for calling common and rare variants in analysis of pooled or individual next-generation sequencing (NGS) data. We formulate variant calling as a hypothesis testing problem and employ a binomial–binomial model to test the significance of observed allele frequency against sequencing error. SNVer reports one single overall P-value for evaluating the significance of a candidate locus being a variant based on which multiplicity control can be obtained. This is particularly desirable because tens of thousands loci are simultaneously examined in typical NGS experiments. Each user can choose the false-positive error rate threshold he or she considers appropriate, instead of just the dichotomous decisions of whether to ‘accept or reject the candidates’ provided by most existing methods. We use both simulated data and real data to demonstrate the superior performance of our program in comparison with existing methods. SNVer runs very fast and can complete testing 300 K loci within an hour. This excellent scalability makes it feasible for analysis of whole-exome sequencing data, or even whole-genome sequencing data using high performance computing cluster. SNVer is freely available at http://snver.sourceforge.net/.

Surface code quantum computing with error rates over 1%

Large-scale quantum computation will only be achieved if experimentally implementable quantum error correction procedures are devised that can tolerate experimentally achievable error rates. We describe a quantum error correction procedure that requires only a 2-D square lattice of qubits that can interact with their nearest neighbors, yet can tolerate quantum gate error rates over 1%. The precise maximum tolerable error rate depends on the error model, and we calculate values in the range 1.1--1.4% for various physically reasonable models. Even the lowest value represents the highest threshold error rate calculated to date in a geometrically constrained setting, and a 50% improvement over the previous record.

Graphical algorithms and threshold error rates for the 2d color code

Recent work on fault-tolerant quantum computation making use of topological error correction shows great potential, with the 2d surface code possessing a threshold error rate approaching 1\%. However, the 2d surface code requires the use of a complex state distillation procedure to achieve universal quantum computation. The color code of is a related scheme partially solving the problem, providing a means to perform all Clifford group gates transversally. We review the color code and its error correcting methodology, discussing one approximate technique based on graph matching. We derive an analytic lower bound to the threshold error rate of 6.25\% under error-free syndrome extraction, while numerical simulations indicate it may be as high as 13.3\%. Inclusion of faulty syndrome extraction circuits drops the threshold to approximately 0.10 \pm 0.01\%.

Joint Subcarrier Matching, Power Allocation and Bit Loading in OFDM Dual-Hop Systems

Orthogonal Frequency Division Multiplexing(OFDM) dual-hop systems can take full advantages of the techniques of both multi-hop communication and OFDM. To achievethis end, we propose a joint subcarrier matching, power allocation and bit loading algorithm operating under a total power constraint and the same Bit Error Rate(BER) threshold over all subcarriers. Simulation results demonstrated system throughput improvement compared to single-hop systems and dual-hop systems with different bit loading algorithms for each relay position, power constraint, and required BER.