Approximate error correction scheme for three-dimensional surface codes based reinforcement learning

Quantum error correction technology is an important method to eliminate errors during the operation of quantum computers.In order to solve the problem of influence of errors on physical qubits,we propose an approximate error correction scheme that performs dimension mapping operations on surface codes.This error correction scheme utilizes the topological properties of error correction codes to map the surface code dimension to three dimensions.Compared to previous error correction schemes,the present three-dimensional surface code exhibits good scalability due to its higher redundancy and more efficient error correction capabilities.By reducing the number of ancilla qubits required for error correction,this approach achieves savings in measurement space and reduces resource consumption costs.In order to improve the decoding efficiency and solve the problem of the correlation between the surface code stabilizer and the 3D space after dimension mapping,we employ a reinforcement learning(RL)decoder based on deep Q-learning,which enables faster identification of the optimal syndrome and achieves better thresholds through conditional optimization.Compared to the minimum weight perfect matching decoding,the threshold of the RL trained model reaches 0.78%,which is 56%higher and enables large-scale fault-tolerant quantum computation.

High Speed Versatile Reed-Solomon Decoder for Correcting Errors and Erasures

A new Chien search method for shortened Reed-Solomon （RS） code is proposed, based on this, a versatile RS decoder for correcting both errors and erasures is designed. Compared with the traditional RS decoder, the weighted coefficient of the Chien search method is calculated sequentially through the three pipelined stages of the decoder. And therefore, the computation of the errata locator polynomial and errata evaluator polynomial needs to be modified. The versatile RS decoder with minimum distance 21 has been synthesized in the Xilinx Virtex-Ⅱ series field programmable gate array （FPGA） xe2v1000-5 and is used by coneatenated coding system for satellite communication. Results show that the maximum data processing rate can be up to 1.3 Gbit/s.

Quantum secret sharing based on quantum error-correcting codes

Quantum secret sharing（QSS） is a procedure of sharing classical information or quantum information by using quantum states. This paper presents how to use a [2k- 1, 1, k] quantum error-correcting code （QECC） to implement a quantum （k, 2k-1） threshold scheme. It also takes advantage of classical enhancement of the [2k-1, 1, k] QECC to establish a QSS scheme which can share classical information and quantum information simultaneously. Because information is encoded into QECC, these schemes can prevent intercept-resend attacks and be implemented on some noisy channels.

USING ERROR-CORRECTING ENCODERS TO DESIGN LOCAL-RANDOM SEQUENCE GENERATORS

This paper proved the statement that a good linear block encoder is in fact a good local-random sequence generator. Furthermore, this statement discovers the deep relationship between the error-correcting coding theory and the modern cryptography.

Single Photon Detection Technology in Underwater Wireless Optical Communication:Modulation Modes and Error Correction Coding Analysis

This study explores the application of single photon detection(SPD)technology in underwater wireless optical communication(UWOC)and analyzes the influence of different modulation modes and error correction coding types on communication performance.The study investigates the impact of on-off keying(OOK)and 2-pulse-position modulation(2-PPM)on the bit error rate(BER)in single-channel intensity and polarization multiplexing.Furthermore,it compares the error correction performance of low-density parity check(LDPC)and Reed-Solomon(RS)codes across different error correction coding types.The effects of unscattered photon ratio and depolarization ratio on BER are also verified.Finally,a UWOC system based on SPD is constructed,achieving 14.58 Mbps with polarization OOK multiplexing modulation and 4.37 Mbps with polarization 2-PPM multiplexing modulation using LDPC code error correction.

Toward Constructing a Continuous Logical Operator for Error-Corrected Quantum Sensing

Error correction has long been suggested to extend the sensitivity of quantum sensors into the Heisenberg Limit. However, operations on logical qubits are only performed through universal gate sets consisting of finite-sized gates such as Clifford + T. Although these logical gate sets allow for universal quantum computation, the finite gate sizes present a problem for quantum sensing, since in sensing protocols, such as the Ramsey measurement protocol, the signal must act continuously. The difficulty in constructing a continuous logical op-erator comes from the Eastin-Knill theorem, which prevents a continuous sig-nal from being both fault-tolerant to local errors and transverse. Since error correction is needed to approach the Heisenberg Limit in a noisy environment, it is important to explore how to construct fault-tolerant continuous operators. In this paper, a protocol to design continuous logical z-rotations is proposed and applied to the Steane Code. The fault tolerance of the designed operator is investigated using the Knill-Laflamme conditions. The Knill-Laflamme condi-tions indicate that the diagonal unitary operator constructed cannot be fault tolerant solely due to the possibilities of X errors on the middle qubit. The ap-proach demonstrated throughout this paper may, however, find success in codes with more qubits such as the Shor code, distance 3 surface code, [15, 1, 3] code, or codes with a larger distance such as the [11, 1, 5] code.

Performance analysis and design of MIMO-OFDM system using concatenated forward error correction codes

This work investigates the performance of various forward error correction codes, by which the MIMO-OFDM system is deployed. To ensure fair investigation, the performance of four modulations, namely, binary phase shift keying(BPSK), quadrature phase shift keying(QPSK), quadrature amplitude modulation(QAM)-16 and QAM-64 with four error correction codes(convolutional code(CC), Reed-Solomon code(RSC)+CC, low density parity check(LDPC)+CC, Turbo+CC) is studied under three channel models(additive white Guassian noise(AWGN), Rayleigh, Rician) and three different antenna configurations(2×2, 2×4, 4×4). The bit error rate(BER) and the peak signal to noise ratio(PSNR) are taken as the measures of performance. The binary data and the color image data are transmitted and the graphs are plotted for various modulations with different channels and error correction codes. Analysis on the performance measures confirm that the Turbo + CC code in 4×4 configurations exhibits better performance.

Low-overhead fault-tolerant error correction scheme based on quantum stabilizer codes

Fault-tolerant error-correction(FTEC)circuit is the foundation for achieving reliable quantum computation and remote communication.However,designing a fault-tolerant error correction scheme with a solid error-correction ability and low overhead remains a significant challenge.In this paper,a low-overhead fault-tolerant error correction scheme is proposed for quantum communication systems.Firstly,syndrome ancillas are prepared into Bell states to detect errors caused by channel noise.We propose a detection approach that reduces the propagation path of quantum gate fault and reduces the circuit depth by splitting the stabilizer generator into X-type and Z-type.Additionally,a syndrome extraction circuit is equipped with two flag qubits to detect quantum gate faults,which may also introduce errors into the code block during the error detection process.Finally,analytical results are provided to demonstrate the fault-tolerant performance of the proposed FTEC scheme with the lower overhead of the ancillary qubits and circuit depth.

Digital Image Watermarking Based on Mixed Error Correcting Code

In this paper, we present a novel technique based on a mixed Error Correcting Code(ECC)-the convolutional code and the repetition code to enhance the robustness of the embedded watermark. Before embedding, the binary watermark is scanned to one-dimension sequence and later inputted into the (3, 1, 2) convolutional encoder and (3, 1) repetition encoder frame by frame, which will improve the error correcting capability of decoder. The output code sequence is scanned to some matrixes as the new watermark messages. The watermarking is selected in low frequency band of the Discrete Wavelet Transform (DWT) and therefore it can resist the destruction of image processing. Experimental results are presented to demonstrate that the robustness of a watermark with mixed ECC is much higher than the traditional one just with repetition coding while suffering JPEG lossy compression, salt and pepper noise and center cutting processing.

Effectiveness and failure modes of error correcting code in industrial 65 nm CMOS SRAMs exposed to heavy ions

Single event upsets(SEUs) induced by heavy ions were observed in 65 nm SRAMs to quantitatively evaluate the applicability and effectiveness of single-bit error correcting code(ECC) utilizing Hamming Code.The results show that the ECC did improve the performance dramatically,with the SEU cross sections of SRAMs with ECC being at the order of 10^(-11) cm^2/bit,two orders of magnitude higher than that without ECC(at the order of 10^(-9) cm^2/bit).Also,ineffectiveness of ECC module,including 1-,2- and 3-bits errors in single word(not Multiple Bit Upsets),was detected.The ECC modules in SRAMs utilizing(12,8) Hamming code would lose work when 2-bits upset accumulates in one codeword.Finally,the probabilities of failure modes involving 1-,2- and 3-bits errors,were calcaulated at 39.39%,37.88%and 22.73%,respectively,which agree well with the experimental results.

Enhancement of Error-Correction Coding of Spatial Watermarks in Gray Code

This paper demonstrates how channel coding can improve the robustness of spatial image watermarks against signal distortion caused by lossy data compression such as the JPEG scheme by taking advantage of the properties of Gray code. Two error-correction coding (ECC) schemes are used here: One scheme, referred to as the vertical ECC (VECC), is to encode information bits in a pixel by error-correction coding where the Gray code is used to improve the performance. The other scheme, referred to as the horizontal ECC (HECC), is to encode information bits in an image plane. In watermarking, HECC generates a codeword representing watermark bits, and each bit of the codeword is encoded by VECC. Simple single-error-correcting block codes are used in VECC and HECC. Several experiments of these schemes were conducted on test images. The result demonstrates that the error-correcting performance of HECC just depends on that of VECC, and accordingly, HECC enhances the capability of VECC. Consequently, HECC with appropriate codes can achieve stronger robustness to JPEG—caused distortions than non-channel-coding watermarking schemes.

Secret Data-Driven Carrier-Free Secret Sharing Scheme Based on Error Correction Blocks of QR Codes

In this paper,a novel secret data-driven carrier-free(semi structural formula)visual secret sharing(VSS)scheme with(2,2)threshold based on the error correction blocks of QR codes is investigated.The proposed scheme is to search two QR codes that altered to satisfy the secret sharing modules in the error correction mechanism from the large datasets of QR codes according to the secret image,which is to embed the secret image into QR codes based on carrier-free secret sharing.The size of secret image is the same or closest with the region from the coordinate of(7,7)to the lower right corner of QR codes.In this way,we can find the QR codes combination of embedding secret information maximization with secret data-driven based on Big data search.Each output share is a valid QR code which can be decoded correctly utilizing a QR code reader and it may reduce the likelihood of attracting the attention of potential attackers.The proposed scheme can reveal secret image visually with the abilities of stacking and XOR decryptions.The secret image can be recovered by human visual system(HVS)without any computation based on stacking.On the other hand,if the light-weight computation device is available,the secret image can be lossless revealed based on XOR operation.In addition,QR codes could assist alignment for VSS recovery.The experimental results show the effectiveness of our scheme.

Spatial Image Watermarking by Error-Correction Coding in Gray Codes

In this paper, error-correction coding (ECC) in Gray codes is considered and its performance in the protecting of spatial image watermarks against lossy data compression is demonstrated. For this purpose, the differences between bit patterns of two Gray codewords are analyzed in detail. On the basis of the properties, a method for encoding watermark bits in the Gray codewords that represent signal levels by a single-error-correcting (SEC) code is developed, which is referred to as the Gray-ECC method in this paper. The two codewords of the SEC code corresponding to respective watermark bits are determined so as to minimize the expected amount of distortion caused by the watermark embedding. The stochastic analyses show that an error-correcting capacity of the Gray-ECC method is superior to that of the ECC in natural binary codes for changes in signal codewords. Experiments of the Gray-ECC method were conducted on 8-bit monochrome images to evaluate both the features of watermarked images and the performance of robustness for image distortion resulting from the JPEG DCT-baseline coding scheme. The results demonstrate that, compared with a conventional averaging-based method, the Gray-ECC method yields watermarked images with less amount of signal distortion and also makes the watermark comparably robust for lossy data compression.

新媒体背景下思政课教学“纠错码”功能优化研究--以“中国近现代史纲要”课为例

在新媒体背景下,思政课教学中充斥着大量的信息“噪声”干扰,不可避免却又直接影响着教学效果的提升,而“中国近现代史纲要”课程“以史育人”的内容特点更易遭受信息“噪声”的干扰,因此有必要引入信息论中“噪声”干扰难以消除时的纠错码应对机制,有效降低新媒体“噪声”对它的影响。利用重塑“纠错码”防范功能、维护“纠错码”纠正反馈功能、革新“纠错码”建设功能等措施辩证发力,可以将新媒体给“中国近现代史纲要”课程带来“噪声”干扰的“变量”转化为提升信息传输实效的“增量”,为提升课程育人实效提供全新思路。

Performance of entanglement-assisted quantum codes with noisy ebits over asymmetric and memory channels

Entanglement-assisted quantum error correction codes(EAQECCs)play an important role in quantum communications with noise.Such a scheme can use arbitrary classical linear code to transmit qubits over noisy quantum channels by consuming some ebits between the sender(Alice)and the receiver(Bob).It is usually assumed that the preshared ebits of Bob are error free.However,noise on these ebits is unavoidable in many cases.In this work,we evaluate the performance of EAQECCs with noisy ebits over asymmetric quantum channels and quantum channels with memory by computing the exact entanglement fidelity of several EAQECCs.We consider asymmetric errors in both qubits and ebits and show that the performance of EAQECCs in entanglement fidelity gets improved for qubits and ebits over asymmetric channels.In quantum memory channels,we compute the entanglement fidelity of several EAQECCs over Markovian quantum memory channels and show that the performance of EAQECCs is lowered down by the channel memory.Furthermore,we show that the performance of EAQECCs is diverse when the error probabilities of qubits and ebits are different.In both asymmetric and memory quantum channels,we show that the performance of EAQECCs is improved largely when the error probability of ebits is reasonably smaller than that of qubits.

Quantum Codes Do Not Increase Fidelity against Isotropic Errors

In this article, we study the ability of error-correcting quantum codes to increase the fidelity of quantum states throughout a quantum computation. We analyze arbitrary quantum codes that encode all qubits involved in the computation, and we study the evolution of n-qubit fidelity from the end of one application of the correcting circuit to the end of the next application. We assume that the correcting circuit does not introduce new errors, that it does not increase the execution time (i.e. its application takes zero seconds) and that quantum errors are isotropic. We show that the quantum code increases the fidelity of the states perturbed by quantum errors but that this improvement is not enough to justify the use of quantum codes. Namely, we prove that, taking into account that the time interval between the application of the two corrections is multiplied (at least) by the number of qubits n (due to the coding), the best option is not to use quantum codes, since the fidelity of the uncoded state over a time interval n times smaller is greater than that of the state resulting from the quantum code correction.

Determination of quantum toric error correction code threshold using convolutional neural network decoders

Quantum error correction technology is an important solution to solve the noise interference generated during the operation of quantum computers.In order to find the best syndrome of the stabilizer code in quantum error correction,we need to find a fast and close to the optimal threshold decoder.In this work,we build a convolutional neural network(CNN)decoder to correct errors in the toric code based on the system research of machine learning.We analyze and optimize various conditions that affect CNN,and use the RestNet network architecture to reduce the running time.It is shortened by 30%-40%,and we finally design an optimized algorithm for CNN decoder.In this way,the threshold accuracy of the neural network decoder is made to reach 10.8%,which is closer to the optimal threshold of about 11%.The previous threshold of 8.9%-10.3%has been slightly improved,and there is no need to verify the basic noise.

A Comparison of Error Correction Models for Student’s Error Codes Based on Deep Learning

Automatically correcting students’code errors using deep learning is an effective way to reduce the burden of teachers and to enhance the effects of students’learning.However,code errors vary greatly,and the adaptability of fixing techniques may vary for different types of code errors.How to choose the appropriate methods to fix different types of errors is still an unsolved problem.To this end,this paper first classifies code errors by Java novice programmers based on Delphi analysis,and compares the effectiveness of different deep learning models(CuBERT,GraphCodeBERT and GGNN)fixing different types of errors.The results indicated that the 3 models differed significantly in their classification accuracy on different error codes,while the error correction model based on the Bert structure showed better code correction potential for beginners’codes.

基于常循环码的纠缠辅助量子Maximum-Distance-Separable码的构造

纠缠辅助量子纠错码可以看作是经典量子纠错码的引申,其与经典量子纠错码的差别在于,如果发送者和接收者双方提前共享纠缠态,在不满足对偶包含的的情况下也可以由任意经典线性码构造出来.本文通过研究分圆陪集的结构性质,利用常循环码构造出几类新的具有较小预先共享纠缠态的纠缠辅助量子Maximum-Distance-Separable(MDS)码.