量子Turbo码

量子纠错编码技术在量子通信和量子计算领域起着非常重要的作用.构造量子纠错编码的主要方法是借鉴经典纠错编码技术,目前几乎所有经典纠错编码方案都已经被移植到量子领域中来,然而在经典编码领域纠错性能最杰出的Turbo码却至今没有量子对应.提出了一种利用量子寄存器网络构造量子递归系统卷积码的简单实现方案,同时利用量子SWAP门设计了一种高效的量子交织器门组网络方案.最后仿照经典Turbo码的设计原理提出串行级联的量子Turbo码,同时提出了可行的译码方法.量子Turbo码不仅丰富了量子纠错码研究的领域,同时为解释 关键词： 量子递归系统卷积码 量子Turbo码 量子纠错编码 量子信息     

量子卷积码的编译码方法

对于量子卷积码理论的研究旨在保护长距离通信中的量子信息序列. 定义了量子态的多项式表示形式,根据Calderbank-Shor-Steane(CSS)型量子码的构造方法,给出了CSS型量子卷积码的一种新的编译码方法,描述了编译码网络. 该方法将码字基态变换为信息多项式与生成多项式的乘积,然后用量子态上的多项式乘法操作实现编译码网络. 最后借鉴经典卷积码的译码思想,给出了具有线性复杂度的量子Viterbi算法. 关键词： 量子信息 量子卷积码 编译码 纠错算法     

针对X-Z型Pauli信道的量子稀疏图码的反馈式和积译码算法

本文针对X-Z型Pauli量子信道构建了一个量子稀疏图码的反馈式和积译码算法.相比较之前的基本和积算法,该反馈式译码策略利用了错误图样的比较, 稳定子中相关元素的值,特别的还根据信道的特征充分考虑了各变量所占错误的比重,并由此来调整信息节点的概率分布.该反馈式策略起到了经典译码中的软判决技术的作用,不但克服了对称简并问题带来的不利影响,更重要的是还给译码器提供了更多的有效信息,从而大大提高了译码器的纠错译码能力.另外,反馈式译码和积译码算法是基于GF(4)的,大大拓展了和积译码器关于量子译码 关键词： 量子稀疏图码 和积算法 量子纠错码 量子信息     

一类基于级联结构的量子好码

借助经典级联码的思想，详细阐述了通过适当选择量子码作为外码和内码，构造一般意义量子级联码的过程.在此基础上，通过选择量子RS码作为外码，一组特殊结构的量子码作为内码，具体构造出了一类量子级联码，证明了其是量子好码.在量子纠错码领域中，这是首次利用经典坏码构造出量子好码.     

基于稳定子码的在噪声信道的量子安全直接通信方案研究

量子安全直接通信是继量子密钥分配后,量子通信领域又一重要的研究领域,它要求通信双方在预先不需要建立共享密钥的情况下就可以实现消息的保密传输。不同于属于非确定通信的量子密钥分配,量子直接通信受信道噪声的影响更大,需要更好的检错纠错能力。本文根据稳定子码纠错理论和GHZ三态纠缠粒子的特性提出了一套基于稳定子码理论的量子直接通信方案,使其在保持无条件安全性的基础上可以对单量子的相位和比特错误进行纠错检错,大大降低了信道的整个通信过程的量子比特错误率。     

多逻辑比特表面码结构设计及其逻辑CNOT门实现

量子计算因具有并行处理能力,相比于经典计算有着指数级的加速,但量子系统具有脆弱性,极易受到噪声的影响,量子纠错码是克服量子噪声的有效手段.量子表面码是一种拓扑稳定子码,由于其结构上的最近邻居特点和较高的容错阈值,表面码在大规模容错量子计算方面具有巨大的潜力.目前已有的基于边界的表面码均为编码一个逻辑比特的表面码,本文主要研究基于边界如何实现多逻辑量子比特的编码,包括设计表面码的结构,根据结构找出对应的稳定子和逻辑操作,进一步根据稳定子设计出基于稳定子实现的编码线路;在研究基于测量和纠正的单量子比特间CNOT实现原理和基于融合操作和分割操作的单逻辑量子比特表面码间CNOT门实现原理的基础上,优化了基于融合操作和分割操作的单逻辑量子比特表面码间CNOT门实现方案,将其扩展到所设计的多逻辑量子比特表面码上实现了多逻辑量子比特表面码之间的CNOT操作,并通过仿真验证量子线路的正确性.本文设计的多逻辑比特表面码克服了单比特表面码不能密铺于量子芯片的缺点且提高了某些逻辑操作的长度,提高了容错能力.基于联合测量的思想降低了对辅助比特的要求且减小了实现过程中对量子资源的需求.     

基于Turbo码的量子高斯密钥分发的数据协调

为了使加密系统中两个合法用户Alice和Bob从量子信道传送的相关的高斯连续变量X和y中获取出密钥,通过一个理想公共授权信道传送部分信息进而从不一致的X和y中得到一致的二进制密钥,这一过程称为协调.本文在样条纠错(Sliced Error Correction,SEC)和多级编码/多路译码(Multi Level coding/Multi Stage Decoding,MLC/MSD)方案的基础上,构建了一套以Turbo纠错码为基础的连续变量量子密钥分发系统的反向数据协调方案.提出了以Turbo码的校验比特流为协调信息的Slepian-Wolf编译码方案.仿真结果表明可在信道信噪比7 dB以上实现20000个连续变量序列的协调.     

量子稳定子码的差错纠正与译码网络构建

寻找差错症状与差错算子之间映射关系是量子译码网络的核心内容,也是量子译码网络实现纠错功能的关键.给出了比特翻转差错症状矩阵和相位翻转差错症状矩阵的定义,将任意Pauli差错算子的差错症状表示为比特翻转差错症状矩阵和相位翻转差错症状矩阵的线性组合.研究发现,量子稳定子码的差错症状矩阵由其校验矩阵所决定,从而可将差错症状矩阵与差错算子之间的映射关系转化为校验矩阵与差错算子之间的映射关系,使得所有关于差错症状的分析都可以通过分析其校验矩阵来实现.这与经典线性码的差错症状与奇偶校验矩阵之间的关系类似,因此可以将经 关键词： 稳定子码 校验矩阵 差错症状 Pauli算子     

紫外激光通信中PPM与Turbo联合编码调制研究

为提高紫外激光通信系统中的编码效率和频带利用率，提出采用PPM（pulse position modulation）调制和Turbo编码相结合的技术来提高效率。此方法不仅能提高频带的利用率，也能提高码间抗干扰能力、纠错能力和降低误码率，并对PPM调制模式下的Turbo码译码公式进行了推导，最后利用Matlab软件实现了该技术的仿真，仿真结果表明：在紫外激光通信中采用PPM和Turbo统一调制编码的技术能进一步降低系统的效率和误码率。     

量子稀疏图码的反馈式迭代译码

量子稀疏图码的译码可以由基于错误图样的和积译码算法来实现.本文在此基础上构建了一个新的反馈式迭代译码算法.其反馈策略不仅仅重新利用了错误图样,而且还利用了稳定子上相应元素的值和信道的错误模型.由此,本方法一方面可以克服传统的量子和积译码算法中遇到的所谓对称简并错误,另一方面还能反馈更多的有用信息到译码器中,帮助其产生有效的译码结果,大大提高译码器的译码能力.另外,本算法并没有增加量子测量的复杂度,而是对测量中所能获得的信息的更充分利用.     

Quantum secure direct communication and deterministic secure quantum communication

In this review article, we review the recent development of quantum secure direct communication (QSDC) and deterministic secure quantum communication (DSQC) which both are used to transmit secret message, including the criteria for QSDC, some interesting QSDC protocols, the DSQC protocols and QSDC network, etc. The difference between these two branches of quantum communication is that DSQC requires the two parties exchange at least one bit of classical information for reading out the message in each qubit, and QSDC does not. They are attractive because they are deterministic, in particular, the QSDC protocol is fully quantum mechanical. With sophisticated quantum technology in the future, the QSDC may become more and more popular. For ensuring the safety of QSDC with single photons and quantum information sharing of single qubit in a noisy channel, a quantum privacy amplification protocol has been proposed. It involves very simple CHC operations and reduces the information leakage to a negligible small level. Moreover, with the one-party quantum error correction, a relation has been established between classical linear codes and quantum one-party codes, hence it is convenient to transfer many good classical error correction codes to the quantum world. The one-party quantum error correction codes are especially designed for quantum dense coding and related QSDC protocols based on dense coding.      

Some New Quantum BCH Codes over Finite Fields

Quantum error correcting codes (QECCs) play an important role in preventing quantum information decoherence. Good quantum stabilizer codes were constructed by classical error correcting codes. In this paper, Bose–Chaudhuri–Hocquenghem (BCH) codes over finite fields are used to construct quantum codes. First, we try to find such classical BCH codes, which contain their dual codes, by studying the suitable cyclotomic cosets. Then, we construct nonbinary quantum BCH codes with given parameter sets. Finally, a new family of quantum BCH codes can be realized by Steane’s enlargement of nonbinary Calderbank-Shor-Steane (CSS) construction and Hermitian construction. We have proven that the cyclotomic cosets are good tools to study quantum BCH codes. The defining sets contain the highest numbers of consecutive integers. Compared with the results in the references, the new quantum BCH codes have better code parameters without restrictions and better lower bounds on minimum distances. What is more, the new quantum codes can be constructed over any finite fields, which enlarges the range of quantum BCH codes.     

Description of a quantum convolutional code

We describe a quantum error correction scheme aimed at protecting a flow of quantum information over long distance communication. It is largely inspired by the theory of classical convolutional codes which are used in similar circumstances in classical communication. The particular example shown here uses the stabilizer formalism. We provide an explicit encoding circuit and its associated error estimation algorithm. The latter gives the most likely error over any memoryless quantum channel, with a complexity growing only linearly with the number of encoded qubits.     

Stabilizer formalism for operator quantum error correction

Operator quantum error correction is a recently developed theory that provides a generalized and unified framework for active error correction and passive error avoiding schemes. In this Letter, we describe these codes using the stabilizer formalism. This is achieved by adding a gauge group to stabilizer codes that defines an equivalence class between encoded states. Gauge transformations leave the encoded information unchanged; their effect is absorbed by virtual gauge qubits that do not carry useful information. We illustrate the construction by identifying a gauge symmetry in Shor's 9-qubit code that allows us to remove 3 of its 8 stabilizer generators, leading to a simpler decoding procedure and a wider class of logical operations without affecting its essential properties. This opens the path to possible improvements of the error threshold of fault-tolerant quantum computing.     

量子通信

量子通信是经典通信和量子力学相结合的一门新兴交叉学科。文章综述了量子通信领域的研究进展，既包括人们所熟知的量子隐形传态、密集编码和量子密码学，也包括刚刚兴起但却有巨大潜力的量子通信复杂度和远程量子通信等领域。文章介绍了量子通信的基本理论框架，同时也涉及了这个领域最新的实验研究的进展。     

Performance characteristics and weight distribution analysis of turbo product code with Reed-Muller component codes

In this paper, we present simulation results for Reed-Muller (RM) turbo codes over AWGN and Rayleigh fading channels. We also compare the simulation results of turbo product codes and block turbo codes with RM component codes over an AWGN channel. We show that minimum distance is not important as far as the BER performance of long codes is concerned. The weight distribution of RM codes of different lengths and turbo product codes with first-order RM component codes are obtained and analyzed for their good performance. We show that the weight distribution asymptotically approaches that of random coding as the code length increases.