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Surface codes: Towards practical large-scale quantum computation

Physical Review A 2012年第3期86卷 032324-032324页

作者： Austin G. Fowler Matteo Mariantoni John M. Martinis Andrew N. Cleland Department of Physics University of California Santa Barbara California 93106-9530 USA and California Nanosystems Institute University of California Santa Barbara California 93106-9530 USA

This article provides an introduction to surface code quantum computing. We first estimate the size and speed of a surface code quantum computer. We then introduce the concept of the stabilizer, using two qubits, and extend this concept to stabilizers acting on a two-dimensional array of physical qubits, on which we implement the surface code. We next describe how logical qubits are formed in the surface code array and give numerical estimates of their fault tolerance. We outline how logical qubits are physically moved on the array, how qubit braid transformations are constructed, and how a braid between two logical qubits is equivalent to a controlled-not. We then describe the single-qubit Hadamard, Ŝ and T̂ operators, completing the set of required gates for a universal quantum computer. We conclude by briefly discussing physical implementations of the surface code. We include a number of Appendices in which we provide supplementary information to the main text.

关键词： QUANTUM computers QUANTUM information theory coding theory QUBITS NUMERICAL analysis FAULT tolerance (Engineering) PHASE transformations (Physics)

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Medical Image Compression Based on Vector Quantization with Variable Block Sizes in Wavelet Domain

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COMPUTATIONAL INTELLIGENCE AND NEUROSCIENCE 2012年第unknown期2012卷 541890-541890页

作者： Jiang, Huiyan Ma, Zhiyuan Hu, Yang Yang, Benqiang Zhang, Libo Northeastern Univ Software Coll Shenyang 110819 Peoples R China Minist Educ Key Lab Med Image Comp Shenyang 110819 Peoples R China Chinese Peoples Liberat Army Gen Hosp Dept Radiol Shenyang 110015 Peoples R China

An optimized medical image compression algorithm based on wavelet transform and improved vector quantization is introduced. The goal of the proposed method is to maintain the diagnostic-related information of the medical image at a high compression ratio. Wavelet transformation was first applied to the image. For the lowest-frequency subband of wavelet coefficients, a lossless compression method was exploited;for each of the high-frequency subbands, an optimized vector quantization with variable block size was implemented. In the novel vector quantization method, local fractal dimension (LFD) was used to analyze the local complexity of each wavelet coefficients, subband. Then an optimal quadtree method was employed to partition each wavelet coefficients, subband into several sizes of subblocks. After that, a modified K-means approach which is based on energy function was used in the codebook training phase. At last, vector quantization coding was implemented in different types of sub-blocks. In order to verify the effectiveness of the proposed algorithm, JPEG, JPEG2000, and fractal coding approach were chosen as contrast algorithms. Experimental results show that the proposed method can improve the compression performance and can achieve a balance between the compression ratio and the image visual quality.

关键词： IMAGE compression DIAGNOSTIC imaging VECTOR quantization WAVELETS (Mathematics) COMPUTER algorithms INFORMATION theory coding theory

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Generalized semiquantum secret-sharing schemes

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Physical Review A 2012年第5期85卷 052309-052309页

作者： Vlad Gheorghiu []Institute for Quantum Information Science and Department of Mathematics and Statistics University of Calgary 2500 University Drive NW Calgary AB Canada T2N 1N4

We investigate quantum secret-sharing schemes constructed from [[n,k,δ]]D nonbinary stabilizer quantum error-correcting codes with carrier qudits of prime dimension D. We provide a systematic way of determining the access structure, which completely determines the forbidden and intermediate structures. We then show that the information available to the intermediate structure can be fully described and quantified by what we call the information group, a subgroup of the Pauli group of k qudits, and we employ this group structure to construct a method for hiding the information from the intermediate structure via twirling of the information group and sharing of classical bits between the dealer and the players. Our scheme allows for the transformation of a ramp (intermediate) quantum secret-sharing scheme into a semiquantum perfect secret-sharing scheme with the same access structure as the ramp one but without any intermediate subsets, and is optimal in the amount of classical bits the dealer has to distribute.

关键词： GENERALIZATION QUANTUM error correcting codes DIMENSIONAL analysis PHASE transformations (Physics) coding theory INFORMATION theory

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High Threshold Error Correction for the Surface Code

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Physical Review Letters 2012年第16期109卷 160503-160503页

作者： James R. Wootton Daniel Loss Department of Physics University of Basel Klingelbergstrasse 82 CH-4056 Basel Switzerland

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.

关键词： ERROR-correcting codes (Information theory) coding theory INFORMATION theory COMPUTER storage devices QUANTUM computers ALGORITHMS POLYNOMIALS

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Optimal error correction in topological subsystem codes

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Physical Review A 2012年第5期85卷 050302(R)-050302(R)页

作者： Ruben S. Andrist H. Bombin Helmut G. Katzgraber M. A. Martin-Delgado Theoretische Physik ETH Zurich CH-8093 Zurich Switzerland Perimeter Institute for Theoretical Physics Waterloo Ontario N2L 2Y5 Canada Department of Physics and Astronomy Texas A&M University College Station Texas 77843-4242 USA Departamento de Física Teórica I Universidad Complutense 28040 Madrid Spain

A promising approach to overcome decoherence in quantum computing schemes is to perform active quantum error correction using topology. Topological subsystem codes incorporate both the benefits of topological and subsystem codes, allowing for error syndrome recovery with only 2-local measurements in a two-dimensional array of qubits. We study the error threshold for topological subsystem color codes under very general external noise conditions. By transforming the problem into a classical disordered spin model, we estimate using Monte Carlo simulations that topological subsystem codes have an optimal error tolerance of 5.5(2)%. This means there is ample space for improvement in existing error-correcting algorithms that typically find a threshold of approximately 2%.

关键词： ERRORS TOPOLOGY coding theory QUANTUM theory NOISE -- Measurement MONTE Carlo method ALGORITHMS

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Network Coded Wireless Cooperative Multicast with Minimum Transmission Cost

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INTERNATIONAL JOURNAL OF DISTRIBUTED SENSOR NETWORKS 2012年第10期8卷 1-12页

作者： Wang, Xiumin Wang, Jin Zhang, Shukui Soochow Univ Sch Comp Sci & Technol Suzhou 215006 Peoples R China Hefei Univ Technol Sch Comp & Informat Hefei 230009 Peoples R China Nanjing Univ State Key Lab Novel Software Technol Nanjing 210093 Jiangsu Peoples R China

We study multicasting over wireless lossy links. Instead of downloading all the data from the source node, we allow the destination nodes themselves to locally exchange the packets, as local communication within a cluster achieves higher packet reception probability with less transmission cost. However, when shall we stop the transmission from the source node? If the source stops too early, the destination nodes locally cannot reconstruct all the original packets, while if the source stops too late, the benefit of cooperative data exchange cannot be fully exploited. In this paper, we propose a network coded hybrid source and cooperative exchange scheme to determine when to stop the source sending and start the exchange process, so as to minimize the total transmission cost. For the case when the clusters are predefined, we derive the expected total transmission cost with our hybrid scheme. Our theoretical results show that under a special condition, the source node should keep sending the packets until all the destinations get the complete information. For the case when the clusters are not predefined, we propose a cluster division algorithm such that the destination nodes within each cluster can conduct data exchange locally with energy efficiency. Finally, simulation results demonstrate the effectiveness of the proposed scheme.

关键词： WIRELESS sensor networks coding theory DATA transmission systems DATA packets & packeting PROBABILITY theory ALGORITHMS

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An Adaptive Opportunistic Network coding Mechanism in Wireless Multimedia Sensor Networks

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INTERNATIONAL JOURNAL OF DISTRIBUTED SENSOR NETWORKS 2012年第12期8卷 1-13页

作者： Shen, Hang Bai, Guangwei Zhao, Lu Tang, Zhenmin Nanjing Univ Sci & Technol Minist Educ Key Lab Intelligent Percept & Syst High Dimens In Nanjing 210094 Jiangsu Peoples R China Nanjing Univ State Key Lab Novel Software Technol Nanjing 210093 Jiangsu Peoples R China Nanjing Univ Technol Dept Comp Sci & Technol Nanjing 210009 Jiangsu Peoples R China

The network coding technique is promising for improving the performance of video communication in wireless multimedia sensor networks. However, some special characteristics of existing wireless network coding mechanisms degrade the performance of video data delivery. This work begins with a thorough investigation and understanding of the performance limitations of existing wireless network coding mechanisms. On this basis, we propose an Adaptive Opportunistic Network coding mechanism (AONC) to improve the transmission quality of video stream in wireless multimedia sensor networks. First, we propose a novel asymmetric coding method to process the video data of different lengths. The aim is to improve data exchange gain. Second, we design an opportunistic forwarding strategy based on dynamic priority to ensure that packets have a better chance to be coded and transmitted, thus achieving much higher throughput. Finally, we present a traffic-aware data scheduling algorithm, working together with the above network coding mechanism, to reduce the loss of potential coding opportunities. Our simulation results demonstrate that, compared with the existing typical network coding mechanisms, AONC can greatly enhance video transmission quality and efficiently utilize bandwidth and energy resources.

关键词： coding theory WIRELESS sensor networks NETWORK performance (Telecommunication) DATA quality DYNAMICAL systems DATA packets & packeting DATA Traffic Management System (Computer system)

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A Mutual Algorithm for Optimizing Distributed Source coding in Wireless Sensor Networks

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INTERNATIONAL JOURNAL OF DISTRIBUTED SENSOR NETWORKS 2012年第2期8卷 1-9页

作者： Abughalieh, Nashat Steenhaut, Kris Lemmens, Bart Nowe, Ann Vrije Univ Brussel Dept Elect & Informat ETRO B-1050 Brussels Belgium Erasmushogesch Brussel IWT B-1070 Brussels Belgium

Wireless Sensor Networks (WSNs) are composed of small wireless nodes equipped with sensors, a processor, and a radio communication unit, all normally powered by batteries. For most WSN applications, the network is expected to function for several months or years. In the common monitoring application scenario, adjacent nodes in a WSN often sense spatially correlated data. Suppressing this correlation can significantly improve the lifetime of the network. The maximum possible network data compression can be achieved using distributed source coding (DSC) techniques when nodes encode at Slepian-Wolf rates. This paper presents contributions to the lifetime optimization problem of WSNs in the form of two algorithms: the Updated-CMAX (UCMAX) power-aware routing algorithm to optimize the routing tree and the Rate Optimization (RO) algorithm to optimize the encoding rates of the nodes. The two algorithms combined offer a solution that maximizes the lifetime of a WSN measuring spatially correlated data. Simulations show that our proposed approach may significantly extend the lifetime of multihop WSNs with nodes that are observing correlated data.

关键词： DISTRIBUTED algorithms coding theory WIRELESS sensor networks DATA compression (Computer science) ROUTING algorithms RADIO (Medium)

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A Rate-Distortion-Based Merging Algorithm for Compressed Image Segmentation

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COMPUTATIONAL AND MATHEMATICAL METHODS IN MEDICINE 2012年第1期2012卷 648320-648320页

作者： Juang, Ying-Shen Hsin, Hsi-Chin Sung, Tze-Yun Shieh, Yaw-Shih Cattani, Carlo Chung Hua Univ Dept Elect Engn Hsinchu 30012 Taiwan Chung Hua Univ Dept Business Adm Hsinchu 30012 Taiwan Natl United Univ Dept Comp Sci & Informat Engn Miaoli 36003 Taiwan Univ Salerno Dept Math I-84084 Fisciano Italy

Original images are often compressed for the communication applications. In order to avoid the burden of decompressing computations, it is thus desirable to segment images in the compressed domain directly. This paper presents a simple rate-distortion-based scheme to segment images in the JPEG2000 domain. It is based on a binary arithmetic code table used in the JPEG2000 standard, which is available at both encoder and decoder;thus, there is no need to transmit the segmentation result. Experimental results on the Berkeley image database show that the proposed algorithm is preferable in terms of the running time and the quantitative measures: probabilistic Rand index (PRI) and boundary displacement error (BDE).

关键词： ALGORITHMS IMAGE compression SEGMENTATION (Image processing) APPLICATION software QUANTITATIVE research coding theory

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Distributed Intrusion Detection of Byzantine Attacks in Wireless Networks with Random Linear Network coding

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INTERNATIONAL JOURNAL OF DISTRIBUTED SENSOR NETWORKS 2012年第12期8卷 1-10页

作者： Chen, Jen-Yeu Tseng, Yi-Ying Natl Dong Hwa Univ Dept Elect Engn Shoufeng 97401 Hualien Taiwan

Network coding (NC) can be applied to achieve the maximal information flow in a network. In energy-constraint wireless networks such as wireless sensor networks, applying NC can further reduce the number of wireless transmissions and hence prolong the life time of sensor nodes. Although applying NC in wireless networks is obviously beneficial, it is possible that a malicious node (Byzantine attacker) can take advantage of the inherent vulnerability of error propagation in the NC scheme to corrupt all the information transmissions. In the NC scheme, an intermediate node linearly combines several incoming messages as its outgoing messages. Thus a data error injected in any intermediate nodes will corrupt the information reaching a destination. Recent research efforts have shown that NC can be combined with classical error control codes and cryptography for secure communications or misbehavior detections. Nevertheless, when it comes to Byzantine attacks, these results have limited effects. In this paper, a distributed algorithm is developed to effectively detect, locate, and isolate the Byzantine attackers in a wireless ad hoc network with random linear network coding (RLNC). To the best of our knowledge, our work is the first to address the problem of Byzantine failures in a wireless network with RLNC.

关键词： WIRELESS sensor networks FAULT tolerance (Engineering) LINEAR systems coding theory CONSTRAINT satisfaction (Artificial intelligence) DATA transmission systems DISTRIBUTED algorithms

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