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Topological subsystem codes from graphs and hypergraphs

Physical Review A 2012年第4期86卷 042336-042336页

作者： Pradeep Sarvepalli Kenneth R. Brown Schools of Chemistry and Biochemistry Computational Science and Engineering and Physics Georgia Institute of Technology Atlanta Georgia 30332 USA

Topological subsystem codes were proposed by Bombin based on 3-face-colorable cubic graphs. Suchara, Bravyi, and Terhal generalized this construction and proposed a method to construct topological subsystem codes using 3-valent hypergraphs that satisfy certain constraints. Finding such hypergraphs and computing their parameters, however, is a nontrivial task. We propose families of topological subsystem codes that were previously not known. In particular, our constructions give codes which cannot be derived from Bombin's construction. We also study the error recovery schemes for the proposed subsystem codes and give detailed schedules for the syndrome measurement that take advantage of the 2-locality of the gauge group. The study also leads to a new and general construction for color codes.

关键词： TOPOLOGY HYPERGRAPHS GRAPH coloring CONSTRAINT satisfaction (Artificial intelligence) GAUGE field theory coding theory

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Towards practical classical processing for the surface code: Timing analysis

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Physical Review A 2012年第4期86卷 042313-042313页

作者： Austin G. Fowler Adam C. Whiteside Lloyd C. L. Hollenberg Centre for Quantum Computation and Communication Technology School of Physics The University of Melbourne Victoria 3010 Australia

Topological quantum error-correction codes have high thresholds and are well suited to physical implementation. The minimum-weight perfect-matching algorithm can be used to efficiently handle errors in such codes. We perform a timing analysis of our current implementation of the minimum-weight perfect-matching algorithm. Our implementation performs the classical processing associated with an n×n lattice of qubits realizing a square surface code storing a single logical qubit of information in a fault-tolerant manner. We empirically demonstrate that our implementation requires only O(n2) average time per round of error correction for code distances ranging from 4 to 512 and a range of depolarizing error rates. We also describe tests we have performed to verify that it always obtains a true minimum-weight perfect matching.

关键词： SURFACES (Physics) QUANTUM theory coding theory ALGORITHMS MATCHING theory QUBITS

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An Efficient Reliable Communication Scheme in Wireless Sensor Networks Using Linear Network coding

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INTERNATIONAL JOURNAL OF DISTRIBUTED SENSOR NETWORKS 2012年第unknown期2012卷 1-11页

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

We address the modeling and design of linear network coding (LNC) for reliable communication against multiple failures in wireless sensor networks (WSNs). To fulfill the objective, we design a deterministic LNC scheme RDLC based on the average number of path failures simultaneously happening in the network other than the maximum number of path failures. The scheme can significantly improve the network throughput comparing with the traditional approaches. In our study, we also investigate the potential of random linear code RRLC for providing reliable communication in WSNs and prove the low bound of the probability that the RRLC can provide the reliable communication. Finally, extensive simulation experiments have been conducted, and the results demonstrate the effectiveness of the proposed LNC schemes.

关键词： WIRELESS sensor networks ENERGY consumption COMPUTER reliability LINEAR systems coding theory COMPUTER engineering FAILURE Analysis System (Computer system)

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Classical simulation of measurement-based quantum computation on higher-genus surface-code states

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Physical Review A 2012年第4期86卷 042301-042301页

作者： Leonard Goff Robert Raussendorf Department of Physics and Astronomy University of British Columbia Vancouver British Columbia Canada V6T 1Z1

We consider the efficiency of classically simulating measurement-based quantum computation on surface-code states. We devise a method for calculating the elements of the probability distribution for the classical output of the quantum computation. The operational cost of this method is polynomial in the size of the surface-code state, but in the worst case scales as 22g in the genus g of the surface embedding the code. However, there are states in the code space for which the simulation becomes efficient. In general, the simulation cost is exponential in the entanglement contained in a certain effective state, capturing the encoded state, the encoding, and the local postmeasurement states. The same efficiencies hold, with additional assumptions on the temporal order of measurements and on the tessellations of the code surfaces, for the harder task of sampling from the distribution of the computational output.

关键词： QUANTUM theory SIMULATION methods & models MEASURE theory DISTRIBUTION (Probability theory) SURFACES (Physics) coding theory

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Self-assembled clusters of spheres related to spherical codes

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Physical Review E 2012年第4期86卷 041124-041124页

作者： Carolyn L. Phillips Eric Jankowski Michelle Marval Sharon C. Glotzer Applied Physics Program University of Michigan Ann Arbor Michigan 48109 USA Department of Chemical Engineering University of Michigan Ann Arbor Michigan 48109 USA Department of Materials Science and Engineering University of Michigan Ann Arbor Michigan 48109 USA

We consider the thermodynamically driven self-assembly of spheres onto the surface of a central sphere. This assembly process forms self-limiting, or terminal, anisotropic clusters (N-clusters) with well-defined structures. We use Brownian dynamics to model the assembly of N-clusters varying in size from two to twelve outer spheres and free energy calculations to predict the expected cluster sizes and shapes as a function of temperature and inner particle diameter. We show that the arrangements of outer spheres at finite temperatures are related to spherical codes, an ideal mathematical sequence of points corresponding to the densest possible sphere packings. We demonstrate that temperature and the ratio of the diameters of the inner and outer spheres dictate cluster morphology. We present a surprising result for the equilibrium structure of a 5-cluster, for which the square pyramid arrangement is preferred over a more symmetric structure. We show this result using Brownian dynamics, a Monte Carlo simulation, and a free energy approximation. Our results suggest a promising way to assemble anisotropic building blocks from constituent colloidal spheres.

关键词： MOLECULAR self-assembly MICROCLUSTERS THERMODYNAMICS ANISOTROPY BROWNIAN motion processes GIBBS' free energy TEMPERATURE effect coding theory

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CATHARE Assessment of Natural Circulation in the PKL Test Facility during Asymmetric Cooldown Transients

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SCIENCE AND TECHNOLOGY OF NUCLEAR INSTALLATIONS 2012年第unknown期2012卷 1-10页

作者： Salah, Anis Bousbia Vlassenbroeck, Jacques Bel V B-1070 Brussels Belgium

Results of the CATHARE code calculations related to asymmetric cooldown tests in the PKL facility are presented. The test under consideration is the G2.1 experiment performed within the OECD/NEA PKL-2 project. It consists of carrying out a cooldown under natural circulation conditions in presence of two (out of four) emptied Steam Generators (SGs) and isolated on their secondary sides. The main goal of the current study is to assess the impact of a chosen cooldown strategy upon the occurrence of a Natural Circulation Interruption (NCI) in the inactive (i.e., noncooling) loops. For this purpose, three G2.1 test runs were investigated. The calculation results emphasize, mainly, the effect of the cooldown strategy, and the conditions that could lead to the occurrence of the NCI phenomenon.

关键词： NUCLEAR facilities COOLDOWN coding theory PHYSICS experiments PERFORMANCE evaluation

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Encoding dynamics for multiscale community detection: Markov time sweeping for the map equation

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Physical Review E 2012年第2期86卷 026112-026112页

作者： Michael T. Schaub Renaud Lambiotte Mauricio Barahona Department of Mathematics Imperial College London London SW7 2AZ United Kingdom Department of Chemistry Imperial College London London SW7 2AZ United Kingdom Department of Mathematics and Naxys University of Namur 5000 Namur Belgium

The detection of community structure in networks is intimately related to finding a concise description of the network in terms of its modules. This notion has been recently exploited by the map equation formalism [Rosvall and Bergstrom, Proc. Natl. Acad. Sci. USA 105, 1118 (2008)] through an information-theoretic description of the process of coding inter- and intracommunity transitions of a random walker in the network at stationarity. However, a thorough study of the relationship between the full Markov dynamics and the coding mechanism is still lacking. We show here that the original map coding scheme, which is both block-averaged and one-step, neglects the internal structure of the communities and introduces an upper scale, the “field-of-view” limit, in the communities it can detect. As a consequence, map is well tuned to detect clique-like communities but can lead to undesirable overpartitioning when communities are far from clique-like. We show that a signature of this behavior is a large compression gap: The map description length is far from its ideal limit. To address this issue, we propose a simple dynamic approach that introduces time explicitly into the map coding through the analysis of the weighted adjacency matrix of the time-dependent multistep transition matrix of the Markov process. The resulting Markov time sweeping induces a dynamical zooming across scales that can reveal (potentially multiscale) community structure above the field-of-view limit, with the relevant partitions indicated by a small compression gap.

关键词： coding theory MARKOV processes COMMUNITY organization EQUATIONS -- Numerical solutions PHASE transformations (Physics) LIMIT theorems (Probability theory)

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Virtual Parallel Computing and a Search Algorithm Using Matrix Product States

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Physical Review Letters 2012年第3期109卷 030503-030503页

作者： Claudio Chamon Eduardo R. Mucciolo Department of Physics Boston University Boston Massachusetts 02215 USA Department of Physics University of Central Florida Orlando Florida 32816 USA

We propose a form of parallel computing on classical computers that is based on matrix product states. The virtual parallelization is accomplished by representing bits with matrices and by evolving these matrices from an initial product state that encodes multiple inputs. Matrix evolution follows from the sequential application of gates, as in a logical circuit. The action by classical probabilistic one-bit and deterministic two-bit gates such as NAND are implemented in terms of matrix operations and, as opposed to quantum computing, it is possible to copy bits. We present a way to explore this method of computation to solve search problems and count the number of solutions. We argue that if the classical computational cost of testing solutions (witnesses) requires less than O(n2) local two-bit gates acting on n bits, the search problem can be fully solved in subexponential time. Therefore, for this restricted type of search problem, the virtual parallelization scheme is faster than Grover’s quantum algorithm.

关键词： PARALLEL computers SEARCH algorithms VIRTUAL reality coding theory LOGIC circuits QUANTUM computers

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Efficient Polar coding of Quantum Information

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Physical Review Letters 2012年第5期109卷 050504-050504页

作者： Joseph M. Renes Frédéric Dupuis Renato Renner Institut für Theoretische Physik ETH Zurich CH-8093 Zürich Switzerland

Polar coding, introduced 2008 by Arıkan, is the first (very) efficiently encodable and decodable coding scheme whose information transmission rate provably achieves the Shannon bound for classical discrete memoryless channels in the asymptotic limit of large block sizes. Here, we study the use of polar codes for the transmission of quantum information. Focusing on the case of qubit Pauli channels and qubit erasure channels, we use classical polar codes to construct a coding scheme that asymptotically achieves a net transmission rate equal to the coherent information using efficient encoding and decoding operations and code construction. Our codes generally require preshared entanglement between sender and receiver, but for channels with a sufficiently low noise level we demonstrate that the rate of preshared entanglement required is zero.

关键词： coding theory QUANTUM information theory POLAR coordinates (Mathematics) QUBITS KNOWLEDGE transfer (Communication)

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An Unbound Network coding for Extended IEEE 802.16j Multihop Relay Network

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INTERNATIONAL JOURNAL OF DISTRIBUTED SENSOR NETWORKS 2012年第unknown期2012卷 1-15页

作者： Sukul, Adisak Chang, J. Morris Bhattarakosol, Pattarasinee Chulalongkorn Univ Dept Math Fac Sci Bangkok 10330 Thailand Iowa State Univ Dept Elect & Comp Engn Ames IA 50011 USA

IEEE 802.16j is an amendment to the IEEE 802.16 broadband wireless access standard to enable the operation of multihop relay stations (RSs). It aims to enhance the coverage, per user throughput of IEEE 802.16e. Comparing with a base station (BS), RS does not need a wireline backhaul and has much lower hardware complexity. Moreover, using RSs can significantly reduce the deployment cost of the system. Unfortunately, there are some tradeoffs in the case of multi-hop RSs. Subscriber stations (SSs), located in a long distance, are suffered from the bottleneck of multi-hop, throughput degradation, and increasing of end-to-end delay. This paper proposes a network coding-based relay scheme for multi-hop relay networks, called NC-BR. It allows RSs to combine two wireless backhaul transmissions into one using the network coding technique. This paper also proposes an improved OFDMA frame structure design for the multi-hop relay network. This technique provides higher utilization for the relay zone by reorganizing the RSs transmission sequence. The analysis and simulation results confirm that the proposed scheme can enhance the throughput gain up to 140% and reduce the end-to-end delay by up to 83%. The simulation results also show that the proposed scheme can reduce the jitter by up to 58%.

关键词： IEEE 802.16 (Standard) ELECTRIC relays WIRELESS sensor networks COMPUTER simulation NETWORK time delays coding theory COMPUTER input-output equipment

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