Entanglement-assisted codeword stabilized quantum codes with imperfect ebits

Quantum error correcting codes (QECCs) in quantum communi- cation systems has been known to exhibit improved performance with the use of error-free entanglement bits (ebits). In practical situations, ebits inevitably suffer from errors, and as a result, the error-correcting capability of the code is diminished. Prior studies have proposed two different schemes as a solu- tion. One uses only one QECC to correct errors on the receiver's side (i.e., Bob) and on the sender's side (i.e., Alice). The other uses different QECCs on each side. In this paper, we present a method to correct errors on both sides by using single nonadditive Entanglement-assisted codeword stabilized quantum error correcting code(EACWS QECC). We use the property that the number of effective error patterns decreases as much as the number of ebits. This property results in a greater number of logical codewords using the same number of physical qubits

Flat bands in Network Superstructures of Atomic Chains

We investigate the origin of the ubiquitous existence of flat bands in the network superstructures of atomic chains, where one-dimensional(1D) atomic chains array periodically. While there can be many ways to connect those chains, we consider two representative ways of linking them, the dot-type and triangle-type links. Then, we construct a variety of superstructures, such as the square, rectangular, and honeycomb network superstructures with dot-type links and the honeycomb superstructure with triangle-type links. These links provide the wavefunctions with an opportunity to have destructive interference, which stabilizes the compact localized state(CLS). The CLS is a localized eigenstate whose amplitudes are finite only inside a finite region and guarantees the existence of a flat band. In the network superstructures, there exist multiple flat bands proportional to the number of atoms of each chain, and the corresponding eigenenergies can be found from the stability condition of the compact localized state. Finally, we demonstrate that the finite bandwidth of the nearly flat bands of the network superstructures arising from the next-nearest-neighbor hopping processes can be suppressed by increasing the length of the chains consisting of the superstructures.Comment: 8pages, 4figure

Progressive Processing of Continuous Range Queries in Hierarchical Wireless Sensor Networks

In this paper, we study the problem of processing continuous range queries in a hierarchical wireless sensor network. Contrasted with the traditional approach of building networks in a "flat" structure using sensor devices of the same capability, the hierarchical approach deploys devices of higher capability in a higher tier, i.e., a tier closer to the server. While query processing in flat sensor networks has been widely studied, the study on query processing in hierarchical sensor networks has been inadequate. In wireless sensor networks, the main costs that should be considered are the energy for sending data and the storage for storing queries. There is a trade-off between these two costs. Based on this, we first propose a progressive processing method that effectively processes a large number of continuous range queries in hierarchical sensor networks. The proposed method uses the query merging technique proposed by Xiang et al. as the basis and additionally considers the trade-off between the two costs. More specifically, it works toward reducing the storage cost at lower-tier nodes by merging more queries, and toward reducing the energy cost at higher-tier nodes by merging fewer queries (thereby reducing "false alarms"). We then present how to build a hierarchical sensor network that is optimal with respect to the weighted sum of the two costs. It allows for a cost-based systematic control of the trade-off based on the relative importance between the storage and energy in a given network environment and application. Experimental results show that the proposed method achieves a near-optimal control between the storage and energy and reduces the cost by 0.989~84.995 times compared with the cost achieved using the flat (i.e., non-hierarchical) setup as in the work by Xiang et al.Comment: 41 pages, 20 figure

Entanglement-assisted codeword stabilized quantum codes

Entangled qubit can increase the capacity of quantum error correcting codes based on stabilizer codes. In addition, by using entanglement quantum stabilizer codes can be construct from classical linear codes that do not satisfy the dual-containing constraint. We show that it is possible to construct both additive and non-additive quantum codes using the codeword stabilized quantum code framework. Nonadditive codes may offer improved performance over the more common sta- bilizer codes. Like other entanglement-assisted codes, the encoding procedure acts only the qubits on Alice's side, and only these qubits are assumed to pass through the channel. However, errors the codeword stabilized quantum code framework gives rise to effective Z errors on Bob side. We use this scheme to construct new entanglement-assisted non-additive quantum codes, in particular, ((5,16,2;1)) and ((7,4,5;4)) codes