Related papers: Topological graph states and quantum error correct…
Given their potential for fault-tolerant operations, topological quantum states are currently the focus of intense activity. Of particular interest are topological quantum error correction codes, such as the surface and planar stabilizer…
We investigate a novel class of quantum error correcting codes to correct errors on both qubits and higher-state quantum systems represented as qudits. These codes arise from an original graph-theoretic representation of sets of quantum…
Scalable quantum computing and communication requires the protection of quantum information from the detrimental effects of decoherence and noise. Previous work tackling this problem has relied on the original circuit model for quantum…
Graph states are generalized from qubits to collections of $n$ qudits of arbitrary dimension $D$, and simple graphical methods are used to construct both additive and nonadditive quantum error correcting codes. Codes of distance 2…
Graph theory is important in information theory. We introduce a quantization process on graphs and apply the quantized graphs in quantum information. The quon language provides a mathematical theory to study such quantized graphs in a…
We introduce a purely graph-theoretical object, namely the coding clique, to construct quantum errorcorrecting codes. Almost all quantum codes constructed so far are stabilizer (additive) codes and the construction of nonadditive codes,…
A fundamental problem in quantum information is to describe efficiently multipartite quantum states. An efficient representation in terms of graphs exists for several families of quantum states (graph, cluster, stabilizer states),…
Quantum states are very delicate, so it is likely some sort of quantum error correction will be necessary to build reliable quantum computers. The theory of quantum error-correcting codes has some close ties to and some striking differences…
The following open problems, which concern a fundamental limit on coding properties of quantum codes with realistic physical constraints, are analyzed and partially answered here: (a) the upper bound on code distances of quantum…
Graph states have been used to construct quantum error correction codes for independent errors. Hypergraph states generalize graph states, and symmetric hypergraph states have been shown to allow for the correction of correlated errors. In…
Quantum Error-Correcting Codes (QECCs) play a crucial role in enhancing the robustness of quantum computing and communication systems against errors. Within the realm of QECCs, stabilizer codes, and specifically graph codes, stand out for…
The discovery of topological order has revolutionized the understanding of quantum matter in modern physics and provided the theoretical foundation for many quantum error correcting codes. Realizing topologically ordered states has proven…
An m-uniform quantum state on n qubits is an entangled state in which every m-qubit subsystem is maximally mixed. Starting with an m-uniform state realized as the graph state associated with an m-regular graph, and a classical [n,k,d \ge…
We establish the connection between a recent new construction technique for quantum error correcting codes, based on graphs, and the so-called stabilizer codes: Each stabilizer code can be realized as a graph code and vice versa.
Topological quantum memory can protect information against local errors up to finite error thresholds. Such thresholds are usually determined based on the success of decoding algorithms rather than the intrinsic properties of the mixed…
Hypergraph states are a special kind of multipartite states encoded by hypergraphs relevant in quantum error correction, measurement--based quantum computation, quantum non locality and entanglement. In a series of two papers, we introduce…
Many protocols of quantum information processing, like quantum key distribution or measurement-based quantum computation, "consume" entangled quantum states during their execution. When participants are located at distant sites, these…
Quantum error-correction codes (QECCs) are a vital ingredient of quantum computation and communication systems. In that context it is highly desirable to design QECCs that can be represented by graphical models which possess a structure…
The present paper is concerned with the concept of the one-way quantum computer, beyond binary-systems, and its relation to the concept of stabilizer quantum codes. This relation is exploited to analyze a particular class of quantum…
In the absence of fault tolerant quantum error correction for analog, Hamiltonian quantum computation, error suppression via energy penalties is an effective alternative. We construct families of distance-$2$ stabilizer subsystem codes we…