Related papers: Graph state representation of the toric code
Deciding if a given family of quantum states is topologically ordered is an important but nontrivial problem in condensed matter physics and quantum information theory. We derive necessary and sufficient conditions for a family of graph…
The name graph state is used to describe a certain class of pure quantum state which models a physical structure on which one can perform measurement-based quantum computing, and which has a natural graphical description. We present the…
Graph states are the main computational building blocks of measurement-based computation and a useful tool for error correction in the gate model architecture. The graph states form a class of quantum states which are eigenvectors for the…
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…
We introduce a graphical representation of stabilizer states and translate the action of Clifford operators on stabilizer states into graph operations on the corresponding stabilizer-state graphs. Our stabilizer graphs are constructed of…
While stabilizer tableaus have proven exceptionally useful as a descriptive tool for additive quantum codes, they offer little guidance for concrete constructions or coding algorithm analysis. We introduce a representation of stabilizer…
In this paper we define homological stabilizer codes which encompass codes such as Kitaev's toric code and the topological color codes. These codes are defined solely by the graphs they reside on. This feature allows us to use properties of…
Graph states, which include for example Bell states, GHZ states and cluster states, form a well-known class of quantum states with applications ranging from quantum networks to error-correction. Deciding whether two graph states are…
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…
We present an algorithm for efficiently simulating a quantum circuit in the graph formalism. In the graph formalism, we represent states as a linear combination of graphs with Clifford operations on their vertices. We show how a…
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…
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.
Graph states are quantum states that can be described by a stabilizer formalism and play an important role in quantum information processing. We consider the action of local unitary operations on graph states and hypergraph states. We focus…
We propose two schemes for implementing graph states useful for fault-tolerant topological measurement-based quantum computation in 2D optical lattices. We show that bilayer cluster and surface code states can be created by global…
Stabilizer states form an important class of states in quantum information, and are of central importance in quantum error correction. Here, we provide an algorithm for deciding whether one stabilizer (target) state can be obtained from…
Given a quantum error correcting code, an important task is to find encoded operations that can be implemented efficiently and fault-tolerantly. In this Letter we focus on topological stabilizer codes and encoded unitary gates that can be…
A graph state and a graph code respectively are defined based on a mathematical simple graph. In this work, we examine a relation between a graph state and a graph code both obtained from the same graph, and show that a graph state is a…
Stabilizer states along with Clifford manipulations (unitary transformations and measurements) thereof -- despite being efficiently simulable on a classical computer -- are an important tool in quantum information processing, with…
Graph states are multi-particle entangled states that correspond to mathematical graphs, where the vertices of the graph take the role of quantum spin systems and edges represent Ising interactions. They are many-body spin states of…