Related papers: An efficient algebraic representation for graph st…
Graph states are widely used in quantum information theory, including entanglement theory, quantum error correction, and one-way quantum computing. Graph states have a nice structure related to a certain graph, which is given by either a…
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 used to represent mathematical graphs as quantum states on quantum computers. They can be formulated through stabilizer codes or directly quantum gates and quantum states. In this paper we show that a quantum graph neural…
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…
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…
Cluster states and graph states in general offer a useful model of the stabilizer formalism and a path toward the development of measurement-based quantum computation. Their defining structure - the stabilizer group - encodes all possible…
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),…
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…
Improving the simulation of quantum circuits on classical computers is important for understanding quantum advantage and increasing development speed. In this paper, we explore a new way to express stabilizer states and further improve the…
Graph states are versatile resources for quantum computation and quantum-enhanced measurement. Their generation illustrates a high level of control over entanglement. We report on the generation of continuous-variable graph states of atomic…
By using highly entangled states, quantum metrology guarantees precision impossible with classical measurements. Unfortunately such states can be very susceptible to noise, and it is a great challenge of the field to maintain quantum…
The quantum circuit model is the default for encoding an algorithm intended for a NISQ computer or a quantum computing simulator. A simple graph and through it, a graph state - quantum state physically manifesting an abstract graph…
Stabilizer states form a ubiquitous family of quantum states that can be graphically represented through the graph state formalism. A fundamental property of graph states is that applying a local complementation - a well-known and…
Fathoming out quantum state space is a challenging endeavor due to its exponentially growing dimensionality. At the expense of being bound in its expressiveness, the discrete and finite subspace of graph states is easier to investigate via…
The phase space for a system of $n$ qubits is a discrete grid of $2^{n} \times 2^{n}$ points, whose axes are labeled in terms of the elements of the finite field $\Gal{2^n}$ to endow it with proper geometrical properties. We analyze the…
We introduce a class of multiqubit quantum states which generalizes graph states. These states correspond to an underlying mathematical hypergraph, i.e. a graph where edges connecting more than two vertices are considered. We derive a…
While stabilizer tableaus have proven useful as a descriptive tool for additive quantum codes, they otherwise offer little guidance for concrete constructions or algorithm analysis. We introduce a representation of stabilizer codes as…
Graph states are a family of stabilizer states which can be tailored towards various applications in photonic quantum computing and quantum communication. In this paper, we present a modular design based on quantum dot emitters coupled to a…
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…
The class of entangled $N$-qubit states known as graph states, and the corresponding stabilizer groups of $N$-qubit Pauli observables, have found a wide range of applications in quantum information processing and the foundations of quantum…