Related papers: Graph states in phase space
Focusing particularly on one-qubit and two-qubit systems, I explain how the quantum state of a system of n qubits can be expressed as a real function--a generalized Wigner function--on a discrete 2^n x 2^n phase space. The phase space is…
We work out the phase-space structure for a system of $n$ qubits. We replace the field of real numbers that label the axes of the continuous phase space by the finite field $\Gal{2^n}$ and investigate the geometrical structures compatible…
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…
Multi-qubit graph states generated by the action of controlled phase shift operators on a separable quantum state of a system, in which all the qubits are in arbitrary identical states, are examined. The geometric measure of entanglement of…
Graph states are a special kind of multiparticle entangled state with great potential for applications in quantum information technologies, especially in measurement-based quantum computers. These states cause significant reductions of the…
We consider graph states generated by the action of controlled phase shift operators on a separable state of a multi-qubit system. The case when all the qubits are initially prepared in arbitrary states is investigated. We obtain 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 original Wigner function provides a way of representing in phase space the quantum states of systems with continuous degrees of freedom. Wigner functions have also been developed for discrete quantum systems, one popular version being…
Grid states form a discrete set of mixed quantum states that can be described by graphs. We characterize the entanglement properties of these states and provide methods to evaluate entanglement criteria for grid states in a graphical way.…
Graph states represent a significant class of multi-partite entangled quantum states with applications in quantum error correction, quantum communication, and quantum computation. In this work, we introduce a novel formalism called the…
We show how to represent the state and the evolution of a quantum computer (or any system with an $N$--dimensional Hilbert space) in phase space. For this purpose we use a discrete version of the Wigner function which, for arbitrary $N$, is…
This article delves into an analysis of the intrinsic entanglement and separability feature in quantum states as depicted by graph Laplacian. We show that the presence or absence of edges in the graph plays a pivotal role in defining the…
We analyze and further develop a new method to represent the quantum state of a system of $n$ qubits in a phase space grid of $N\times N$ points (where $N=2^n$). The method, which was recently proposed by Wootters and co--workers (Gibbons…
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…
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),…
We investigate the properties of different levels of entanglement in graph states which correspond to connected graphs. Combining the operational definition of graph states and the postulates of entanglement measures, we prove that in…
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…
Graph states are an important class of multipartite entangled quantum states. We propose a new approach for distributing graph states across a quantum network. We consider a quantum network consisting of nodes-quantum computers within which…
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…
Corresponding to a hypergraph $G$ with $d$ vertices, a quantum hypergraph state is defined by $|G\rangle = \frac{1}{\sqrt{2^d}}\sum_{n = 0}^{2^d - 1} (-1)^{f(n)} |n \rangle$, where $f$ is a $d$-variable Boolean function depending on the…