Related papers: Mapping graph state orbits under local complementa…
Orbits of graphs under local complementation (LC) and edge local complementation (ELC) have been studied in several different contexts. For instance, there are connections between orbits of graphs and error-correcting codes. We define a new…
Graph states are a fundamental entanglement resource for multipartite quantum applications which are in general challenging to transform efficiently. While fusion operations for merging entangled states are well-developed, no direct…
Quantum networks with bipartite resources and shared randomness present the simplest infrastructure for implementing a future quantum internet. Here, we shall investigate which kinds of entanglement can or cannot be generated from this kind…
We address the question of quantifying entanglement in pure graph states. Evaluation of multipartite entanglement measures is extremely hard for most pure quantum states. In this paper we demonstrate how solving one problem in graph theory,…
Random circuit models often describe local dynamics using generic two-qubit gates, which have proven successful in capturing entanglement growth and operator spreading in many contexts. This approach naturally leads to the expectation that…
We consider graph states generated by operator of evolution with Ising Hamiltonian. The geometric measure of entanglement of a spin with other spins in the graph state is obtained analytically and quantified on IBM's quantum computer, IBM Q…
Graph states are special kinds of multipartite entangled states that correspond to mathematical graphs where the vertices take the role of quantum spin systems and the edges represent interactions. They not only provide an efficient model…
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…
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…
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 a family of quantum states defined by directed graphs, where the oriented edges represent interactions between ordered qubits. As a measure of entanglement, we adopt the Entanglement Distance - a quantity derived from the…
Graph states are well-entangled quantum states that are defined based on a graph. Of course, if two graphs are isomorphic their associated states are the same. Also, we know local operations do not change the entanglement of quantum states.…
Entanglement is a special feature of the quantum world that reflects the existence of subtle, often non-local, correlations between local degrees of freedom. In topological theories such non-local correlations can be given a very intuitive…
We use the geometry of the moment map to investigate properties of pure entangled states of composite quantum systems. The orbits of equally entangled states are mapped by the moment map on coadjoint orbits of local transformations (unitary…
The graph state formalism is a useful abstraction of entanglement. It is used in some multipartite purification schemes and it adequately represents universal resources for measurement-only quantum computation. We focus in this paper on the…
Local unitary invariants allow one to test whether multipartite states are equivalent up to local basis changes. Equivalently, they specify the geometry of the "orbit space" obtained by factoring out local unitary action from the state…
Graph structures are ubiquitous throughout the natural sciences. Here we consider graph-structured quantum data and describe how to carry out its quantum machine learning via quantum neural networks. In particular, we consider training data…
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…
Graph states (or cluster states) are the entanglement resource that enables one-way quantum computing. They can be grown by projective measurements on the component qubits. Such measurements typically carry a significant failure…
Entanglement is a crucial resource for quantum information processing, and so protocols to generate high fidelity entangled states on various hardware platforms are in demand. While spin chains have been extensively studied to generate…