Related papers: Graphical description of local Gaussian operations…

Graph signals are signals with an irregular structure that can be described by a graph. Graph neural networks (GNNs) are information processing architectures tailored to these graph signals and made of stacked layers that compose graph…

Quantum state discrimination plays a central role in defining the possible and impossible operations through a restricted class of quantum operations. A seminal result by Bennett et al. [Phys. Rev. A 59, 1070 (1999)] demonstrates the…

The Hammersley-Clifford theorem states that if the support of a Markov random field has a safe symbol then it is a Gibbs state with some nearest neighbour interaction. In this paper we generalise the theorem with an added condition that the…

We propose a new classification for the entanglement in graph states based on generalized con- currence. The numerical results indicate that the eight different three-qubit graph states in three categories, 64 four-qubit graph states in…

Local sets, a graph structure invariant under local complementation, have been originally introduced in the context of quantum computing for the study of quantum entanglement within the so-called graph state formalism. A local set in a…

The rapid growth of graph data creates significant scalability challenges as most graph algorithms scale quadratically with size. To mitigate these issues, Graph Condensation (GC) methods have been proposed to learn a small graph from a…

In this article, we discuss the local rigidity of Clifford-Klein forms of homogeneous spaces of 1-connected completely solvable Lie groups. In fact, we introduce a splitting of the local rigidity: vertical rigidity and horizontal rigidity.…

Graph-theoretic structures play a central role in the description and analysis of quantum systems. In this work, we introduce a new class of quantum states, called $A_\alpha$-graph states, which are constructed from either unweighted or…

We propose a general method for preparing stabilizer states with reduced two-qubit gate count and depth compared to the state of the art. The method starts from a graph state representation of the stabilizer state and iteratively reduces…

We introduce a new family of models for measurement-based quantum computation which are deterministic and approximately universal. The resource states which play the role of graph states are prepared via 2-qubit gates of the form…

With the increased complexity of power systems due to the integration of smart grid technologies and renewable energy resources, more frequent changes have been introduced to system status, and the traditional serial mode of state…

We explore absolutely maximal entanglement (AME) and k-uniformity in continuous-variable (CV) quantum systems, and show that-unlike in qudit systems-such entanglement is readily realizable in both Gaussian and non-Gaussian quantum states of…

We tackle the problem of Clifford isometry compilation, i.e, how to synthesize a Clifford isometry into an executable quantum circuit. We propose a simple framework for synthesis that only exploits the elementary properties of the Clifford…

This work establishes rigorous, novel and widely applicable stability guarantees and transferability bounds for graph convolutional networks -- without reference to any underlying limit object or statistical distribution. Crucially,…

We study invariance of KMS states on graph C*-algebras coming from strongly connected and circulant graphs under the classical and quantum symmetry of the graphs. We show that the unique KMS state for strongly connected graphs is invariant…

A Locally Checkable Labeling (LCL) is a specification describing a set of labels that are valid with respect to a set of conditions that characterize a local part of a solution to a global problem. Conditions can only refer to nodes and…

We study a log-gas on a network (a finite, simple graph) confined in a bounded subset of a local field (i.e. R, C, Q_{p} the field of p-adic numbers). In this gas, a log-Coulomb interaction between two charged particles occurs only when the…

We have generalised the concept of graph states to what we have called mixed graph states, which we define in terms of mixed graphs, that is graphs with both directed and undirected edges, as the density matrix stabilized by the associated…

A recent development in graph-minor theory is to study local separators, vertex-sets that separate graphs locally but not necessarily globally. The local separators of a graph roughly correspond to the genuine separators of its local…

Continual graph learning (CGL) aims to learn from dynamically evolving graphs while mitigating catastrophic forgetting. Existing CGL approaches typically adopt a task-based formulation, where the data stream is partitioned into a sequence…