Related papers: Properties of multi-qubit variational quantum stat…
Recent progress in quantum computing and quantum simulation of many-body systems with arrays of neutral atoms using Rydberg excitation has provided unforeseen opportunities towards computational advantage in solving various optimization…
Algebro-geometric methods have proven to be very successful in the study of graphical models in statistics. In this paper we introduce the foundations to carry out a similar study of their quantum counterparts. These quantum graphical…
Consider the setting of \emph{randomly weighted graphs}, namely, graphs whose edge weights are chosen independently according to probability distributions with finite support over the non-negative reals. Under this setting, properties of…
The degree to which a pure quantum state is entangled can be characterized by the distance or angle to the nearest unentangled state. This geometric measure of entanglement, already present in a number of settings [A. Shimony, Ann. NY.…
Quantum graphity is a background independent model for emergent geometry, in which space is represented as a complete graph. The high-energy pre-geometric starting point of the model is usually considered to be the complete graph, however…
Transformers are increasingly employed for graph data, demonstrating competitive performance in diverse tasks. To incorporate graph information into these models, it is essential to enhance node and edge features with positional encodings.…
We study the entanglement between a certain qubit and the remaining system in rank- 2 mixed states prepared on the quantum computer. The protocol, which we propose for this purpose, is based on the relation of geometric measure of…
This work exploits a framework whereby a graph (in the mathematical sense) serves to connect a classical system to a state space that we call `quantum-like' (QL). The QL states comprise arbitrary superpositions of states in a tensor product…
We introduce the concept of quantum weight as a ground state property of quantum many-body systems that is encoded in the static structure factor and characterizes density fluctuation at long wavelengths. The quantum weight carries a wealth…
We show that quantum entanglement states are associated with multilinear polynomials that cannot be factored. By using these multilinear polynomials, we propose a geometric representation for entanglement states. In particular, we show that…
The manifold of pure quantum states is a complex projective space endowed with the unitary-invariant geometry of Fubini and Study. According to the principles of geometric quantum mechanics, the detailed physical characteristics of a given…
We investigate spectral properties of quantum graphs in the form of a periodic chain of rings with a connecting link between each adjacent pair, assuming that wave functions at the vertices are matched through conditions manifestly…
In this work, we propose novel families of positional encodings tailored to graph neural networks obtained with quantum computers. These encodings leverage the long-range correlations inherent in quantum systems that arise from mapping the…
A voltage graph is a finite directed graph whose edges are labeled by elements of a finite group $G$. A classical construction of Gross and Tucker associates to every voltage graph with vertex set $V$ a so-called derived graph with vertex…
A scheme is presented for realizing a quantum phase gate with three-level atoms, solid-state qubits--often called artificial atoms, or ions that share a quantum data bus such as a single mode field in cavity QED system or a collective…
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 three compact graph states that can be used to perform a measurement-based Toffoli gate. Given a weighted graph of six, seven or eight qubits, we show that success probabilities of 1/4, 1/2 and 1 respectively can be achieved.…
We examine transmission through a quantum graph vertex to which auxiliary edges with constant potentials are attached. We find a characterization of vertex couplings for which the transmission probability from a given "input" line to a…
Graph states are a key resource for a number of applications in quantum information theory. Due to the inherent noise in noisy intermediate-scale quantum (NISQ) era devices, it is important to understand the effects noise has on the…
In this work, we present a comprehensive exploration of the entanglement and graph connectivity properties of graph states. We quantify the entanglement in pseudo graph states using the entanglement distance, a recently introduced measure…