Related papers: QuOp: A Quantum Operator Representation for Nodes
The Quantum Approximate Optimization Algorithm can naturally be applied to combinatorial search problems on graphs. The quantum circuit has p applications of a unitary operator that respects the locality of the graph. On a graph with…
Node embedding is a key technique for representing graph nodes as vectors while preserving structural and relational properties, which enables machine learning tasks like feature extraction, clustering, and classification. While classical…
Graph embedding is a recurrent problem in quantum computing, for instance, quantum annealers need to solve a minor graph embedding in order to map a given Quadratic Unconstrained Binary Optimization (QUBO) problem onto their internal…
This paper presents a novel methodology that transforms discrete-time quantum walks into a graph embedding technique, offering a fresh perspective on graph representation methods.Through mathematical manipulations, the approach of this…
The rapid development of reliable Quantum Processing Units (QPU) opens up novel computational opportunities for machine learning. Here, we introduce a procedure for measuring the similarity between graph-structured data, based on the…
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…
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 undertake a study of the notion of a quantum graph over arbitrary finite-dimensional $C^*$-algebras $B$ equipped with arbitrary faithful states. Quantum graphs are realised principally as either certain operators on $L^2(B)$, the quantum…
We develop a unified quantum framework for subgraph counting in graphs. We encode a graph on $N$ vertices into a quantum state on $2\lceil \log_2 N \rceil$ working qubits and $2$ ancilla qubits using its adjacency list, with worst-case gate…
Quantum walks provide a natural framework to approach graph problems with quantum computers, exhibiting speedups over their classical counterparts for tasks such as the search for marked nodes or the prediction of missing links.…
Quadratic unconstrained binary optimization (QUBO) tasks are very important in chemistry, finance, job scheduling, and so on, which can be represented using graph structures, with the variables as nodes and the interaction between them as…
At present, there are a large number of quantum neural network models to deal with Euclidean spatial data, while little research have been conducted on non-Euclidean spatial data. In this paper, we propose a novel quantum graph…
In this paper, we propose a new way to represent graphs in quantum space. In that approach, we replace the rows of the adjacency matrix of the graph by state vectors in the occupation number representation. Unlike the traditional definition…
A finite dimensional operator that commutes with some symmetry group admits quotient operators, which are determined by the choice of associated representation. Taking the quotient isolates the part of the spectrum supporting the chosen…
We review quantum chaos on graphs. We construct a unitary operator which represents the quantum evolution on the graph and study its spectral and wavefunction statistics. This operator is the analogue of the classical evolution operator on…
Quantum annealing (QA) has emerged as a powerful technique to solve optimization problems by taking advantages of quantum physics. In QA process, a bottleneck that may prevent QA to scale up is minor embedding step in which we embed…
Node embeddings act as the information interface for graph neural networks, yet their empirical impact is often reported under mismatched backbones, splits, and training budgets. This paper provides a controlled benchmark of embedding…
Quantum computation offers potential exponential speedups for simulating certain physical systems, but its application to nonlinear dynamics is inherently constrained by the requirement of unitary evolution. We propose the quantum Koopman…
With the development of quantum algorithms, high-cost computations are being scrutinized in the hope of a quantum advantage. While graphs offer a convenient framework for multiple real-world problems, their analytics still comes with high…
We propose a novel quantum neural network architecture for unsupervised learning of classical and quantum data based on the kernelized version of Kohonen's self-organizing map. The central idea behind our algorithm is to replace the…