Related papers: QuOp: A Quantum Operator Representation for Nodes
Graph matching involves combinatorial optimization based on edge-to-edge affinity matrix, which can be generally formulated as Lawler's Quadratic Assignment Problem (QAP). This paper presents a QAP network directly learning with the…
Comparative analyses of graph structured datasets underly diverse problems. Examples of these problems include identification of conserved functional components (biochemical interactions) across species, structural similarity of large…
Large scale numerical experiments are commonplace today in theoretical physics. The high performance algorithms described herein are the most compact, efficient methods known for representing and analyzing systems modeled well by sets or…
MaxCut is a key NP-Hard combinatorial optimization graph problem with extensive theoretical and industrial applications, including the Ising model and chip design. While quantum computing offers new solutions for such combinatorial…
Quantum computation, in particular Grover's algorithm, has aroused a great deal of interest since it allows for a quadratic speedup to be obtained in search procedures. Classical search procedures for an $N$ element database require at most…
We construct a sheaf-theoretic representation of quantum observables algebras over a base category equipped with a Grothendieck topology, consisting of epimorphic families of commutative observables algebras, playing the role of local…
Unsupervised graph alignment aims to find the node correspondence across different graphs without any anchor node pairs. Despite the recent efforts utilizing deep learning-based techniques, such as the embedding and optimal transport…
Graph embedding has become a powerful tool for learning latent representations of nodes in a graph. Despite its superior performance in various graph-based machine learning tasks, serious privacy concerns arise when the graph data contains…
A range of quantum algorithms, especially those leveraging variational parameterization and circuit-based optimization, are being studied as alternatives for solving classically intractable combinatorial optimization problems (COPs).…
It is known that every (single-qudit) Clifford operator maps the full set of generalized Pauli matrices (GPMs) to itself under unitary conjugation, which is an important quantum operation and plays a crucial role in quantum computation and…
Quantum circuits are considered more powerful than classical circuits and require exponential resources to simulate classically. Clifford circuits are a special class of quantum circuits that can be simulated in polynomial time but still…
Quantum counting is a key quantum algorithm that aims to determine the number of marked elements in a database. This algorithm is based on the quantum phase estimation algorithm and uses the evolution operator of Grover's algorithm because…
Representations of the quantum q-oscillator algebra are studied with particular attention to local Hamiltonian representations of the Schroedinger type. In contrast to the standard harmonic oscillators such systems exhibit a continuous…
Graph neural networks (GNNs) are deep learning models designed specifically for graph data, and they typically rely on node features as the input to the first layer. When applying such a type of network on the graph without node features,…
In this thesis, we investigate whether quantum algorithms can be used in the field of machine learning for both long and near term quantum computers. We will first recall the fundamentals of machine learning and quantum computing and then…
While Graph Neural Networks (GNNs) have proven highly effective at modeling relational data, pairwise connections cannot fully capture multi-way relationships naturally present in complex real-world systems. In response to this, Topological…
We present a quantum algorithm for the simulation of molecular systems that is asymptotically more efficient than all previous algorithms in the literature in terms of the main problem parameters. As in previous work [Babbush et al., New…
The aim of this paper is to introduce a new graphic representation of quantum states by means of a specific application: the analysis of two models of quantum copying machines. The graphic representation by diagrams of states offers a clear…
It is known that any quantum algorithm for Graph Isomorphism that works within the framework of the hidden subgroup problem (HSP) must perform highly entangled measurements across Omega(n log n) coset states. One of the only known models…
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…