Related papers: QuOp: A Quantum Operator Representation for Nodes
Consider a graph having quantum systems lying at each node. Suppose that the whole thing evolves in discrete time steps, according to a global, unitary causal operator. By causal we mean that information can only propagate at a bounded…
Hilbert space representations of quantum SU(2) by multiplication operators on a local chart are constructed, where the local chart is given by tensor products of square integrable functions on a quantum disc and on the classical unit…
Quantum algorithms profit from the interference of quantum states in an exponentially large Hilbert space and the fact that unitary transformations on that Hilbert space can be broken down to universal gates that act only on one or two…
Recently, graph neural networks (GNNs) have become an important and active research direction in deep learning. It is worth noting that most of the existing GNN-based methods learn graph representations within the Euclidean vector space.…
Non-local operations play a crucial role in computer vision enabling the capture of long-range dependencies through weighted sums of features across the input, surpassing the constraints of traditional convolution operations that focus…
The classical development of neural networks has been primarily for mappings between a finite-dimensional Euclidean space and a set of classes, or between two finite-dimensional Euclidean spaces. The purpose of this work is to generalize…
In the graph node embedding problem, embedding spaces can vary significantly for different data types, leading to the need for different GNN model types. In this paper, we model the embedding update of a node feature as a Hamiltonian orbit…
Quantum algorithms for binary optimization problems have been the subject of extensive study. However, the application of quantum algorithms to integer optimization problems remains comparatively unexplored. In this paper, we study the…
Predicting and analyzing global behaviour of complex systems is challenging due to the intricate nature of their component interactions. Recent work has started modelling complex systems using networks endowed with multiway interactions…
The choice of mathematical representation when describing physical systems is of great consequence, and this choice is usually determined by the properties of the problem at hand. Here we examine the little-known wave operator…
Existing quantum routing implicitly mimics classical routing principles, with finding the ``best'' path (aka pathfinding), according to a selected routing metric, as a core mechanism for establishing end-to-end entanglement. However,…
Graph embedding has become an increasingly important technique for analyzing graph-structured data. By representing nodes in a graph as vectors in a low-dimensional space, graph embedding enables efficient graph processing and analysis…
Quantum Max Cut (QMC) problem for systems of qubits is an example of a 2-local Hamiltonian problem, and a prominent paradigm in computational complexity theory. This paper investigates the algebraic structure of a higher-dimensional analog…
This paper is an introduction to diagrammatic methods for representing quantum processes and quantum computing. We review basic notions for quantum information and quantum computing. We discuss topological diagrams and some issues about…
We introduce a simple initial working system in which relations (such as part-whole) are directly represented via an architecture with operating and learning rules fundamentally distinct from standard artificial neural network methods.…
Although tensor networks are powerful tools for simulating low-dimensional quantum physics, tensor network algorithms are very computationally costly in higher spatial dimensions. We introduce quantum gauge networks: a different kind of…
We introduce a unified framework -- Quantum Neural Ordinary and Partial Differential Equations (QNODEs and QNPDEs) -- which extends the continuous-time formalism of classical neural ordinary and partial differential equations into quantum…
We present a quantum algorithm that additively approximates the value of a tensor network to a certain scale. When combined with existing results, this provides a complete problem for quantum computation. The result is a simple new way of…
We present a quantum algorithm for sampling an edge on a path between two nodes s and t in an undirected graph given as an adjacency matrix, and show that this can be done in query complexity that is asymptotically the same, up to log…
Quantum computing (QC) is a new computational paradigm whose foundations relate to quantum physics. Notable progress has been made, driving the birth of a series of quantum-based algorithms that take advantage of quantum computational…