相关论文: Minor-embedding in adiabatic quantum computation: …
Semigroup theory is a branch of abstract algebra, and it provides mathematical tools for the theory of computation. Finite semigroups can describe state transition systems and thus they model physically realizable computers. Engineering…
Graph embeddings have become a key and widely used technique within the field of graph mining, proving to be successful across a broad range of domains including social, citation, transportation and biological. Graph embedding techniques…
UMAP is a non-parametric graph-based dimensionality reduction algorithm using applied Riemannian geometry and algebraic topology to find low-dimensional embeddings of structured data. The UMAP algorithm consists of two steps: (1) Compute a…
In the parallel processing field, graph embedding is motivated by simulation interconnection networks to another. The quadtree is an important technique used to present spatial data and is used in many application domains, especially…
The quantum adiabatic algorithm is a Hamiltonian based quantum algorithm designed to find the minimum of a classical cost function whose domain has size N. We show that poor choices for the Hamiltonian can guarantee that the algorithm will…
Quantum annealing promises to be an effective heuristic for complex NP-hard problems. However, clear demonstrations of quantum advantage are wanting, primarily constrained by the difficulty of embedding the problem into the quantum…
Graph is an important data representation which appears in a wide diversity of real-world scenarios. Effective graph analytics provides users a deeper understanding of what is behind the data, and thus can benefit a lot of useful…
We explore the relationship between two figures of merit for an adiabatic quantum computation process: the success probability $P$ and the minimum gap $\Delta_{min}$ between the ground and first excited states, investigating to what extent…
Graph Neural Networks (GNNs) are widely used for learning on graph-structured data, but scaling GNN training to massive graphs remains challenging. To enable scalable distributed training, graphs are divided into smaller partitions that are…
Say that an edge of a graph G dominates itself and every other edge adjacent to it. An edge dominating set of a graph G = (V,E) is a subset of edges E' of E which dominates all edges of G. In particular, if every edge of G is dominated by…
We consider optimal distributed computation of a given function of distributed data. The input (data) nodes and the sink node that receives the function form a connected network that is described by an undirected weighted network graph. The…
In this paper we give a lower bound for the least distortion embedding of a distance regular graph into Euclidean space. We use the lower bound for finding the least distortion for Hamming graphs, Johnson graphs, and all strongly regular…
Quantum annealing is a generic solver for optimization problems that uses fictitious quantum fluctuation. The most groundbreaking progress in the research field of quantum annealing is its hardware implementation, i.e., the so-called…
Given a connected undirected weighted graph, we are concerned with problems related to partitioning the graph. First of all we look for the closest disconnected graph (the minimum cut problem), here with respect to the Euclidean norm. We…
We present a comprehensive review of past research into adiabatic quantum computation and then propose a scalable architecture for an adiabatic quantum computer that can treat NP-hard problems without requiring local coherent operations.…
We study the complexity of the following related computational tasks concerning a fixed countable graph G: 1. Does a countable graph H provided as input have a(n induced) subgraph isomorphic to G? 2. Given a countable graph H that has a(n…
Quantum annealing (QA) has great potential to solve combinatorial optimization problems efficiently. However, the effectiveness of QA algorithms is heavily based on the embedding of problem instances, represented as logical graphs, into the…
Graph is an important data representation ubiquitously existing in the real world. However, analyzing the graph data is computationally difficult due to its non-Euclidean nature. Graph embedding is a powerful tool to solve the graph…
Achieving densely connected hardware graphs is a challenge for most quantum computing platforms today, and a particularly crucial one for the case of quantum annealing applications. In this context, we present a scalable architecture for…
Compiling a high-level quantum circuit down to a low-level description that can be executed on state-of-the-art quantum computers is a crucial part of the software stack for quantum computing. One step in compiling a quantum circuit to some…