Related papers: Utilizing Graph Sparsification for Pre-processing …
The Max-Cut problem is a fundamental NP-hard problem, which is attracting attention in the field of quantum computation these days. Regarding the approximation algorithm of the Max-Cut problem, algorithms based on semidefinite programming…
Analyzing massive data sets has been one of the key motivations for studying streaming algorithms. In recent years, there has been significant progress in analysing distributions in a streaming setting, but the progress on graph problems…
We propose a scalable framework for solving the Maximum Cut (MaxCut) problem in large graphs using projected gradient ascent on quadratic objectives. Our approach is differentiable and leverages GPUs for gradient-based optimization. It is…
We introduce parity quantum optimization with the aim of solving optimization problems consisting of arbitrary $k$-body interactions and side conditions using planar quantum chip architectures. The method introduces a decomposition of the…
Graph sparsification is a technique that approximates a given graph by a sparse graph with a subset of vertices and/or edges. The goal of an effective sparsification algorithm is to maintain specific graph properties relevant to the…
This article empirically examines the computational cost of solving a known hard problem, graph clustering, using novel purpose-built computer hardware. We express the graph clustering problem as an intra-cluster distance or dissimilarity…
Due to the expected disparity in quantum vs. classical clock speeds, quantum advantage for branch and bound algorithms is more likely achievable in settings involving large search trees and low operator evaluation costs. Therefore, in this…
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…
The LogQ algorithm encodes Quadratic Unconstrained Binary Optimization (QUBO) problems with exponentially fewer qubits than the Quantum Approximate Optimization Algorithm (QAOA). The advantages of conventional LogQ are accompanied by a…
This paper explores the application of Quadratic Unconstrained Binary Optimization (QUBO) models in solving the Travelling Salesman Problem (TSP) through Quantum Annealing algorithms and Graph Neural Networks. Quantum Annealing (QA), a…
Quantum Approximate Optimization Algorithms (QAOA) have demonstrated a strong potential in addressing graph-based optimization problems. However, the execution of large-scale quantum circuits remains constrained by the limitations of…
Graph sparsification is a well-established technique for accelerating graph-based learning algorithms, which uses edge sampling to approximate dense graphs with sparse ones. Because the sparsification error is random and unknown, users must…
Graph rewriting is a popular tool for the optimisation and modification of graph expressions in domains such as compilers, machine learning and quantum computing. The underlying data structures are often port graphs - graphs with labels at…
Combinatorial optimization (CO) problems are challenging as the computation time grows exponentially with the input. Graph Neural Networks (GNNs) show promise for researchers in solving CO problems. This study investigates the effectiveness…
In this paper, we consider the problem of designing cut sparsifiers and sketches for directed graphs. To bypass known lower bounds, we allow the sparsifier/sketch to depend on the balance of the input graph, which smoothly interpolates…
Quantum image processing is a growing field attracting attention from both the quantum computing and image processing communities. We propose a novel method in combining a graph-theoretic approach for optimal surface segmentation and hybrid…
The current noisy intermediate-scale quantum (NISQ) era is characterized by substantial errors and noise, which limit the practical feasibility of deep, many-qubit circuits. To address these constraints, quantum circuit cutting has emerged…
This paper addresses the challenge of scaling quantum computing by employing distributed quantum algorithms across multiple processors. We propose a novel circuit partitioning method that leverages graph partitioning to optimize both qubit…
The (non-uniform) sparsest cut problem is the following graph-partitioning problem: given a "supply" graph, and demands on pairs of vertices, delete some subset of supply edges to minimize the ratio of the supply edges cut to the total…
The MaxCut problem is a fundamental problem in Combinatorial Optimization, with significant implications across diverse domains such as logistics, network design, and statistical physics. The algorithm represents innovative approaches that…