Related papers: Quantum Algorithms for Connectivity and Related Pr…
We study the design of robust subexponential algorithms for classical connectivity problems on intersection graphs of similarly sized fat objects in $\mathbb{R}^d$. In this setting, each vertex corresponds to a geometric object, and two…
Quantum neural networks (QNNs), an interdisciplinary field of quantum computing and machine learning, have attracted tremendous research interests due to the specific quantum advantages. Despite lots of efforts developed in computer vision…
The cut-set $\partial(S)$ of a graph $G=(V,E)$ is the set of edges that have one endpoint in $S\subset V$ and the other endpoint in $V\setminus S$, and whenever $G[S]$ is connected, the cut $[S,V\setminus S]$ of $G$ is called a connected…
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…
We study two variants of \textsc{Maximum Cut}, which we call \textsc{Connected Maximum Cut} and \textsc{Maximum Minimal Cut}, in this paper. In these problems, given an unweighted graph, the goal is to compute a maximum cut satisfying some…
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…
Quantum graphs have attracted attention from mathematicians for some time. A quantum graph is defined by having a Laplacian on each edge of a metric graph and imposing boundary conditions at the vertices to get an eigenvalue problem. A…
Existing and near-term quantum computers can only perform two-qubit gates between physically connected qubits. Research has been done on compilers to rewrite quantum programs to match hardware constraints. However, the quantum processor…
We present a general method for the implementation of quantum algorithms that optimizes both gate count and circuit depth. Our approach introduces connectivity-adapted CNOT-based building blocks called Parity Twine chains. It outperforms…
The graph matching optimization problem is an essential component for many tasks in computer vision, such as bringing two deformable objects in correspondence. Naturally, a wide range of applicable algorithms have been proposed in the last…
Quantum algorithms for several problems in graph theory are considered. Classical algorithms for finding the lowest weight path between two points in a graph and for finding a minimal weight spanning tree involve searching over some space.…
We study two problems related to recovering causal graphs from interventional data: (i) $\textit{verification}$, where the task is to check if a purported causal graph is correct, and (ii) $\textit{search}$, where the task is to recover the…
In this paper, we give quantum algorithms for two fundamental computation problems: solving polynomial systems over finite fields and optimization where the arguments of the objective function and constraints take values from a finite field…
Mining subgraphs with interesting structural properties from networks (or graphs) is a computationally challenging task. In this paper, we propose two algorithms for enumerating all connected induced subgraphs of a given cardinality from…
For the vast majority of local graph problems standard dynamic programming techniques give c^tw V^O(1) algorithms, where tw is the treewidth of the input graph. On the other hand, for problems with a global requirement (usually…
Quantum algorithms can deliver asymptotic speedups over their classical counterparts. However, there are few cases where a substantial quantum speedup has been worked out in detail for reasonably-sized problems, when compared with the best…
To demonstrate supremacy of quantum computing, increasingly large-scale superconducting quantum computing chips are being designed and fabricated. However, the complexity of simulating quantum systems poses a significant challenge to…
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…
In this study, we investigate the problem of classifying, characterizing, and designing efficient algorithms for hard inference problems on planar graphs, in the limit of infinite size. The problem is considered hard if, for a deterministic…
We investigate the Maximum Cut (MaxCut) problem on different graph classes with the Quantum Approximate Optimization Algorithm (QAOA) using symmetries. In particular, heuristics on the relationship between graph symmetries and the…