Related papers: Applications of the quantum algorithm for st-conne…
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.…
An algorithm for quantum computing Hamiltonian cycles of simple, cubic, bipartite graphs is discussed. It is shown that it is possible to evolve a quantum computer into an entanglement of states which map onto the set of all possible paths…
Given an undirected, unweighted graph with $n$ vertices and $m$ edges, the maximum cut problem is to find a partition of the $n$ vertices into disjoint subsets $V_1$ and $V_2$ such that the number of edges between them is as large as…
Let $G$ be an $n$-vertex graph with $m$ edges. When asked a subset $S$ of vertices, a cut query on $G$ returns the number of edges of $G$ that have exactly one endpoint in $S$. We show that there is a bounded-error quantum algorithm that…
Group convolutions and cross-correlations, which are equivariant to the actions of group elements, are commonly used in mathematics to analyze or take advantage of symmetries inherent in a given problem setting. Here, we provide efficient…
We introduce a novel quantum algorithm for determining graph connectedness using a constant number of measurements. The algorithm can be extended to find connected components with a linear number of measurements. It relies on non-unitary…
We analyze the problem of discovering long cycles inside a graph. We propose and test two algorithms for this task. The first one is based on recent advances in statistical mechanics and relies on a message passing procedure. The second…
Entanglement is a key resource in quantum communication, but bipartite schemes are often insufficient for advanced protocols like quantum secret sharing or distributed computing. Graph states offer a flexible way to represent and manage…
Given $x, y$ on an unweighted undirected graph $G$, the goal of the pathfinding problem is to find an $x$-$y$ path. In this work, we first construct a graph $G$ based on welded trees and define a pathfinding problem in the adjacency list…
We present linear time {\it in-place} algorithms for several basic and fundamental graph problems including the well-known graph search methods (like depth-first search, breadth-first search, maximum cardinality search), connectivity…
Identifying a biclique with the maximum number of edges bears considerable implications for numerous fields of application, such as detecting anomalies in E-commerce transactions, discerning protein-protein interactions in biology, and…
Entanglement plays a crucial role in quantum physics and is the key resource in quantum information processing. However, entanglement detection and quantification are believed to be hard due to the operational impracticality of existing…
Quantum algorithms for graph problems are considered, both in the adjacency matrix model and in an adjacency list-like array model. We give almost tight lower and upper bounds for the bounded error quantum query complexity of Connectivity,…
The Quantum Approximate Optimization Algorithm can naturally be applied to combinatorial search problems on graphs. The quantum circuit has p applications of a unitary operator that respects the locality of the graph. On a graph with…
We introduce a mapping between graphs and pure quantum bipartite states and show that the associated entanglement entropy conveys non-trivial information about the structure of the graph. Our primary goal is to investigate the family of…
Early but promising results in quantum computing have been enabled by the concurrent development of quantum algorithms, devices, and materials. Classical simulation of quantum programs has enabled the design and analysis of algorithms and…
We consider problems to make a given bidirected graph strongly connected with minimum cardinality of additional signs or additional arcs. For the former problem, we show the minimum number of additional signs and give a linear-time…
Recently, it is shown that quantum computers can be used for obtaining certain information about the solution of a linear system Ax=b exponentially faster than what is possible with classical computation. Here we first review some key…
We study quantum algorithms for testing bipartiteness and expansion of bounded-degree graphs. We give quantum algorithms that solve these problems in time O(N^(1/3)), beating the Omega(sqrt(N)) classical lower bound. For testing expansion,…
In this work, we unify several quantum algorithmic frameworks for boolean functions that are based on the quantum adversary bound. First, we show that the $st$-connectivity framework subsumes the (adaptive/extended) learning graph…