相关论文: Quantum Algorithm for Identifying Hidden Graphs: S…

Numerous conceptually important quantum algorithms rely on a black-box device known as an oracle, which is typically difficult to construct without knowing the answer to the problem that the algorithm is intended to solve. A notable example…

We present three new quantum algorithms in the quantum query model for \textsc{graph-collision} problem: \begin{itemize} \item an algorithm based on tree decomposition that uses $O\left(\sqrt{n}t^{\sfrac{1}{6}}\right)$ queries where $t$ is…

We show that any two Hadamard graphs on the same number of vertices are quantum isomorphic. This follows from a more general recipe for showing quantum isomorphism of graphs arising from certain association schemes. The main result is built…

We consider a random sparse graph with bounded average degree, in which a subset of vertices has higher connectivity than the background. In particular, the average degree inside this subset of vertices is larger than outside (but still…

On neutral atom platforms, preparing specific quantum states is usually achieved by pulse shaping, i.e., by optimizing the time-dependence of the Hamiltonian related to the system. This process can be extremely costly, as it requires…

The spectrum of a network or graph $G=(V,E)$ with adjacency matrix $A$, consists of the eigenvalues of the normalized Laplacian $L= I - D^{-1/2} A D^{-1/2}$. This set of eigenvalues encapsulates many aspects of the structure of the graph,…

Graph clustering is an important technique to understand the relationships between the vertices in a big graph. In this paper, we propose a novel random-walk-based graph clustering method. The proposed method restricts the reach of the…

We consider the minimal k-grouping problem: given a graph G=(V,E) and a constant k, partition G into subgraphs of diameter no greater than k, such that the union of any two subgraphs has diameter greater than k. We give a silent…

We consider the problem of finding a marked vertex in a graph from an arbitrary starting distribution, using a quantum walk based algorithm. We work in the framework introduced by Belovs which showed how to detect the existence of a marked…

In the thesis, we use a recently developed tight characterisation of quantum query complexity, the adversary bound, to develop new quantum algorithms and lower bounds. Our results are as follows: * We develop a new technique for the…

The analysis of the computational power of single-query quantum algorithms is important because they must extract maximal information from one oracle call, revealing fundamental limits of quantum advantage and enabling optimal,…

We study the forrelation problem: given a pair of $n$-bit Boolean functions $f$ and $g$, estimate the correlation between $f$ and the Fourier transform of $g$. This problem is known to provide the largest possible quantum speedup in terms…

Let G be an input graph with n vertices and m edges and let k be a fixed parameter. We provide a single exponential FPT algorithm with running time O(c^kn(n+m)), c= min {18,k} that turns graph G into an interval graph by deleting at most k…

Node embedding is a key technique for representing graph nodes as vectors while preserving structural and relational properties, which enables machine learning tasks like feature extraction, clustering, and classification. While classical…

Quantum walks provide a powerful framework for achieving algorithmic speedup in quantum computing. This paper presents a quantum search algorithm for 2-tessellable graphs, a generalization of bipartite graphs, achieving a quadratic speedup…

We analyse the eigenvalue and eigenvector structure of the flip-flop quantum walk on regular graphs, explicitly demonstrating how it is quadratically faster than the classical random walk. Then we use it in a controlled spatial search…

Graph labelling is one of the noticed contexts in combinatorics and graph theory. Graceful labelling for a graph $G$ with $e$ edges, is to label the vertices of $G$ with $0, 1, \cdots, e$ such that, if we specify to each edge the difference…

Quantum Information Theory promises to speed up computation so is observed in real quantum computers as proved to its classical counterpart. This revolutionizes every field linked directly or indirectly with computation. Grover algorithm in…

Quantum walk is a useful model to simulate complex quantum systems and to build quantum algorithms; in particular, to develop spatial search algorithms on graphs, which aim to find a marked vertex as quickly as possible. Quantum walks are…

We study the query complexity of determining if a graph is connected with global queries. The first model we look at is matrix-vector multiplication queries to the adjacency matrix. Here, for an $n$-vertex graph with adjacency matrix $A$,…