Related papers: Quantum Algorithm for Identifying Hidden Graphs: S…

This paper presents a novel methodology that transforms discrete-time quantum walks into a graph embedding technique, offering a fresh perspective on graph representation methods.Through mathematical manipulations, the approach of this…

In this work, we propose a novel quantum algorithm for edge detection in digital grayscale images, based on the sequency-ordered Walsh-Hadamard transform. The proposed method significantly improves upon existing quantum techniques for edge…

Recently, Ambainis gave an O(N^(2/3))-query quantum walk algorithm for element distinctness, and more generally, an O(N^(L/(L+1)))-query algorithm for finding L equal numbers. We point out that this algorithm actually solves a much more…

Continuous-time quantum walks provide a natural framework to tackle the fundamental problem of finding a node among a set of marked nodes in a graph, known as spatial search. Whether spatial search by continuous-time quantum walk provides a…

We study a variant of the subgraph isomorphism problem that is of high interest to the quantum computing community. Our results give an algorithm to perform pattern matching in quantum circuits for many patterns simultaneously,…

In this paper we present a quantum algorithm solving the triangle finding problem in unweighted graphs with query complexity $\tilde O(n^{5/4})$, where $n$ denotes the number of vertices in the graph. This improves the previous upper bound…

We design quantum algorithms for maximum matching. Working in the query model, in both adjacency matrix and adjacency list settings, we improve on the best known algorithms for general graphs, matching previously obtained results for…

Solitude verification is arguably one of the simplest fundamental problems in distributed computing, where the goal is to verify that there is a unique contender in a network. This paper devises a quantum algorithm that exactly solves the…

This paper shows that, if we could examine the entire history of a hidden variable, then we could efficiently solve problems that are believed to be intractable even for quantum computers. In particular, under any hidden-variable theory…

The problems of computing eccentricity, radius, and diameter are fundamental to graph theory. These parameters are intrinsically defined based on the distance metric of the graph. In this work, we propose quantum algorithms for the diameter…

We define a discrete-time, coined quantum walk on weighted graphs that is inspired by Szegedy's quantum walk. Using this, we prove that many lackadaisical quantum walks, where each vertex has $l$ integer self-loops, can be generalized to a…

This paper presents a quantum algorithm for triangle finding over sparse graphs that improves over the previous best quantum algorithm for this task by Buhrman et al. [SIAM Journal on Computing, 2005]. Our algorithm is based on the recent…

Given the extensive application of classical random walks to classical algorithms in a variety of fields, their quantum analogue in quantum walks is expected to provide a fruitful source of quantum algorithms. So far, however, such…

We present Quantum Graph Hash (QGH-256), a novel quantum spectral hashing algorithm that generates high-entropy fingerprints from message-induced graphs. Each input message is mapped to a weighted graph via a discrete random walk on an n X…

This paper introduces a completely new approach to encryption based on group theoretic quantum framework. Quantum cryptography has essentially focused only on key distribution and proceeded with classical encryption algorithm with the…

This article presents a novel and succinct algorithmic framework via alternating quantum walks, unifying quantum spatial search, state transfer and uniform sampling on a large class of graphs. Using the framework, we can achieve exact…

Quantum random walks on graphs have been shown to display many interesting properties, including exponentially fast hitting times when compared with their classical counterparts. However, it is still unclear how to use these novel…

We present a quantum algorithm for the dihedral hidden subgroup problem with time and query complexity $O(\exp(C\sqrt{\log N}))$. In this problem an oracle computes a function $f$ on the dihedral group $D_N$ which is invariant under a…

We study space and time efficient quantum algorithms for two graph problems -- deciding whether an $n$-vertex graph is a forest, and whether it is bipartite. Via a reduction to the s-t connectivity problem, we describe quantum algorithms…

The ultimate objective of this paper is to create a stepping stone to the development of new quantum algorithms. The strategy chosen is to begin by focusing on the class of abelian quantum hidden subgroup algorithms, i.e., the class of…