Related papers: Quantum walk algorithm for element distinctness
De novo DNA sequence assembly is based on finding paths in overlap graphs, which is a NP-hard problem. We developed a quantum algorithm for de novo assembly based on quantum walks in graphs. The overlap graph is partitioned repeatedly to…
The quantum search algorithm is a technique for searching N possibilities in only sqrt(N) steps. Although the algorithm itself is widely known, not so well known is the series of steps that first led to it, these are quite different from…
Quantum partial search algorithm is approximate search. It aims to find a target block (which has the target items). It runs a little faster than full Grover search. In this paper, we consider quantum partial search algorithm for multiple…
The so-called welded tree problem provides an example of a black-box problem that can be solved exponentially faster by a quantum walk than by any classical algorithm. Given the name of a special ENTRANCE vertex, a quantum walk can find…
The enormous successes have been made by quantum algorithms during the last decade. In this paper, we combine the quantum random walk (QRW) with the problem of data clustering, and develop two clustering algorithms based on the one…
In this survey, we describe two recent developments in quantum algorithms. The first new development is a quantum algorithm for evaluating a Boolean formula consisting of AND and OR gates of size N in time O(\sqrt{N}). This provides quantum…
The main results on quantum walk search are scattered over different, incomparable frameworks, most notably the hitting time framework, originally by Szegedy, the electric network framework by Belovs, and the MNRS framework by Magniez,…
Quantum walks on graphs are ubiquitous in quantum computing finding a myriad of applications. Likewise, random walks on graphs are a fundamental building block for a large number of algorithms with diverse applications. While the…
We study quantum algorithms for spatial search on finite dimensional grids. Patel et al. and Falk have proposed algorithms based on a quantum walk without a coin, with different operators applied at even and odd steps. Until now, such…
We describe a general method to obtain quantum speedups of classical algorithms which are based on the technique of backtracking, a standard approach for solving constraint satisfaction problems (CSPs). Backtracking algorithms explore a…
This paper proposes a highly efficient quantum algorithm for portfolio optimisation targeted at near-term noisy intermediate-scale quantum computers. Recent work by Hodson et al. (2019) explored potential application of hybrid…
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…
Quantum walks (QW) are of crucial importance in the development of quantum information processing algorithms. Recently, several quantum algorithms have been proposed to implement network analysis, in particular to rank the centrality of…
A quantum particle evolving by Schr\"odinger's equation contains, from the kinetic energy of the particle, a term in its Hamiltonian proportional to Laplace's operator. In discrete space, this is replaced by the discrete or graph Laplacian,…
Quantum walks are powerful tools not only to construct the quantum speedup algorithms but also to describe specific models in physical processes. Furthermore, the discrete time quantum walk has been experimentally realized in various…
One of the most basic computational problems is the task of finding a desired item in an ordered list of N items. While the best classical algorithm for this problem uses log_2 N queries to the list, a quantum computer can solve the problem…
Quantum walks, both discrete and continuous, serve as fundamental tools in quantum information processing with diverse applications. This work introduces a hybrid quantum walk model that integrates the coin mechanism of discrete walks with…
There exist two types of configurations of marked vertices on a two-dimensional grid, known as the {\it exceptional configurations}, which are hard to find by the discrete-time quantum walk algorithms. In this article, we provide a…
Searching for collisions in random functions is a fundamental computational problem, with many applications in symmetric and asymmetric cryptanalysis. When one searches for a single collision, the known quantum algorithms match the query…
Diverse facets Of the Theory of Quantum Walks on Graph are reviewed Till now .In specific, Quantum network routing, Quantum Walk Search Algorithm, Element distinctness associated to the eigenvalues of Graphs and the use of these relation…