Related papers: Generalized exceptional quantum walk search
We construct a new type of quantum walks on simplicial complexes as a natural extension of the well-known Szegedy walk on graphs. One can numerically observe that our proposing quantum walks possess linear spreading and localization as in…
The recursion equation analysis of Grover's quantum search algorithm presented by Biham et al. [PRA 60, 2742 (1999)] is generalized. It is applied to the large class of Grover's type algorithms in which the Hadamard transform is replaced by…
The running time of a quantum walk search algorithm depends on both the structure of the search space (graph) and the configuration of marked locations. While the first dependence have been studied in a number of papers, the second…
It is currently known from the work of Shoup and Nechaev that a generic algorithm to solve the discrete logarithm problem in a group of prime order must have complexity at least $k\sqrt{N}$ where $N$ is the order of the group. In many…
We present an efficient general method for realizing a quantum walk operator corresponding to an arbitrary sparse classical random walk. Our approach is based on Grover and Rudolph's method for preparing coherent versions of efficiently…
This paper presented two general quantum search algorithms. We derived the iterated formulas and the simpler approximate formulas and the precise formula for the amplitude in the desired state. A mathematical proof of Grover's algorithm…
The Grover walk is one of the most well-studied quantum walks on graphs. In this paper, we investigate its periodicity to reveal the relationship between the quantum walk and the underlying graph, focusing particularly on the…
Quantum walks, being the quantum analogue of classical random walks, are expected to provide a fruitful source of quantum algorithms. A few such algorithms have already been developed, including the `glued trees' algorithm, which provides…
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…
Some of the secret sharing schemes having unique quantum features like parallelism and entanglement are supposed to be relatively secure. Different schemes proposed by various researchers over the years have features which could be specific…
In our previous works, we have studied quantum random walk search algorithm on hypercube, with traversing coin constructed by using generalized Householder reflection and a phase multiplier. When the same phases are used each iteration, the…
The (standard) average mixing matrix of a continuous-time quantum walk is computed by taking the expected value of the mixing matrices of the walk under the uniform sampling distribution on the real line. In this paper we consider…
Grover's search algorithm is designed to be executed on a quantum mechanical computer. In this paper, the probabilistic wp-calculus is used to model and reason about Grover's algorithm. It is demonstrated that the calculus provides a…
The improved quantum scheduling algorithm proposed by Grover has been generalized using the generalized quantum search algorithm, in which a unitary operator replaces the Walsh-Hadamard transform, and $\pi/2$ phase rotations replace the…
The quantum walk is a powerful tool to develop quantum algorithms, which usually are based on searching for a vertex in a graph with multiple marked vertices, Ambainis's quantum algorithm for solving the element distinctness problem being…
Given two sets A and B and two oracles O(A) and O(B) that can identify the elements of these sets respectively, the goal is to find an element common to both sets using minimum number of oracle queries. Each application of either O(A) or…
Quantum walk has been successfully used to search for targets on graphs with vertices identified as the elements of a database. This spacial search on a two-dimensional periodic grid takes $\mathcal{O}\left(\sqrt{N\log N}\right)$ oracle…
We study spatial search with continuous-time quantum walks on real-world complex networks. We use smaller replicas of the Internet network obtained with a recent geometric renormalization method introduced by Garc\'ia-P\'erez et al., Nat.…
We clarify that coined quantum walk is determined by only the choice of local quantum coins. To do so, we characterize coined quantum walks on graph by disjoint Euler circles with respect to symmetric arcs. In this paper, we introduce a new…
High-dimensional quantum systems can offer extended possibilities and multiple advantages while developing advanced quantum technologies. In this paper, we propose a class of quantum-walk architecture networks that admit the efficient…