Related papers: Quantum walk-based search algorithms with multiple…
Quantum walks underlie an important class of quantum computing algorithms, and represent promising approaches in various simulations and practical applications. Here we design stroboscopically monitored quantum walks and their subsequent…
We present analytical treatment of quantum walks on a cycle graph. The investigation is based on a realistic physical model of the graph in which decoherence is induced by continuous monitoring of each graph vertex with nearby quantum point…
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,…
Recently, the quaternionic quantum walk was formulated by the first author as a generalization of discrete-time quantum walks. We treat the right eigenvalue problem of quaternionic matrices to analysis the spectra of its transition matrix.…
We present a detailed circuit implementation of Szegedy's quantization of the Metropolis-Hastings walk. This quantum walk is usually defined with respect to an oracle. We find that a direct implementation of this oracle requires costly…
In this paper, we analyze the potential for new types of searches using the formalism of scattering random walks on Quantum Computers. Given a particular type of graph consisting of nodes and connections, a "Tree Maze", we would like to…
We present a theoretical framework for the analysis of amplitude transfer in Quantum Variational Algorithms (QVAs) for combinatorial optimisation with mixing unitaries defined by vertex-transitive graphs, based on their continuous-time…
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 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…
We investigate coined quantum walk search and state transfer algorithms, focusing on the complete $M$-partite graph with $N$ vertices in each partition. First, it is shown that by adding a loop to each vertex the search algorithm finds the…
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…
A quantum walk is the quantum analogue of a random walk. While it is relatively well understood how quantum walks can speed up random walk hitting times, it is a long-standing open question to what extent quantum walks can speed up the…
The lazy random walk, where the walker has some probability of staying put, is a useful tool in classical algorithms. We propose a quantum analogue, the lackadaisical quantum walk, where each vertex is given $l$ self-loops, and we…
Quantum walks can reconstruct quantum algorithms for quantum computation, where the precise controls of quantum state transfers between arbitrary distant sites are required. Here, we investigate quantum walks using a periodically…
A quantum walk places a traverser into a superposition of both graph location and traversal "spin." The walk is defined by an initial condition, an evolution determined by a unitary coin/shift-operator, and a measurement based on the…
The graph isomorphism problem asks whether two graphs are identical up to vertex relabeling. While the exact problem admits quasi-polynomial-time classical algorithms, many applications in molecular comparison, noisy network analysis, and…
Continuous-time quantum walks have proven to be an extremely useful framework for the design of several quantum algorithms. Often, the running time of quantum algorithms in this framework is characterized by the quantum hitting time: the…
Quantum walks provide a natural framework to approach graph problems with quantum computers, exhibiting speedups over their classical counterparts for tasks such as the search for marked nodes or the prediction of missing links.…
We introduce a simple diagrammatic approach for estimating how a randomly walking quantum particle searches on a graph in continuous-time, which involves sketching small weighted graphs with self-loops and considering degenerate…
This paper proposes a computational procedure that applies a quantum algorithm to train classical artificial neural networks. The goal of the procedure is to apply quantum walk as a search algorithm in a complete graph to find all synaptic…