Related papers: Discrete-time Semiclassical Szegedy Quantum Walks

Quantum walks are standard tools for searching graphs for marked vertices, and they often yield quadratic speedups over a classical random walk's hitting time. In some exceptional cases, however, the system only evolves by sign flips,…

Fast computational algorithms are in constant demand, and their development has been driven by advances such as quantum speedup and classical acceleration. This paper intends to study search algorithms based on quantum walks in quantum…

Quantum walks have emerged as a transformative paradigm in quantum information processing and can be applied to various graph problems. This study explores discrete-time quantum walks on simplicial complexes, a higher-order generalization…

In this paper we isolate the combinatorial property responsible (at least in part) for the computational speedups recently observed in some quantum walk algorithms. We find that continuous-time quantum walks can exploit the covering space…

Random walks simulate the randomness of objects, and are key instruments in various fields such as computer science, biology and physics. The counter part of classical random walks in quantum mechanics are the quantum walks. Quantum walk…

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…

Quantum walks, the quantum analogue of the classical random walk, have been shown to underpin quantum algorithms for fluid dynamics. We propose the quantum half-adder gate method for quantum walks as a good benchmark algorithm, specifically…

For a quantum walk on a graph, there exist many kinds of operators for the discrete-time evolution. We give a general relation between the characteristic polynomial of the evolution matrix of a quantum walk on edges and that of a kind of…

A quantum computer, i.e. utilizing the resources of quantum physics, superposition of states and entanglement, could furnish an exponential gain in computing time. A simulation using such resources is called a quantum simulation. The…

We study scattering quantum walks on highly symmetric graphs and use the walks to solve search problems on these graphs. The particle making the walk resides on the edges of the graph, and at each time step scatters at the vertices. All of…

We look at two possible routes to classical behavior for the discrete quantum random walk on the line: decoherence in the quantum ``coin'' which drives the walk, or the use of higher-dimensional coins to dilute the effects of interference.…

We introduce the quantum stochastic walk (QSW), which determines the evolution of generalized quantum mechanical walk on a graph that obeys a quantum stochastic equation of motion. Using an axiomatic approach, we specify the rules for all…

We define quantization scheme for discrete-time random walks on the half-line consistent with Szegedy's quantization of finite Markov chains. Motivated by the Karlin and McGregor description of discrete-time random walks in terms of…

Discrete quantum walks are periodically driven systems with discrete time evolution. In contrast to ordinary Floquet systems, no microscopic Hamiltonian exists, and the one-period time evolution is given directly by a series of unitary…

We show how a quantum walk can be used to find a marked edge or a marked complete subgraph of a complete graph. We employ a version of a quantum walk, the scattering walk, which lends itself to experimental implementation. The edges are…

Classical random walk formalism shows a significant role across a wide range of applications. As its quantum counterpart, the quantum walk is proposed as an important theoretical model for quantum computing. By exploiting the quantum…

A discrete-time quantum walk on a graph is the repeated application of a unitary evolution operator to a Hilbert space corresponding to the graph. If this unitary evolution operator has an associated group of symmetries, then for certain…

This work proposes a computational procedure that uses a quantum walk in a complete graph to train classical artificial neural networks. The idea is to apply the quantum walk to search the weight set values. However, it is necessary to…

The lackadaisical quantum walk is a lazy version of a discrete-time, coined quantum walk, where each vertex has a weighted self-loop that permits the walker to stay put. They have been used to speed up spatial search on a variety of graphs,…

Computational advantages gained by quantum algorithms rely largely on the coherence of quantum devices and are generally compromised by decoherence. As an exception, we present a quantum algorithm for graph isomorphism testing whose…