Related papers: Hitting Time of Quantum Walks with Perturbation
We investigate the hitting times of random walks on graphs, where a hitting time is defined as the number of steps required for a random walker to move from one node to another. While much of the existing literature focuses on calculating…
We make use of matrix representations of completely positive maps in order to study open quantum dynamics on graphs, with emphasis on quantum walks and the associated trajectories obtained via a monitoring of the position. We discuss the…
We give a quantum algorithm for finding a marked element on the grid when there are multiple marked elements. Our algorithm uses quadratically fewer steps than a random walk on the grid, ignoring logarithmic factors. This is the first known…
It has been proved by Kempe that discrete quantum walks on the hypercube (HC) hit exponentially faster than the classical analog. The same was also observed numerically by Krovi and Brun for a slightly different property, namely, the…
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…
In recent years, quantum walks have been widely researched and have shown exciting properties. One such is a quadratic speed-up in hitting time compared to its classical counterpart. In this paper, we design a quantum circuit for the MNRS…
We consider a model of open quantum random walk and together with a quantum trajectory approach we are able to examine a notion of hitting time. We see that many constructions, such as minimal solutions to hitting time problems, are…
In this paper, we consider Szegedy's walk, a type of discrete time quantum walk, and corresponding continuous time quantum walk related to the birth and death chain. We show that the scaling limit of time averaged distribution for the…
The mean squared displacement has been widely used as the primary metric for comparing quantum and classical random walks, with quantum walks showing quadratic scaling versus linear scaling for classical walks. However, this comparison may…
Quantum walks can be defined in two quite distinct ways: discrete-time and continuous-time quantum walks (DTQWs and CTQWs). For classical random walks, there is a natural sense in which continuous-time walks are a limit of discrete-time…
An ideal quantum walk transitions from one vertex to another with perfect fidelity, but in physical systems, the particle may be hindered by potential energy barriers. Then the particle has some amplitude of tunneling through the barriers,…
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,…
We present an adiabatic quantum algorithm for the abstract problem of searching marked vertices in a graph, or spatial search. Given a random walk (or Markov chain) $P$ on a graph with a set of unknown marked vertices, one can define a…
We consider random walks in which the walk originates in one set of nodes and then continues until it reaches one or more nodes in a target set. The time required for the walk to reach the target set is of interest in understanding the…
Classical first-passage times under restart are used in a wide variety of models, yet the quantum version of the problem still misses key concepts. We study the quantum hitting time with restart using a monitored quantum walk. The restart…
We demonstrate an implementation of the hitting time of a discrete time quantum random walk on cubelike graphs using IBM's Qiskit platform. Our implementation is based on efficient circuits for the Grover and Shift operators. We verify the…
Quantum walk acts obviously different from its classical counterpart, but decoherence will lessen and close the gap between them. To understand this process, it is necessary to investigate the evolution of quantum walk under different…
We have studied how decoherence affects a quantum walk on the line. As expected, it is highly sensitive, consisting as it does of an extremely delocalized particle. We obtain an expression for the rate at which the standard deviation falls…
Hitting times provide a fundamental measure of distance in random processes, quantifying the expected number of steps for a random walk starting at node $u$ to reach node $v$. They have broad applications across domains such as network…
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,…