Related papers: Direct Equivalence between Dynamics of Quantum Wal…
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…
Open Quantum Walks (OQW) are a type of quantum walk governed by the system's interaction with its environment. We explore the time evolution and the limit behavior of the OQW framework for Quantum Computation and show how we can represent…
Quantum walks are at the heart of modern quantum technologies. They allow to deal with quantum transport phenomena and are an advanced tool for constructing novel quantum algorithms. Quantum walks on graphs are fundamentally different from…
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…
Quantum walks function as essential means to implement quantum simulators, allowing one to study complex and often directly inaccessible quantum processes in controllable systems. In this contribution, the notion of a driven Gaussian…
The continuous-time quantum walk is a particle evolving by Schr\"odinger's equation in discrete space. Encoding the space as a graph of vertices and edges, the Hamiltonian is proportional to the discrete Laplacian. In some physical systems,…
We demonstrate that continuous time quantum walks on several types of branching graphs, including graphs with loops, are identical to quantum walks on simpler linear chain graphs. We also show graph types for which such equivalence does not…
The study of quantum walks has been shown to have a wide range of applications in areas such as artificial intelligence, the study of biological processes, and quantum transport. The quantum stochastic walk, which allows for incoherent…
A quantum walk is a time-homogeneous quantum-mechanical process on a graph defined by analogy to classical random walk. The quantum walker is a particle that moves from a given vertex to adjacent vertices in quantum superposition. Here we…
The concept of open quantum walks (OQW), quantum walks exclusively driven by the interaction with the external environment, is reviewed. OQWs are formulated as discrete completely positive maps on graphs. The basic properties of OQWs 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…
Continuous-time quantum walks (CTQWs) on static graphs provide efficient methods for search and sampling as well as a model for universal quantum computation. We consider an extension of CTQWs to the case of dynamic graphs, in which an…
We compare discrete-time quantum walks on graphs to their natural classical equivalents, which we argue are lifted Markov chains, that is, classical Markov chains with added memory. We show that these can simulate quantum walks, allowing us…
Some of the most enduring questions in physics--including the quantum measurement problem and the quantization of gravity--involve the interaction of a quantum system with a classical environment. Two linearly coupled harmonic oscillators…
This paper investigates continuous-time quantum walks on directed bipartite graphs based on a graph's adjacency matrix. We prove that on bipartite graphs, probability transport between the two node partitions can be completely suppressed by…
Simulation and programming of current quantum computers as Noisy Intermediate-Scale Quantum (NISQ) devices represent a hot topic at the border of current physical and information sciences. The quantum walk process represents a basic…
A new model of quantum random walks is introduced, on lattices as well as on finite graphs. These quantum random walks take into account the behavior of open quantum systems. They are the exact quantum analogues of classical Markov chains.…
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, in virtue of the coherent superposition and quantum interference, possess exponential superiority over its classical counterpart in applications of quantum searching and quantum simulation. The quantum enhanced power is…
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…