Related papers: Quantum walks as mathematical foundation for quant…
We analyze the application of the history state formalism to quantum walks. The formalism allows one to describe the whole walk through a pure quantum history state, which can be derived from a timeless eigenvalue equation. It naturally…
Quantum walks provide simple models of various fundamental processes. It is pivotal to know when the dynamics underlying a walk lead to quantum advantages just by examining its statistics. A walk with many indistinguishable particles and…
We introduce a new type of discrete quantum walks, called vertex-face walks, based on orientable embeddings. We first establish a spectral correspondence between the transition matrix $U$ and the vertex-face incidence structure. Using the…
A random walk is known as a random process which describes a path including a succession of random steps in the mathematical space. It has increasingly been popular in various disciplines such as mathematics and computer science.…
The quantum walk was originally proposed as a quantum mechanical analogue of the classical random walk, and has since become a powerful tool in quantum information science. In this paper, we show that discrete time quantum walks provide a…
Quantum networks are complex systems formed by the interaction among quantum processors through quantum channels. Analogous to classical computer networks, quantum networks allow for the distribution of quantum computation among quantum…
Quantum walks can be used either as tools for quantum algorithm development or as entanglement generators, potentially useful to test quantum hardware. We present a novel algorithm based on a discrete Hadamard quantum walk on a line with…
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…
We investigate quantum walks in multiple dimensions with different quantum coins. We augment the model by assuming that at each step the amplitudes of the coin state are multiplied by random phases. This model enables us to study in detail…
A discrete time quantum walk is known to be the single-particle sector of a quantum cellular automaton. Searching in this mathematical framework has interested the community since a long time. However, most results consider spatial search…
Discrete quantum walks are dynamical protocols for controlling a single quantum particle. Despite of its simplicity, quantum walks display rich topological phenomena and provide one of the simplest systems to study and understand…
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.…
Inspired by recent breakthroughs with topological quantum materials, which pave the way to novel, high-efficiency, low-energy magnetoelectric devices and fault-tolerant quantum information processing, inter alia, topological quantum walks…
We investigate a system of two atoms in an optical lattice, performing a quantum walk by state-dependent shift operations and a coin operation acting on the internal states. The atoms interact, e.g., by cold collisions, whenever they are in…
In this Chapter, we present some interesting properties of quantum walks on the line. We concentrate our attention in the emergence of invariance and provide some insights into the ultimate origin of the observed behavior. In the first part…
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.…
Open quantum walks (OQW) are formulated as quantum Markov chains on graphs. It is shown that OQWs are a very useful tool for the formulation of dissipative quantum computing algorithms and for dissipative quantum state preparation. In…
In some of the earliest work on quantum mechanical computers, Feynman showed how to implement universal quantum computation by the dynamics of a time-independent Hamiltonian. I show that this remains possible even if the Hamiltonian is…
A continuous-time quantum walk on a dynamic graph evolves by Schr\"odinger's equation with a sequence of Hamiltonians encoding the edges of the graph. This process is universal for quantum computing, but in general, the dynamic graph that…
Discrete time quantum walks are known to be universal for quantum computation. This has been proven by showing that they can simulate a universal gate set. In this paper we examine computation in terms of language acceptance and present two…