Related papers: Coined Quantum Walks as Quantum Markov Chains
Quantum random walk in a two-dimensional lattice with randomly distributed traps is investigated. Distributions of quantum walkers are evaluated dynamically for the cases of Hadamard, Fourier, and Grover coins, and quantum to classical…
Szegedy's quantum walk is an algorithm for quantizing a general Markov chain. It has plenty of applications such as many variants of optimizations. In order to check its properties in an error-free environment, it is important to have a…
Quantum walks, the quantum mechanical counterpart of classical random walks, is an advanced tool for building quantum algorithms that has been recently shown to constitute a universal model of quantum computation. Quantum walks is now a…
A quantum walk model which reflects the $2$-cell embedding on the orientable closed surface of a graph in the dynamics is introduced. We show that the scattering matrix is obtained by finding the faces on the underlying surface which have…
In this paper, we propose a circuit design for implementing quantum walks on complex networks. Quantum walks are powerful tools for various graph-based applications such as spatial search, community detection, and node classification.…
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…
In this paper, we numerically study quantum walks on two kinds of two-dimensional graphs: cylindrical strip and Mobius strip. The two kinds of graphs are typical two-dimensional topological graph. We study the crossing property of quantum…
Quantum walks, both discrete (coined) and continuous time, on a general graph of N vertices with undirected edges are reviewed in some detail. The resource requirements for implementing a quantum walk as a program on a quantum computer are…
A discrete time quantum walk is known to be the single-particle sector of a quantum cellular automaton. For a long time, these models have interested the community for their nice properties such as locality or translation invariance. This…
We present a novel Adaptive Distribution Generator that leverages a quantum walks-based approach to generate high precision and efficiency of target probability distributions. Our method integrates variational quantum circuits with…
Random walk algorithms are crucial for sampling and approximation problems in statistical physics and theoretical computer science. The mixing property is necessary for Markov chains to approach stationary distributions and is facilitated…
Coined quantum walks may be interpreted as the motion in position space of a quantum particle with a spin degree of freedom; the dynamics are determined by iterating a unitary transformation which is the product of a spin transformation and…
We explore a continuous-time quantum walk starting at a single vertex on the discrete path and cycle with a cubic nonlinearity. Such nonlinearities arise in Bose-Einstein condensates described by the Gross-Pitaevskii equation or by…
The random walk formalism is used across a wide range of applications, from modelling share prices to predicting population genetics. Likewise quantum walks have shown much potential as a frame- work for developing new quantum algorithms.…
We introduce a variation of the discrete time quantum walk, the nonreversal quantum walk, which does not step back onto a position which it has just occupied. This allows us to simulate a dimer and we achieve it by introducing a new type of…
Motivated by discrete kinetic models for non-cooperative molecular motors on periodic tracks, we consider random walks (also not Markov) on quasi one dimensional (1d) lattices, obtained by gluing several copies of a fundamental graph in a…
Discrete-time quantum walks can be regarded as quantum dynamical simulators since they can simulate spatially discretized Schr\"{o}dinger, massive Dirac, and Klein-Gordon equations. Here, two different types of Fibonacci discrete-time…
A proof that continuous time quantum walks are universal for quantum computation, using unweighted graphs of low degree, has recently been presented by Childs [PRL 102 180501 (2009)]. We present a version based instead on the discrete time…
Recently, quantized versions of random walks have been explored as effective elements for quantum algorithms. In the simplest case of one dimension, the theory has remained divided into the discrete-time quantum walk and the continuous-time…
We survey the equations of continuous-time quantum walks on simple one-dimensional lattices, which include the finite and infinite lines and the finite cycle, and compare them with the classical continuous-time Markov chains. The focus of…