相关论文: A random walk approach to quantum algorithms

Quantum versions of random walks have diverse applications that are motivating experimental implementations as well as theoretical studies. However, the main impetus behind this interest is their use in quantum algorithms, which have always…

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 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 random walk is a possible approach to construct new quantum algorithms. Several groups have investigated the quantum random walk and experimental schemes were proposed. In this paper we present the experimental implementation of…

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…

Recently, several groups have investigated quantum analogues of random walk algorithms, both on a line and on a circle. It has been found that the quantum versions have markedly different features to the classical versions. Namely, the…

Quantum walks are powerful tools not only to construct the quantum speedup algorithms but also to describe specific models in physical processes. Furthermore, the discrete time quantum walk has been experimentally realized in various…

Quantum walks are a promising framework that can be used to both understand and implement quantum information processing tasks. The quantum stochastic walk is a recently developed framework that combines the concept of a quantum walk with…

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…

This tutorial article showcases the many varieties and uses of quantum walks. Discrete time quantum walks are introduced as counterparts of classical random walks. The emphasis is on the connections and differences between the two types of…

Quantum walks are referred to as quantum analogs to random walks in mathematics. They have been studied as quantum algorithms in quantum information for quantum computers. There are two types of quantum walks. One is 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…

Quantum walks on graphs are ubiquitous in quantum computing finding a myriad of applications. Likewise, random walks on graphs are a fundamental building block for a large number of algorithms with diverse applications. While the…

Given the extensive application of classical random walks to classical algorithms in a variety of fields, their quantum analogue in quantum walks is expected to provide a fruitful source of quantum algorithms. So far, however, such…

Classical randomized algorithms use a coin toss instruction to explore different evolutionary branches of a problem. Quantum algorithms, on the other hand, can explore multiple evolutionary branches by mere superposition of states. Discrete…

Quantum versions of random walks on the line and the cycle show a quadratic improvement over classical random walks in their spreading rates and mixing times respectively. Non-unitary quantum walks can provide a useful optimisation of these…

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…

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 letter we introduce the concept of a driven quantum walk. This work is motivated by recent theoretical and experimental progress that combines quantum walks and parametric down- conversion, leading to fundamentally different…

Quantum walk is one of the main tools for quantum algorithms. Defined by analogy to classical random walk, a quantum walk is a time-homogeneous quantum process on a graph. Both random and quantum walks can be defined either in continuous or…