Related papers: Implementing the quantum random walk
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…
We implement the proof of principle for the quantum walk of one ion in a linear ion trap. With a single-step fidelity exceeding 0.99, we perform three steps of an asymmetric walk on the line. We clearly reveal the differences to its…
The development of quantum algorithms based on quantum versions of random walks is placed in the context of the emerging field of quantum computing. Constructing a suitable quantum version of a random walk is not trivial: pure quantum…
The quantum random walk has drawn special interests because its remarkable features to the classical counterpart could lead to new quantum algorithms. In this paper, we propose a feasible scheme to implement quantum random walks on a line…
We experimentally demonstrate a quantum walk on a line in phase space using one and two trapped ion. A walk with up to 23 steps is realized by subjecting an ion to state-dependent displacement operations interleaved with quantum coin…
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 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.…
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 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…
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…
We present an introduction to coined quantum walks on regular graphs, which have been developed in the past few years as an alternative to quantum Fourier transforms for underpinning algorithms for quantum computation. We then describe our…
Recently, it has been shown that one-dimensional quantum walks can mix more quickly than classical random walks, suggesting that quantum Monte Carlo algorithms can outperform their classical counterparts. We study two quantum walks on the…
We suggest a theoretical scheme for the simulation of quantum random walks on a line using beam splitters, phase shifters and photodetectors. Our model enables us to simulate a quantum random walk with use of the wave nature of classical…
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…
We show that a multi-step quantum walk can be realized for a single trapped ion with interpolation between quantum and random walk achieved by randomizing the generalized Hadamard coin flip phase. The signature of the quantum walk is…
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…
This paper presents a novel quantum walk approach to simulating parton showers on a quantum computer. We demonstrate that the quantum walk paradigm offers a natural and more efficient approach to simulating parton showers on quantum…
We show how multi-walker quantum walks can be implemented in a quantum quincunx created via cavity quantum electrodynamics. The implementation of a quantum walk with a multi-walker opens up the interesting possibility to introduce…
For a continuous-time quantum walk on a line the variance of the position observable grows quadratically in time, whereas, for its classical counterpart on the same graph, it exhibits a linear, diffusive, behaviour. A quantum walk, thus,…
Quantum versions of random walks on the line and cycle show a quadratic improvement in their spreading rate and mixing times respectively. The addition of decoherence to the quantum walk produces a more uniform distribution on the line, and…