Quantum walks: a comprehensive review

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 solid field of research of quantum computation full of exciting open problems for physicists, computer scientists, mathematicians and engineers. In this paper we review theoretical advances on the foundations of both discrete- and continuous-time quantum walks, together with the role that randomness plays in quantum walks, the connections between the mathematical models of coined discrete quantum walks and continuous quantum walks, the quantumness of quantum walks, a summary of papers published on discrete quantum walks and entanglement as well as a succinct review of experimental proposals and realizations of discrete-time quantum walks. Furthermore, we have reviewed several algorithms based on both discrete- and continuous-time quantum walks as well as a most important result: the computational universality of both continuous- and discrete- time quantum walks.Comment: Paper accepted for publication in Quantum Information Processing Journa

Survey of local algorithms

A local algorithm is a distributed algorithm that runs in constant time, independently of the size of the network. Being highly scalable and fault-tolerant, such algorithms are ideal in the operation of large-scale distributed systems. Furthermore, even though the model of local algorithms is very limited, in recent years we have seen many positive results for non-trivial problems. This work surveys the state-of-the-art in the field, covering impossibility results, deterministic local algorithms, randomised local algorithms, and local algorithms for geometric graphs.Peer reviewe

An investigation into alternative methods for the simulation and analysis of growth models

Complex systems are a rapidly increasing area of research covering numerous disciplines including economics and even cancer research, as such the optimisation of the simulations of these systems is important. This thesis will look specifically at two cellular automata based growth models the Eden growth model and the Invasion Percolation model. These models tend to be simulated storing the cluster within a simple array. This work demonstrates that for models which are highly sparse this method has drawbacks in both the memory consumed and the overall runtime of the system. It demonstrates that more modern data structures such as the HSH tree can offer considerable benefits to these models.Next, instead of optimising the software simulation of the Eden growth model, we detail a memristive-based cellular automata architecture that is capable of simulating the Eden growth model called the MEden model. It is demonstrated that not only is this method faster, up to 12; 704 times faster than the software simulation, it also allows for the same system to be used for the simulation of both EdenB and EdenC clusters without the need to be reconfigured; this is achieved through the use of two different parameters present in the model Pmax and Pchance. Giving the model a broader range of possible clusters which can aid with Monte-Carlo simulations of the model.Finally, two methods were developed to be able to identify a difference between fractally identical clusters; connected component labelling and convolution neural networks are the methods used to achieve this. It is demonstrated that both of these methods allow for the identification of individual Eden clusters able to classify them as either an EdenA, EdenB, or EdenC cluster, a highly nontrivial matter with current methods. It is also able to tell when a cluster was not an Eden cluster even though it fell in the fractal range of an Eden cluster. These features mean that the verification of a new method for the simulation of the Eden model could now be automated

Optimisation problems in wireless sensor networks : Local algorithms and local graphs

This thesis studies optimisation problems related to modern large-scale distributed systems, such as wireless sensor networks and wireless ad-hoc networks. The concrete tasks that we use as motivating examples are the following: (i) maximising the lifetime of a battery-powered wireless sensor network, (ii) maximising the capacity of a wireless communication network, and (iii) minimising the number of sensors in a surveillance application. A sensor node consumes energy both when it is transmitting or forwarding data, and when it is performing measurements. Hence task (i), lifetime maximisation, can be approached from two different perspectives. First, we can seek for optimal data flows that make the most out of the energy resources available in the network; such optimisation problems are examples of so-called max-min linear programs. Second, we can conserve energy by putting redundant sensors into sleep mode; we arrive at the sleep scheduling problem, in which the objective is to find an optimal schedule that determines when each sensor node is asleep and when it is awake. In a wireless network simultaneous radio transmissions may interfere with each other. Task (ii), capacity maximisation, therefore gives rise to another scheduling problem, the activity scheduling problem, in which the objective is to find a minimum-length conflict-free schedule that satisfies the data transmission requirements of all wireless communication links. Task (iii), minimising the number of sensors, is related to the classical graph problem of finding a minimum dominating set. However, if we are not only interested in detecting an intruder but also locating the intruder, it is not sufficient to solve the dominating set problem; formulations such as minimum-size identifying codes and locating–dominating codes are more appropriate. This thesis presents approximation algorithms for each of these optimisation problems, i.e., for max-min linear programs, sleep scheduling, activity scheduling, identifying codes, and locating–dominating codes. Two complementary approaches are taken. The main focus is on local algorithms, which are constant-time distributed algorithms. The contributions include local approximation algorithms for max-min linear programs, sleep scheduling, and activity scheduling. In the case of max-min linear programs, tight upper and lower bounds are proved for the best possible approximation ratio that can be achieved by any local algorithm. The second approach is the study of centralised polynomial-time algorithms in local graphs – these are geometric graphs whose structure exhibits spatial locality. Among other contributions, it is shown that while identifying codes and locating–dominating codes are hard to approximate in general graphs, they admit a polynomial-time approximation scheme in local graphs

Computer Science To Go (CS2Go): Developing a course to introduce and teach Computer Science and Computational Thinking to secondary school students

Computer Science To Go (CS2Go) is a course designed to teach Transition Year Students about Computer Science and Computational Thinking. This project has been conducted over two years and this thesis charts the development of the course from the initial research stage, through the lesson creation sections to the testing and evaluation of the course material. Over 80 hours of engaging, informative and challenging material has been developed for use in the classroom. Alongside the lesson plans, assessment and monitoring tools have been created, including a novel tool to assess students Computational Thinking skills. The content was tested in two major studies after an initial pilot study. This initial pilot study proved useful in constructing the full CS2Go course. Overall the course has been well received with teachers and students engaging well with the content. A web portal has also been created to allow for easy dissemination of all the CS2Go material. The further development of this web portal will turn CS2Go into a one-stop shop for teachers and educators hoping to find CS teaching material