Monte Carlo Graph Search for Quantum Circuit Optimization

The building blocks of quantum algorithms and software are quantum gates, with the appropriate combination of quantum gates leading to a desired quantum circuit. Deep expert knowledge is necessary to discover effective combinations of quantum gates to achieve a desired quantum algorithm for solving a specific task. This is especially challenging for quantum machine learning and signal processing. For example, it is not trivial to design a quantum Fourier transform from scratch. This work proposes a quantum architecture search algorithm which is based on a Monte Carlo graph search and measures of importance sampling. It is applicable to the optimization of gate order, both for discrete gates, as well as gates containing continuous variables. Several numerical experiments demonstrate the applicability of the proposed method for the automatic discovery of quantum circuits.Comment: 14 pages, 9 figure

Cellular Automata

Modelling and simulation are disciplines of major importance for science and engineering. There is no science without models, and simulation has nowadays become a very useful tool, sometimes unavoidable, for development of both science and engineering. The main attractive feature of cellular automata is that, in spite of their conceptual simplicity which allows an easiness of implementation for computer simulation, as a detailed and complete mathematical analysis in principle, they are able to exhibit a wide variety of amazingly complex behaviour. This feature of cellular automata has attracted the researchers' attention from a wide variety of divergent fields of the exact disciplines of science and engineering, but also of the social sciences, and sometimes beyond. The collective complex behaviour of numerous systems, which emerge from the interaction of a multitude of simple individuals, is being conveniently modelled and simulated with cellular automata for very different purposes. In this book, a number of innovative applications of cellular automata models in the fields of Quantum Computing, Materials Science, Cryptography and Coding, and Robotics and Image Processing are presented

Quantum Biomimetics

136 p.En esta tesis proponemos el concepto de Biomimética Cuántica orientado hacia la reproducción de comportamientos propios de los seres vivos en protocolos de información cuántica. En concreto, las propiedades que aspiramos a imitar emergen como resultado de fenómenos de interacción en diferentes escalas, resultando inaccesibles para un tratamiento matemático acorde al ofrecido por las plataformas de tecnologías cuánticas. Por tanto, el objetivo de la tesis es el de diseñar modelos con cabida para las mencionadas características biológicas pero simplificados de forma que puedan ser adaptados en protocolos experimentales. La tesis se divide en tres partes, una por cada rasgo biológico diferente empleado como inspiración: selección natural, memoria e inteligencia. El estudio presentado en la primera parte culmina con la obtención de un modelo de vida artificial con una identidad exclusivamente cuántica, que no solo permite la escenificación del modelo de selección natural a escala microscópica si no que proporciona un posible marco para la implementación de algoritmos genéticos y problemas de optimización en plataformas cuánticas. En la segunda parte se muestran algoritmos asociados con la simulación de evolución temporal regida por ecuaciones con una dependencia explicita en términos deslocalizados temporalmente. Estos permiten la incorporación de la retroalimentación y posalimentación al conjunto de herramientas en información cuántica. La tercera y última parte versa acerca de la posible simbiosis entre los algoritmos de aprendizaje y los protocolos cuánticos. Mostramos como aplicar técnicas de optimización clásicas para tratar problemas cuánticos así como la codificación y resolución de problemas en dinámicas puramente cuánticas

A Field Guide to Genetic Programming

xiv, 233 p. : il. ; 23 cm.Libro ElectrónicoA Field Guide to Genetic Programming (ISBN 978-1-4092-0073-4) is an introduction to genetic programming (GP). GP is a systematic, domain-independent method for getting computers to solve problems automatically starting from a high-level statement of what needs to be done. Using ideas from natural evolution, GP starts from an ooze of random computer programs, and progressively refines them through processes of mutation and sexual recombination, until solutions emerge. All this without the user having to know or specify the form or structure of solutions in advance. GP has generated a plethora of human-competitive results and applications, including novel scientific discoveries and patentable inventions. The authorsIntroduction -- Representation, initialisation and operators in Tree-based GP -- Getting ready to run genetic programming -- Example genetic programming run -- Alternative initialisations and operators in Tree-based GP -- Modular, grammatical and developmental Tree-based GP -- Linear and graph genetic programming -- Probalistic genetic programming -- Multi-objective genetic programming -- Fast and distributed genetic programming -- GP theory and its applications -- Applications -- Troubleshooting GP -- Conclusions.Contents xi 1 Introduction 1.1 Genetic Programming in a Nutshell 1.2 Getting Started 1.3 Prerequisites 1.4 Overview of this Field Guide I Basics 2 Representation, Initialisation and GP 2.1 Representation 2.2 Initialising the Population 2.3 Selection 2.4 Recombination and Mutation Operators in Tree-based 3 Getting Ready to Run Genetic Programming 19 3.1 Step 1: Terminal Set 19 3.2 Step 2: Function Set 20 3.2.1 Closure 21 3.2.2 Sufficiency 23 3.2.3 Evolving Structures other than Programs 23 3.3 Step 3: Fitness Function 24 3.4 Step 4: GP Parameters 26 3.5 Step 5: Termination and solution designation 27 4 Example Genetic Programming Run 4.1 Preparatory Steps 29 4.2 Step-by-Step Sample Run 31 4.2.1 Initialisation 31 4.2.2 Fitness Evaluation Selection, Crossover and Mutation Termination and Solution Designation Advanced Genetic Programming 5 Alternative Initialisations and Operators in 5.1 Constructing the Initial Population 5.1.1 Uniform Initialisation 5.1.2 Initialisation may Affect Bloat 5.1.3 Seeding 5.2 GP Mutation 5.2.1 Is Mutation Necessary? 5.2.2 Mutation Cookbook 5.3 GP Crossover 5.4 Other Techniques 32 5.5 Tree-based GP 39 6 Modular, Grammatical and Developmental Tree-based GP 47 6.1 Evolving Modular and Hierarchical Structures 47 6.1.1 Automatically Defined Functions 48 6.1.2 Program Architecture and Architecture-Altering 50 6.2 Constraining Structures 51 6.2.1 Enforcing Particular Structures 52 6.2.2 Strongly Typed GP 52 6.2.3 Grammar-based Constraints 53 6.2.4 Constraints and Bias 55 6.3 Developmental Genetic Programming 57 6.4 Strongly Typed Autoconstructive GP with PushGP 59 7 Linear and Graph Genetic Programming 61 7.1 Linear Genetic Programming 61 7.1.1 Motivations 61 7.1.2 Linear GP Representations 62 7.1.3 Linear GP Operators 64 7.2 Graph-Based Genetic Programming 65 7.2.1 Parallel Distributed GP (PDGP) 65 7.2.2 PADO 67 7.2.3 Cartesian GP 67 7.2.4 Evolving Parallel Programs using Indirect Encodings 68 8 Probabilistic Genetic Programming 8.1 Estimation of Distribution Algorithms 69 8.2 Pure EDA GP 71 8.3 Mixing Grammars and Probabilities 74 9 Multi-objective Genetic Programming 75 9.1 Combining Multiple Objectives into a Scalar Fitness Function 75 9.2 Keeping the Objectives Separate 76 9.2.1 Multi-objective Bloat and Complexity Control 77 9.2.2 Other Objectives 78 9.2.3 Non-Pareto Criteria 80 9.3 Multiple Objectives via Dynamic and Staged Fitness Functions 80 9.4 Multi-objective Optimisation via Operator Bias 81 10 Fast and Distributed Genetic Programming 83 10.1 Reducing Fitness Evaluations/Increasing their Effectiveness 83 10.2 Reducing Cost of Fitness with Caches 86 10.3 Parallel and Distributed GP are Not Equivalent 88 10.4 Running GP on Parallel Hardware 89 10.4.1 Master–slave GP 89 10.4.2 GP Running on GPUs 90 10.4.3 GP on FPGAs 92 10.4.4 Sub-machine-code GP 93 10.5 Geographically Distributed GP 93 11 GP Theory and its Applications 97 11.1 Mathematical Models 98 11.2 Search Spaces 99 11.3 Bloat 101 11.3.1 Bloat in Theory 101 11.3.2 Bloat Control in Practice 104 III Practical Genetic Programming 12 Applications 12.1 Where GP has Done Well 12.2 Curve Fitting, Data Modelling and Symbolic Regression 12.3 Human Competitive Results – the Humies 12.4 Image and Signal Processing 12.5 Financial Trading, Time Series, and Economic Modelling 12.6 Industrial Process Control 12.7 Medicine, Biology and Bioinformatics 12.8 GP to Create Searchers and Solvers – Hyper-heuristics xiii 12.9 Entertainment and Computer Games 127 12.10The Arts 127 12.11Compression 128 13 Troubleshooting GP 13.1 Is there a Bug in the Code? 13.2 Can you Trust your Results? 13.3 There are No Silver Bullets 13.4 Small Changes can have Big Effects 13.5 Big Changes can have No Effect 13.6 Study your Populations 13.7 Encourage Diversity 13.8 Embrace Approximation 13.9 Control Bloat 13.10 Checkpoint Results 13.11 Report Well 13.12 Convince your Customers 14 Conclusions Tricks of the Trade A Resources A.1 Key Books A.2 Key Journals A.3 Key International Meetings A.4 GP Implementations A.5 On-Line Resources 145 B TinyGP 151 B.1 Overview of TinyGP 151 B.2 Input Data Files for TinyGP 153 B.3 Source Code 154 B.4 Compiling and Running TinyGP 162 Bibliography 167 Inde

Reinforcement Learning

Brains rule the world, and brain-like computation is increasingly used in computers and electronic devices. Brain-like computation is about processing and interpreting data or directly putting forward and performing actions. Learning is a very important aspect. This book is on reinforcement learning which involves performing actions to achieve a goal. The first 11 chapters of this book describe and extend the scope of reinforcement learning. The remaining 11 chapters show that there is already wide usage in numerous fields. Reinforcement learning can tackle control tasks that are too complex for traditional, hand-designed, non-learning controllers. As learning computers can deal with technical complexities, the tasks of human operators remain to specify goals on increasingly higher levels. This book shows that reinforcement learning is a very dynamic area in terms of theory and applications and it shall stimulate and encourage new research in this field

Probabilistic Image Models and their Massively Parallel Architectures : A Seamless Simulation- and VLSI Design-Framework Approach

Algorithmic robustness in real-world scenarios and real-time processing capabilities are the two essential and at the same time contradictory requirements modern image-processing systems have to fulfill to go significantly beyond state-of-the-art systems. Without suitable image processing and analysis systems at hand, which comply with the before mentioned contradictory requirements, solutions and devices for the application scenarios of the next generation will not become reality. This issue would eventually lead to a serious restraint of innovation for various branches of industry. This thesis presents a coherent approach to the above mentioned problem. The thesis at first describes a massively parallel architecture template and secondly a seamless simulation- and semiconductor-technology-independent design framework for a class of probabilistic image models, which are formulated on a regular Markovian processing grid. The architecture template is composed of different building blocks, which are rigorously derived from Markov Random Field theory with respect to the constraints of \it massively parallel processing \rm and \it technology independence\rm. This systematic derivation procedure leads to many benefits: it decouples the architecture characteristics from constraints of one specific semiconductor technology; it guarantees that the derived massively parallel architecture is in conformity with theory; and it finally guarantees that the derived architecture will be suitable for VLSI implementations. The simulation-framework addresses the unique hardware-relevant simulation needs of MRF based processing architectures. Furthermore the framework ensures a qualified representation for simulation of the image models and their massively parallel architectures by means of their specific simulation modules. This allows for systematic studies with respect to the combination of numerical, architectural, timing and massively parallel processing constraints to disclose novel insights into MRF models and their hardware architectures. The design-framework rests upon a graph theoretical approach, which offers unique capabilities to fulfill the VLSI demands of massively parallel MRF architectures: the semiconductor technology independence guarantees a technology uncommitted architecture for several design steps without restricting the design space too early; the design entry by means of behavioral descriptions allows for a functional representation without determining the architecture at the outset; and the topology-synthesis simplifies and separates the data- and control-path synthesis. Detailed results discussed in the particular chapters together with several additional results collected in the appendix will further substantiate the claims made in this thesis

DNA computation

This is the first ever doctoral thesis in the field of DNA computation. The field has its roots in the late 1950s, when the Nobel laureate Richard Feynman first introduced the concept of computing at a molecular level. Feynman's visionary idea was only realised in 1994, when Leonard Adleman performed the first ever truly molecular-level computation using DNA combined with the tools and techniques of molecular biology. Since Adleman reported the results of his seminal experiment, there has been a flurry of interest in the idea of using DNA to perform computations. The potential benefits of using this particular molecule are enormous: by harnessing the massive inherent parallelism of performing concurrent operations on trillions of strands, we may one day be able to compress the power of today's supercomputer into a single test tube. However, if we compare the development of DNA-based computers to that of their silicon counterparts, it is clear that molecular computers are still in their infancy. Current work in this area is concerned mainly with abstract models of computation and simple proof-of-principle experiments. The goal of this thesis is to present our contribution to the field, placing it in the context of the existing body of work. Our new results concern a general model of DNA computation, an error-resistant implementation of the model, experimental investigation of the implementation and an assessment of the complexity and viability of DNA computations. We begin by recounting the historical background to the search for the structure of DNA. By providing a detailed description of this molecule and the operations we may perform on it, we lay down the foundations for subsequent chapters. We then describe the basic models of DNA computation that have been proposed to date. In particular, we describe our parallel filtering model, which is the first to provide a general framework for the elegant expression of algorithms for NP-complete problems. The implementation of such abstract models is crucial to their success. Previous experiments that have been carried out suffer from their reliance on various error-prone laboratory techniques. We show for the first time how one particular operation, hybridisation extraction, may be replaced by an error-resistant enzymatic separation technique. We also describe a novel solution read-out procedure that utilizes cloning, and is sufficiently general to allow it to be used in any experimental implementation. The results of preliminary tests of these techniques are then reported. Several important conclusions are to be drawn from these investigations, and we report these in the hope that they will provide useful experimental guidance in the future. The final contribution of this thesis is a rigorous consideration of the complexity and viability of DNA computations. We argue that existing analyses of models of DNA computation are flawed and unrealistic. In order to obtain more realistic measures of the time and space complexity of DNA computations we describe a new strong model, and reassess previously described algorithms within it. We review the search for "killer applications": applications of DNA computing that will establish the superiority of this paradigm within a certain domain. We conclude the thesis with a description of several open problems in the field of DNA computation