quantum computing and communications

[...]... based on the first semester of a two-semester subject dedicated to Ph.D students and undergraduates in electrical engineering and computer sciences at Budapest University of Technology and Economics This first semester covers a thorough basic introduction to the quantum computing world and discusses quantumassisted computing and communications where we use the new paradigm to improve (assist) the performance... build distinct roads for citizens and for messengers and the army of the king all around your empire, but there is only one road for all in geometry!’1 Basically we agree with Menaikhmos: learning and understanding quantum computing and communications need time and effort from the reader However, we are convinced that if the way the knowledge is served is chosen carefully and fits more or less to previous... 48 48 49 50 52 54 56 57 59 Part II Quantum Algorithms 4 Two Simple Quantum Algorithms 4.1 Superdense Coding 4.2 Quantum Teleportation 4.3 Further Reading 63 63 65 68 CONTENTS 5 Quantum Parallelism 5.1 Introduction 5.2 Deutsch–Jozsa Algorithm 5.3 Simon Algorithm 5.4 Further Reading 6 Quantum Fourier Transform and its Applications 6.1 Quantum Fourier Transform 6.2 Quantum Phase Estimation 6.2.1 Idealistic... enough and cheap enough and manageable enough and etc and not the most precise or the cheapest or the most manageable or etc Hence error analysis must always be kept at the focus of investigations All these endeavors are motivated by the fact that engineers should learn how to design new practical solutions We always have this philosophy in sight when addressing various topics of quantum computing and communications. .. 239 239 241 14 Complex Baseband-equivalent Description of Bandlimited Signals 245 15 Useful Links 247 References 249 Solutions of Exercises 261 Index 279 Preface Quantum computing and communications is one of the promising new fields of the new millennium This emerging topic has reached the age when not only physicists and mathematicians but also engineers are becoming more and more interested in it This... would like to provide some useful hints and tools similarly to seamen who check their maps and compasses before sailing out to sea This book can be divided logically into three well-defined parts Part I explains the basics of quantum computing and communications As the next level Part II introduces well-known quantum algorithms while advanced readers can find several quantum assisted solutions for state-of-the-art... 23 2.8 Abstract quantum circuit of the generalized interferometer 23 Controlled NOT gate 26 2.6 2.9 xx LIST OF FIGURES 2.10 SWAP gate made of CNOTs 28 2.11 Bell state generator quantum circuit 29 2.12 Generalized quantum entangler 30 2.13 Quantum COPY machine 39 2.14 Abstract quantum circuit of the generalized interferometer 41 3.1 P (m = 2) and P (m = 2) = 1 vs α 55 3.2 P (1 | |ϕ1 ) and P (1 | |ϕ1... Circuit of Un−1 85 6.3 Quantum circuit implementing QFT 85 6.4 Quantum circuit producing |µn 87 6.5 Quantum circuit computing the phase 88 6.6 Illustration of probability amplitude regions before measurement with different index transformations 90 3.4 5.3 6.7 log10 (P (h)) 6.8 log10 (P (h)) gate in case c = 10, p = 4 and αu = 0.4π in case c = 10 and αu = 0.4 · 2π when p varies between 0 and 10 94 95 LIST... decision about the number of iterations 135 ˜ and Ps vs 7.7 ˜ Pε , Ps , Pε 7.8 Quantum counting circuit 139 7.9 Ωγ (M ), Ωγ+ (M ), Ωγ− (M ) vs q if M = 1024 and N = 4096 141 M N 137 7.10 c(M, q) (assuming equality in the definition) vs q if M = 1, 4, 64, 2048 and N = 4096 141 7.11 Connection between M and q assuming system ˘ parameters Pε = 0.1 and 2N = 4096 144 7.12 Quantum circuit for searching in an unsorted... strange and sometimes challenging lands of the quantum world Do not hesitate, the new world is waiting for you The Authors How to use this book According to ancient legend, one day Alexander the Great, conqueror of the ‘that time known world’ (Greece, Egypt, Persia), asked Menaikhmos the famous mathematician to teach him geometry in an easier and faster way Menaikhmos smiled at this wish and answered: . Wiley & Sons, Ltd Quantum Computing and Communications An Engineering Approach Quantum Computing and Communications An Engineering Approach S ´ andor Imre and Ferenc Bal ´ azs Both of Budapest. Quantum Computing and Communications An Engineering Approach S ´ andor Imre and Ferenc Bal ´ azs Both of Budapest University of Technology and Economics, Hungary John Wiley & Sons, Ltd Quantum. learning and understanding quantum computing and communications need time and effort from the reader. However, we are convinced that if the way the knowledge is served is chosen carefully and fits more