By Sandor Imre, Ferenc Balazs
Preface.How to take advantage of this book.Acknowledgements.List of Figures.Acronyms.PART I: creation TO QUANTUM COMPUTING.1. Motivations.2. Quantum Computing Basics.3. Measurements.PART II: QUANTUM ALGORITHMS.4. basic Quantum Algorithms.5. Quantum Parallelism.6. Quantum Fourier rework and its Applications.PART III: QUANTUM-ASSISTED suggestions OF INFOCOM PROBLEMS.7. looking in an Unsorted Database.8. Quantum established Multiuser Detection.9. Quantum dependent Code Breaking.10. Quantum dependent Key Distribution.11. browsing the internet on Quantum Basics.PART IV: APPENDICES.12. Mathematical Background.13. Derivations with regards to the Generalized Grover Algorithm.14. complicated Baseband-Equivalent Description of Bandlimited Signals.15. necessary Links.References.Solution of Exercises.Index
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Additional info for Quantum computing for communications : an engineering approach
Roughly speaking Schr¨odinger suggested assigning so-called probability amplitudes to nano-scale events instead of classical probabilities. Unlike classical probability p which should be real and can have values between 0 and 1 probability amplitudes c are complex numbers. g. alternative or independent events. Moreover the observed classical probability can be determined in a very simple way namely p = |c|2 . Unfortunately we are able to access probability amplitudes 2 √ √ I I = I. 10 QUANTUM COMPUTING BASICS 0 c00 0 c00 c01 1 c10 c11 0 0 1 1 c01 1 c10 c11 Fig.
Furthermore we are interested in the transition probabilities Pkl of a special single gate which is equivalent to the two-gate conﬁguration. It is reasonable to assume that the two tossings are independent thus basic probability theory advises us how to calculate different Pkl P00 = p00 p00 + p01 p10 , P01 = p01 p11 + p00 p01 , P10 = p11 p10 + p10 p00 , P11 = p11 p11 + p10 p01 . 5, that is using two concatenated gates provides the same result as a single one which 1 Readers from telecom may consider binary symmetric channel as an equivalent problem.
To make the set of Pauli-gates complete we deﬁne the Pauli-Y gate in the following way a b −jb = −jb|0 + ja|1 , ja |ψ = Y |ϕ = 0 j −j 0 which results in exchanged probability amplitudes multiplied by j. The effect of Pauli gates can be easily visualized exploiting the Bloch sphere from the previous subsection. Rotations around the x, y and z axes can be generated by Pauli gates. 6. 8. Its quantum logic name is phase-rotator gate or phase gate and it performs the following operation a b a |ψ = P (α)|ϕ = 1 0 0 ejα ejα b = a|0 + ejα b|1 .
Quantum computing for communications : an engineering approach by Sandor Imre, Ferenc Balazs