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Lecture 2: Quantum Math Basics 1 Complex Numbers

www.cs.cmu.edu

Quantum Computation (CMU 18-859BB, Fall 2015) Lecture 2: Quantum Math Basics September 14, 2015 Lecturer: John Wright Scribe: Yongshan Ding 1 Complex Numbers From last lecture, we have seen some of the essentials of the quantum circuit model of compu-tation, as well as their strong connections with classical randomized model of computation.

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A Gentle Introduction Eleanor Rieffel and Wolfgang Polak - CAS

mmrc.amss.cas.cn

7.8.3 A Quantum Circuit for Fast Fourier Transform 156 7.9 References 158 7.10 Exercises 159 8 Shor’s Algorithm 163 8.1 Classical Reduction to Period-Finding 164 8.2 Shor’s Factoring Algorithm 164 8.2.1 The Quantum Core 165 8.2.2 Classical Extraction of the Period from the Measured Value 166 8.3 Example Illustrating Shor’s Algorithm 167

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Quantum Computation and Quantum Information

mmrc.amss.cas.cn

4.6 Summary of the quantum circuit model of computation 202 4.7 Simulation of quantum systems 204 4.7.1 Simulation in action 204 4.7.2 The quantum simulation algorithm 206 4.7.3 An illustrative example 209 4.7.4 Perspectives on quantum simulation 211 5 The quantum Fourier transform and its applications 216

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