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COT6600 - COT6600 Quantum Computing Fall 2010 Lecture M Wd...

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COT6600 Quantum Computing – Fall 2010 Lecture: M – Wd 1:30 -2:45 Eng 0383 Instructor: Dan C. Marinescu Office HEC 439 B Office hours: M-Wd 2:45 – 3:45 PM Class outline Quantum Computing and Quantum Information Theory – The Big Picture Mathematical Foundation Algebraic structures (groups, fields, vector spaces) Complex numbers Complex vector spaces o Bases and Dimensions o Inner Products o Linear Operators o Hermitian and Unitary Matrices o Eigenvectors and Eigenvalues of Quantum Operators o Tensor Products of Vector Spaces o Spectral Decomposition of an Operator Elements of Quantum Mechanics o Quantum State Postulate o Dynamics Postulate o Measurements Postulate o Uncertainty Principle o Density Operator o Pure and Mixed States o Entanglement; Monogamy of Entanglement Qubits and their Physical Implementation o Quantum Gates and Quantum Circuits o One-qubit gates: X, Y, Z, Hadamard, Phase-shift o Two-qubit gates: CNOT o Three-qubit gates: Fredkin and Toffoli Universality of Quantum Circuits, Solovay-Kitaev Theorem, Clifford Group Quantum Computational Models Introduction to Quantum Algorithms o Deutsch Algorithm o Deutsch-Jozsa Algorithm o Bernstein-Vazirani Algorithm o Simon's Algorithm Algorithms with Superpolynomial Speed-up
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o Efficient Quantum Circuits for the Fourier Transform o Quantum Phase Estimation o Shor's Algorithm for Factoring Integers and Determining Discrete Logarithms Chinese Reminder Theorem Euclid’s Algorithm Reduction of Factoring to Order Finding. o Algorithms for Hidden Subgroup Problems o Algorithms for Hidden Nonlinear Structures Algorithms Based on Amplitude Amplification o Grover's quantum search algorithm o Amplitude Amplification Quantum Complexity Theory. Complexity Classes BQP (Bounded Quantum Polynomial Time) Quantum Teleportation and Dense Coding Physical Implementation of Quantum Computers References: D. C. Marinescu and G. M. Marinescu, “Approaching Quantum Computing,” Prentice Hall, 2004. D.C. Marinescu and G. M. Marinescu, “From Classical to Quantum Information,’’ Academic Press, 2010. Online version at http://www.cs.ucf.edu/~dcm/QCV2.pdf M. Nielsen and I. Chuang, “Quantum Computing,” Cambridge University Press, 2000. R.P. Feynman, “Lectures on Computation,” Addison-Wesley, Reading, MA, 1996. N. D. Mermin, “Quantum Computer Science: An Introduction,” Cambridge University Press, 2007.
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