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Quantum computing

Quantum computing. Motivation. Two approaches to increase efficiency: Nanotechnologies Quantum computers Take advantage of quantum effects and design quantum algorithms. Reversibility. Content. Qubits Multiple qubits Computational basis Quantum gates Bell states circuit

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Quantum computing

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  1. Quantum computing

  2. Motivation • Two approaches to increase efficiency: • Nanotechnologies • Quantum computers • Take advantage of quantum effects and design quantum algorithms. • Reversibility

  3. Content • Qubits • Multiple qubits • Computational basis • Quantum gates • Bell states circuit • Teleportation circuit

  4. Qubits • The equivalent to a classical bit • Can be in the states or as classical bits • But also in a superposition state • Possibility of representing different numbers at the same time with only one qubit • But measurement put it back in the state or with probabilities and

  5. Multiple qubits • 4 computational basis states for a 2 qubit system • Superposition state

  6. Computational basis

  7. Quantum NOT gate

  8. Hadamard gate • After measurement becomes or

  9. CNOT gate

  10. Toffoli gate

  11. Bell states circuit

  12. Quantum teleportation

  13. Quantum teleportation

  14. Quantum teleportation

  15. Bibliography • M.A. Nielsen & I.L. Chuang, Quantum Computation and Quantum Information, Cambridge University Press, 2000. • P. Kaye, R. Laflamme & M. Mosca, An Introduction to Quantum Computing, Oxford University Press, 2007. • M. Nakahara & T. Ohmi, Quantum Computing: from Linear Algebra to Physical Realizations, CRC Press, 2008. • T. Hey, Quantum Computing: an introduction, Computing & Control Engineering Journal, vol. 10, n°3, 105-112, 1999. • A. Barenco & al., Elementary gates for quantum computation, Phys. Rev., A52, 3457-3467, 1995. • D. Deutsch, R. Jozsa, Rapid Solution of Problems by Quantum Computation, Proceedings: Mathematical and Physical sciences, vol. 439, n°1907, 553-558, 1992. • P. Shor, Algorithms for Quantum Computation: Discrete Logarithms and Factoring, Proceedings: 35th Annual Symposium on Fundamentals of Comp. Science (FOCS), 124-134, 1994.

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