Quantum computing

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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
Transcript
Quantum computingMotivation
  • 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
  • Teleportation circuit
  • 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
  • Multiple qubits
  • 4 computational basis states for a 2 qubit system
  • Superposition state
  • Computational basisQuantum NOT gateHadamard gate
  • After measurement becomes or
  • CNOT gateToffoli gateBell states circuitQuantum teleportationQuantum teleportationQuantum teleportationBibliography
  • 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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