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Quantum Computing

Quantum Computing. U f. Nick Bonesteel. H. H. Discovering Physics, Nov. 16, 2012. q. H. f. What is a quantum computer, and what can we do with one?. A Classical Bit: Two Possible States. 0. A Classical Bit: Two Possible States. 1. Single Bit Operation: NOT. NOT. x y 0 1

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Quantum Computing

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  1. Quantum Computing Uf Nick Bonesteel H H Discovering Physics, Nov. 16, 2012 q H f

  2. What is a quantum computer, and what can we do with one?

  3. A Classical Bit: Two Possible States 0

  4. A Classical Bit: Two Possible States 1

  5. Single Bit Operation: NOT NOT x y 0 1 1 0 y x 0

  6. Single Bit Operation: NOT NOT x y 0 1 1 0 y x 1

  7. A Quantum Bit or “Qubit” 0

  8. A Quantum Bit or “Qubit” 1

  9. A Quantum Bit or “Qubit” 0

  10. A Quantum Bit or “Qubit” 0 1

  11. A Quantum Bit or “Qubit” Quantum superposition of 0 and 1 0 1

  12. A Quantum Bit or “Qubit” 1

  13. A Quantum Bit or “Qubit” 0 1

  14. A Quantum Bit or “Qubit” 0

  15. A Quantum Bit: A Continuum of States q 0 1 cos sin q q +

  16. q q - f + i cos 0 sin e 1 2 2 A Quantum Bit: A Continuum of States Actually, qubit states live on the surface of a sphere. q f

  17. A Quantum Bit: A Continuum of States But the circle is enough for us today. q 0 1 cos sin q q +

  18. X A Quantum NOT Gate

  19. X X A Quantum NOT Gate

  20. X A Quantum NOT Gate

  21. X X A Quantum NOT Gate

  22. H H Hadamard Gate

  23. H H Hadamard Gate

  24. H H Hadamard Gate

  25. H H Hadamard Gate

  26. H H Hadamard Gate H is its own inverse

  27. H H Hadamard Gate H is its own inverse

  28. H H Hadamard Gate H is its own inverse

  29. H H Hadamard Gate H is its own inverse

  30. Fair Coin Trick Coin

  31. Balanced Function or Unbalanced Function or

  32. Uf A Two QubitSubroutine to Evaluate f(x)

  33. Uf A Two QubitSubroutine to Evaluate f(x) Input x can be either 0 or 1 Output is f(x) Initialize to state “0”

  34. Uf A Two QubitSubroutine to Evaluate f(x) Input x can be either 0 or 1 This qubit can also be in state “1”

  35. Uf A Two QubitSubroutine to Evaluate f(x) Input x can be either 0 or 1 Bar stands for “NOT” This qubit can also be in state “1” 0 = 1, 1 = 0

  36. Uf Uf A Two QubitSubroutine to Evaluate f(x) Unbalanced Balanced or or

  37. Uf A Quantum Algorithm (Deutsch-Jozsa ‘92) H H H

  38. Uf A Quantum Algorithm (Deutsch-Jozsa ‘92) H H H

  39. Uf A Quantum Algorithm (Deutsch-Jozsa ‘92) H H H

  40. Uf A Quantum Algorithm (Deutsch-Jozsa ‘92) H H H

  41. Uf A Quantum Algorithm (Deutsch-Jozsa ‘92) H H H

  42. Uf A Quantum Algorithm (Deutsch-Jozsa ‘92) H H H Only ran Uf subroutine once, but f(0) and f(1) both appear in the state of the computer!

  43. Uf A Quantum Algorithm (Deutsch-Jozsa ‘92) H H H If f is balanced: f(0) = f(1) and f(0) = f(1)

  44. Uf A Quantum Algorithm (Deutsch-Jozsa ‘92) H H H If f is balanced: f(0) = f(1) and f(0) = f(1)

  45. Uf A Quantum Algorithm (Deutsch-Jozsa ‘92) H H H If f is balanced: f(0) = f(1) and f(0) = f(1)

  46. Uf A Quantum Algorithm (Deutsch-Jozsa ‘92) H H H If f is unbalanced: f(0) = f(1) and f(0) = f(1)

  47. Uf A Quantum Algorithm (Deutsch-Jozsa ‘92) H H H If f is unbalanced: f(0) = f(1) and f(0) = f(1)

  48. Uf A Quantum Algorithm (Deutsch-Jozsa ‘92) H H H If f is unbalanced: f(0) = f(1) and f(0) = f(1)

  49. Uf A Quantum Algorithm (Deutsch-Jozsa ‘92) H H H Balanced: Unbalanced:

  50. Uf A Quantum Algorithm (Deutsch-Jozsa ‘92) H H H Balanced: Unbalanced:

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