1. Ismétlés

2. General model of quantum algorithms InitializationParallelization Amplitude ampl. Measu- rement Classical input Classical output Quantum output Quantum input

3. A Deutsch-Józsa algoritmus

4. Deutsch-Józsa-algoritmus

5. Quantum Fourier Transform

6. Classical Quantum Classical Discrete Fourier Transform (DFT) Quantum Discrete Fourier Transform (QFT)

7. How to implement QFT 3 Copyright © 2005 John Wiley & Sons Ltd.

8. How to implement QFT 6 Remarks –Complexity: –QFT is not for computing Fourier coefficients in a faster way since they are represented by probability amplitudes!

9. Kérjük kedves utasainkat ellenőrizzék az Önök előtti ülés háttámlájában található biztonsági útmutatót. A mentőmellények a székek alatt találhatók, a vészkijárat jobb hátul. Kérjük csatolják be biztonsági öveiket és fejezzék be a dohányzást! Felszállunk.

10. Quantum Phase Estimation

11. The problem Each unitary transform having eigenvector has eigenvalues in the form of. Phase ratio:

12. Idealistic case – back to the QFT

17. Quantum Phase Estimator How to initialize ?

18. Practical case IQFT will work not correctly

19. Prob. amplitudes

20. Error analysis

22. Quantum Phase Estimator

23. Error analysis

25. The RSA algorithm

29. Order finding – Shor algorithm

30. Connection between factoring and order finding

31. Prime factorization

36. The Shor Algoritm Ki, hogy csinálná??????

37. General model of quantum algorithms InitializationParallelization Amplitude ampl. Measu- rement Classical input Classical output Quantum output Quantum input

42. From quregister to tensor product of qubits Phase estimator: Shor: Connection between them:

43. Uniformly distributed eigenvectors by means of initialization of the lower quregister:

46. Using Shor’s order finding algorithm to break RSA

51. QFT as a generalized Hadamard Transform Hadamard: QFT: