Ismétlés

General model of quantum algorithms

Initialization ParallelizationAmplitude

ampl.Measu-rement

Classical input

Classicaloutput

Quantumoutput

Quantuminput

A Deutsch-Józsa algoritmus

Deutsch-Józsa-algoritmus

Quantum Fourier Transform

Classical Quantum

• Classical Discrete Fourier Transform (DFT)

• Quantum Discrete Fourier Transform (QFT)

How to implement QFT 3

Copyright © 2005 John Wiley & Sons Ltd.

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!

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.

Quantum Phase Estimation

The problem

• Each unitary transform having eigenvector has eigenvalues in the form of .

• Phase ratio:

Idealistic case – back to the QFT

Quantum Phase Estimator

• How to initialize ?

Practical case

• IQFT will work not correctly

Prob. amplitudes

Error analysis

Error analysis

Quantum Phase Estimator

Error analysis

Error analysis

The RSA algorithm

Order finding – Shor algorithm

Connection between factoring and order finding

Prime factorization

The Shor Algoritm

• Ki, hogy csinálná??????

General model of quantum algorithms

Initialization ParallelizationAmplitude

ampl.Measu-rement

Classical input

Classicaloutput

Quantumoutput

Quantuminput

• From quregister to tensor product of qubits

• Phase estimator:

• Shor:

• Connection between them:

• Uniformly distributed eigenvectors by means of initialization of the lower quregister:

Using Shor’s order finding algorithm to break RSA

QFT as a generalized Hadamard Transform

• Hadamard:

• QFT: