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

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Presentation transcript:

Ismétlés

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

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

Quantum Phase Estimator

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 InitializationParallelization Amplitude ampl. Measu- rement Classical input Classical output Quantum output Quantum input

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:

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