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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:
