Shor Algorithm

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Shor Algorithm

• Anuj Dawar

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Finding the eigenvalue is the same as finding its
phase ?
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We initialize to all states
we measure the phase
Index register to store the eigenvalue
Target register
Unitary operator for which we calculate phase of
eigenvalue using phase kickback
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Formulas for the phase estimation algorithm
(
)
This is the input to QFT
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Because e j? is an eigenvallue of U
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Assume k an integer
Number of bits
We found phase
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Concluding, we can calculate phase
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Easy to multiply but difficult to factor big
integers.
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Assume
We want to find the smallest r such that the
above is true
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Greatest common denominator
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So now what remains is to be able to find period,
but this is something well done with spectral
transforms.
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Phase is 1/r
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Reductions
Solve RSA
Factor big integers
Find period
Estimate Phase
Fourier Transform
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