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Quantum Computing

Sergey Tikhomirov

Lecture 11

https://sites.google.com/site/sergeytikhomirov/teaching/2025-quantum

WhatsApp group

https://chat.whatsapp.com/DWCoppTR6yu57qR5hDtt36

sergey.tikhomirov@gmail.com

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Phase estimation

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Phase estimation.

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Phase estimation.

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Phase estimation. Auxiliary scheme

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Phase estimation. Main part

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Phase estimation. Main part

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Phase estimation. Full scheme

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Phase estimation. Alternative notation

�

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Phase estimation. Not precise result.

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Phase estimation. Not precise result.

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Phase estimation. Not eigenstate

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Phase estimation. Summary

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Integer factoring �(Shor algorithm)

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Integer factoring. Shor algorithm.

Quantum Computers become famous because of this algorithm

It solves a concrete important practical problem

And creates issues for secure communications/cryptography

It is a concrete algorithm, without any assumption like «there exists oracle…» or so…

The algorithm has not only quantum part, but non-trivial classical part and mathematical reasoning

I will describe only quantum part

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Integer factoring. Shor algorithm.

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Actual problem. Order finding.

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Actual problem. Order finding.

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The algorithm.

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The algorithm.

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The algorithm.

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Problem 1.

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Problem 1.

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The algorithm.

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Problem 2.

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Period finding.