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Quantum Computing

Sergey Tikhomirov

Lecture 4

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

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WhatsApp group

https://chat.whatsapp.com/DWCoppTR6yu57qR5hDtt36

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sergey.tikhomirov@gmail.com

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Dirac (bra-ket) notation

 

vector

co-vector

bra

ket

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Dirac (bra-ket) notation

 

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1 qbit Gates

 

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1 qbit Gates.Pauli matrixes

  • Pauli matrixes�����They are unitary and self-adjoint��They form a basis in the space of self-adjoint operators

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1 qbit Gates. Rotation gates

Those gates are usually implemented

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1 qbit Gates. Arbitrarily 1-qbit gate

 

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1 qbit Gates. Square root

 

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Gates

  • 1-qbit gates
  • 2-qbit gates
  • Some multi qbit gates

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2 qbit Gates. Controlled-Not

 

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2 qbit Gates. Controlled-U

 

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2 qbit Gates. Controlled by 0

 

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2 qbit Gates. Representation of C-U

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2 qbit Gates. Arbitrarily gate

 

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Semi-classical control operators

  1. Consider the scheme combining quantum and classical computations

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  • Question: Does it add something new?
  • Is it correct « » and what does it mean?

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If result is «1»

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Semi-classical control operators

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Special 2qbit-operators

 

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Special 2qbit-operators. Swap. Connectivity graph.

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Special 2qbit-operators. Some relations.

Which operator?

Between any of the special operators there exists a connecting scheme.