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Quantum Computing

Sergey Tikhomirov

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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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What the course is about?

  • Quantum computer is a device, which works using quantum mechanics ☺
  • But to study quantum computing there is no need to know quantum mechanics

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  • I will introduce mathematical model
    • qBit, Quantum Gate, Measurement
    • Why exactly this model? Because of quantum mechanics.

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What mathematics is needed?

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Platforms and Literature

  1. Gate-based quantum computers. �Universal quantum computing.
    • IBM Quantum Experience
    • Quantum Playground (Google)
    • Quantum-circuit.com
  2. Adiabatic quantum computer
    • DWave: Quantum Leap

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  • Literature
    • Books
      • Williams, Exploration in Quantum Computing, 2011
      • Nielsen, Chuang, Quantum Computation and Quantum Exploration, 2010
    • Papers
      • Elementary gates for quantum computation, 1995,
      • Quantum linear systems algorithms, 2018

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The model

  1. Quantum Bit
  2. Quantum Gates, Quantum Scheme
  3. Measurements

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Quantum Bit State

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Quantum Bit State

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exact meaning of this I will tell later

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Quantum Bit State

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Quantum Bit State. Interpretation in linear algebra.

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Quantum Bit vs Classical Bit.

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Bloch Sphere.

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Bloch Sphere. Examples.

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Bloch Sphere. Examples.

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Bloch Sphere. Questions.

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Two qBit State

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Similarly to single qBit

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Two qBit State

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Two independent qBits

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Two qBits. Tensor Product. Notation

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Multi qBit State

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Similarly to 1-, 2- qBit

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Multi qBit State

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Multi qBit State

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Similarly to 1-, 2- qBit

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Multi qBit State. Notational remarks.

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Multi qBit State. Very important point.

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NEVER DO LIKE THIS

 

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Multi qBit State. Vector notation

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Multi qBit State. More Notation.

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The model

  1. Quantum Bit -- Done
  2. Quantum Gates
  3. Measurements

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See you on Thursday!