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Introduction to Quantum Computing

Dr. Shreya Banerjee

Image and Video Analysis Lab Presentation

18.05.2024

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Center for Quantum Science and Technology

Siksha ‘O’ Anusandhan University, Bhubaneswar

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Outline

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    • Qubit
    • Gate
    • Circuit

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Historical Overview

  • 1900-1920: Development of Quantum Mechanics.

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  • 1920 Onwards: Physicists successfully applied quantum mechanics to understand fundamental particles and properties of nature.

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  • 1970-1980: Instead of explaining quantum phenomenon as found in nature, can they be simulated??

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Information Theory

Quantum Mechanics

Computer Science

Quantum Computing

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Qubits (Quantum Bits)

  • They are quantum analogue to classical ‘bit’(s).
  • We can think about them as abstract mathematical concepts (vectors).
  • They are also physically realizable.

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Two level system: Spin ½ systems

  • The spin number describes how many symmetrical facets a particle has in one full rotation.
  • A spin of 1/2 means that the particle must be rotated by two full turns (through 720°) before it has the same configuration as when it started.

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Mathematical framework

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Qubits: Representation

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Qubits: Representation

 

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Qubits: State

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MEASUREMENT

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Measurement

MEASUREMENT

Quantum World

Classical World

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Measurement

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  • Through measurement, we know, which ‘state’ the qubit is in.

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  • However, since after measurement, we are in the classical world, we can only measure the qubit in either ‘0’ or ‘1’.

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  • Multiple measurements are the key to unlocking the door.

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Measurement

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Multiple Qubits

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Multiple Qubits

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Manipulating a qubit: ‘Gate’

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Common Gates in Quantum Computing.

  • Single Qubit Gates:

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  • =

 

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Gate Operations

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Two Qubit Gate Operation (Controlled Gates)

  • Controlled Not: CNOT/CX=

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  • Acts on the combined system of two qubits. Takes the first one as ‘Control’, depending on its state, acts (or does not act) on the second qubit.

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  • General Convention is:

If the first qubit is ‘0’, the second qubit remains the same.

If the first qubit is 1, the ‘NOT’ acts on the second qubit.

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Action of a �Two-qubit gate:

q0

q1

Input (q0)

Input (q1)

Output (q0)

Output (q1)

0

0

0

0

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1

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1

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Control

Target

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Quantum Circuit

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is one of the celebrated ‘Bell ’ states. This state is entangled. Here, if one measures the first qubit only, the second qubit is sure to end up in the same state as the first. Also, there is no way to write the state of the individual systems as the form of a tensor product.

q0

q1

H

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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Thank you

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