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Quantum Algorithms

01 /Applications of a Quantum Computer 02 /Breaking encryption 03 /The classical one-time pad 04 /Grover’s algorithm 05 /Quantum fourier transform 06 /Shor's algorithm 07 /Solving linear equations with quantum computers 08 /Quantum Machine Learning 09 /Simulating chemistry 10 /Distributed quantum computing 11 /Quantum Inspire 12 /Deutsch – Jozsa algorithm

Quantum fourier transform

To be able to understand more elaborate and powerful algorithms, we need to review and be able to identify routines that play important roles.

In this section you will learn about the Quantum fourier transform (QFT), a quantum analog to the classical discrete fourier transform that works over the amplitudes of the wavefunction.

The Quantum fourier transform is a subroutine in algorithms such like Shor's algorithm and Quantum phase estimation. In this video, QFT is presented in a rather visual representation to get more intuition on what QFT actually does. It contains an explanation of QFT for 2 qubits by María Flors Mor Ruiz and Elsie Loukiantchenko, Applied Physics MSc students at TU Delft.

Prerequisite knowledge

Further thinking

How would the circuit look like for only 1 qubit?

In the 2 qubits system, what would be the result of the following expression? QFT(|0> + |2>)

Solution

Further reading

  • Nielsen and Chuang - Quantum Computation and Information (Chapter 5)
  • N. David Mermin - Quantum Computer Science (Chapter 3.5)