Quantum Fourier Transform Circuit

A quantum circuit (sometimes called a quantum network or a quantum gate array) consists of wires and logic gates. It can be represented by a × unitary matrix, where is the number of qubits. We want to factor this matrix, representing it as scalar and tensor (Kronecker) products of simpler one-qubit and two-qubit matrices.
The input register of the quantum Fourier transform (QFT) circuit contains -qubit basis states that can be written as the Kronecker product of the binary states. The Hadamard gate operates on the single qubit. The controlled gate is represented by the unitary matrix . The output qubits are expressed in the general form , where is a binary fraction. The final result of QFT is obtained after swapping the output qubits (not shown here) and taking the Kronecker product. For the three-qubit case the final answer is


  • [Snapshot]
  • [Snapshot]
  • [Snapshot]
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.

Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2018 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+