Quantum Computing Fundamentals by Chuck Easttom

Author:Chuck Easttom [Chuck Easttom]
Language: eng
Format: epub
Publisher: Addison-Wesley Professional
Published: 2021-06-15T16:00:00+00:00

Equation 8.4 The Classical Discrete Fourier Transform

This is for k = 0, 1, 2, …, n–1. In Equation 8.4, the ωN = e2πi/n and is the nth root of unity. The root of unity is any complex number that yields 1 when raised to some positive integer power n. This is sometimes called a de Moivre number after French mathematician de Moivre. He is known for the de Moivre formula that links complex numbers to trigonometry as well as his work on probability theory.

The quantum Fourier transform acts in a similar manner, operating on a quantum state. The quantum Fourier transform uses the same formula you saw in Equation 8.4. However, it is operating on quantum states such as shown in Equation 8.5

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