Quantum phase kick-back provides us with tools to use quantum phases to learn specific properties of a unitary or a system, provided we can measure them. But how do you measure these relative phases? 

In this video, Postdoctoral Researcher Ben Criger (QuTech) talks you through an algorithm to estimate these relative phases: Quantum phase estimation. After a short discussion on the precision of phase estimation, Ben introduces the concept of binary fractions, which comes in handy in the rest of the example. Finally, the quantum phase estimation algorithm will be explained, which forms the basis of one of the more profound quantum algorithms: the Quantum Fourier Transform.

Required knowledge

• Quantum phase kick-back
• Quantum circuits, unitaries, and controlled unitary operations
• Eigenstates & Bloch states

Further thinking

Why is the algorithm at the end called the “Quantum Fourier Transform”? What is the analogy to its classical counterpart?

Solution

Further reading

Ben introduces in the video the concept of binary fractions. If you want to know more about that, you can look at:

• https://www.electronics-tutorials.ws/binary/binary-fractions.html

The quantum phase estimation and Quantum Fourier Transform has also been covered quite thoroughly in 

• Nielsen, M. A., & Chuang, I. (2002). Quantum computation and quantum information.