Quantum Phase Estimation

In this chapter, we will discuss the quantum phase estimation (QPE) algorithm. This is a very important algorithm in quantum computing. For example, it is used in the Harrow–Hassidim–Lloyd (HHL) algorithm for solving systems of linear equations. This is also a place where we will test our understanding of qubits and quantum gates. If you can understand every detail of this chapter well, you are pretty good with quantum computing already and should be able to understand more advanced algorithms by yourself. We will first discuss the controlled unitary rotation gate (based on what we learned in the last chapter). Then we will go through a 3-qubit QPE numerical example just to appreciate how the wavefunctions evolve in the circuit. And then we will implement it on IBM-Q. Finally, we will discuss the general circuit for QPE.