15.2 Quantum Phase Estimation
The goal of QPE is to estimate the unknown phase φ ∈[0,1) for a given unitary operator U with an eigenvector 
and eigenvalue exp(2πiφ). Consider a register of size m and define
Thus with b∗ = b1
bm, we obtain that
is the best m-bit approximation of φ from below. The QPE procedure uses two registers, with the first containing m qubits initially in the state 
. Selecting m relies on the number of digits of accuracy for the estimate of φ, and the probability with which we wish to obtain a successful phase estimation procedure.
QPE allows us to implement a measurement for any Hermitian operator. Note that we always measure individual qubits. If we want to measure a more complex observable, we can use a QPE that implements the von Neumann measurement scheme [227]. The routine prepares an eigenstate of the Hermitian operator in one register and stores the corresponding...
