10.3 Constructing the PQC
The question of how to construct a high-quality candidate state used to calculate expectations is of fundamental importance. Unless we have some prior knowledge about the ground state and where to search for it in the Hilbert space of the n-qubit system, the first task would be to generate a range of candidate states that will cover the whole Hilbert space without being heavily concentrated in any one region. Let us see how this can be done for the single-qubit and multi-qubit systems.
10.3.1 One-qubit ansatz
We return to the Bloch sphere that visualises the possible states of a one-qubit system. Figure 10.1 shows how the qubit state can change from its initial state 
to the intermediate state 
and then to the final state 
through a rotation around the y axis followed by a rotation around the z axis.
Figure 10.1: Bloch sphere: visualisation of one-qubit rotations.
It is possible to reach any point on the Bloch sphere starting from 
with...
