I've always assumed that "quantum locking" was a term invented by the writers of Dr Who, but this video suggests otherwise.
What is quantum locking? Is it real?
Apparently, a key detail is that the superconducting layer on the disk is very thin.
Usually superconducting levitation demonstrations use thicker layers of superconductors which completely deflect the field from magnets - so they float above the magnet but also tend to wobble around a bit.
This demo uses a very thin superconducting layer - this allows the magnetic field to penetrate the superconductor at a small number of defect sites. The small but non-zero magnetic field passing through the defect sites 'locks' the superconductor into whatever orientation is set initially - and also prevents the wobbly shaking normally seen in Meisner-effect levitation.
No 'Weeping Angels' are involved.
The video link is not working for me for some reason so my answer may not be a comment on what the video is showing, but these are my thoughts.
My understanding of "locking" is that you lock the phase of one system to another. The term quantum is used if you are talking about the quantum phase of the state. It seems superfluous, but serves as a reminder that we are not necessarily talking about the average phase. For example in the Heisenberg picture you could write:
Now, the objective could be to "lock" the phases of these two operators i.e obtain a condition via an interaction such that $\Delta\phi=0$. In a practical sense, any time you wish to do something with the phases of fields, interference is a logical way to go about it. This kind of phase locking is accomplished in some sense when you deal with light matter interactions, where one field is the atomic spin wave (i.e atomic states are in a coherent superposition) and the other fields are optical.
For example see Locking Local Oscillator Phase to the Atomic Phase via Weak Measurement and Here(pdf). There are also many examples from Cavity QED (I can list them if you wish but you get the general idea).
I realize that this may be completely different from what the video shows, but this is my understanding of the terminology.