In what sense is it 'more complicated to navigate through a Hilbert space to find more complex states'?

In the lecture titled Entanglement and Complexity: Gravity and Quantum Mechanics, Professor Leonard Susskind implies (at time 17:49) that the complexity of a quantum state impacts how 'complicated' it is to 'navigate your way through the Hilbert space to find that state'.

I've heard this and similar sentiments a few times. Why is it true? How are Hilbert spaces 'navigated through' and why does seeking a more 'complex' [*] state make this navigation more 'difficult' [**]?

[*] meaning more entangled?

[**] difficult in what sense? Time consuming?

• perhaps he is referring to the high dimensionality of the space? – lurscher Aug 29 '18 at 22:34
• Have you tried to use a Hilbert compass? And don't get me started on the Hilbert sextant - talk about complex! – Jon Custer Aug 29 '18 at 22:38

In continuum quantum systems, probably the next best thing is to measure the integrated norm of the Hamiltonian $H(t)$ along a path. This is a lot like action, hence complexity = action.