Can quantum computer provide random or just pseudo-random number, or none of both? It's a bit confusing me, since collapse of wave function once measured.
Both. If quantum mechanics is correct, then an unpredictable RNG circuit is extremely simple:
(Note: even if you're a proponent of a deterministic interpretation, like many worlds, this circuit remains fundamentally unpredictable. Philosophers may debate whether or not it's "really" random, but predictability is ultimately what matters in practice for cryptography and so forth.)
It gets better, actually. Thanks to the existence of Bell tests, we can use quantum computers to create so-called "Einstein-certified" random numbers that are guaranteed to be unpredictable unless faster-than-light communication was used to bias them.
For more information see the well-written article 'Quantum Randomness' by Scott Aaronson.