Haven't found much on the topic there, so asking away.

Let's say i have a practicable quantum computer or other device capable of rapid factorization of large enough integers.

What are the consequences to a developed bitcoin network?

Any way it could let me cheat in generation?

Any way it would let me cheat in transactions?

With a device of this kind i can get the private key from public key, right?

So after receiving a bitcoin from someone, can i subsequently successfully fake a transfer of all there was on his side?

Actually the usefulness of all these odd features of quantum computing. Well, thanks to those quantum mechanical quirks, a quantum computer could crunch complicated calculations much quicker than the fastest computers today. Because the qubit exists in a superposition of one and zero, rather than one or the other, it can use ones, zeroes, and the superposition of both. By being able to encode multiple possibilities in its fundamental units and It can tackle the problem more efficient than Normal computer.