Could I theoretically mine a block faster than 10 minutes? I have been reading a lot about this 10 minute block in the Bitcoin network.  I'm slightly confused because I thought mining was a somewhat random process, mostly based on how powerful your mining facilities are.  So if I had a quantum computer and could really churn through calculations, couldn't I mine a block faster than 10 minutes?  Or is there something in the network taht would prevent me from submitting my mined block until 10 minutes had passed since the last mined block?
Nope, nothing prevents it.  The actual time from one block to the next is random, and it very often happens to be less than ten minutes, just by chance.  

Ten minutes is the target time.  The block difficulty adjusts with the goal of having ten minutes be the average time between blocks.  Of course if the average is ten minutes, then you would expect some blocks to be faster and others slower.