Quantum computing is an entire field of study unto itself. I barely have a student's understanding of how it works, let alone how it impacts cryptology, and further -- that of Bitcoin.
In essence, here is what I have ascertained in my research (please feel free to correct me):
Bitcoin is secured in part by difficult to solve math problems*. To illustrate one of these math problems, we can envision two boats separated by 1000 miles of ocean. One of the boats is manned by pirates and it badly wants to catch the second boat which is manned by engineers. Both boats have a maximum speed of 30 mph on still water, but the ocean's current moves against them at 29.99 mph. Sometimes the pirates improve their engine, or throw someone overboard (thereby reducing their frictional coefficient) and gain some speed; but the engineer's boat has a good looking glass and can keep pace with any speed improvements that the pirates make.
One day the pirate's captain makes a deal with Cthulu and Davy Jones to obtain a quantum engine - which is really just a ghostly second engine (bear with me, the pirates only have one engine slot.) It is way better than one engine even though it occupies the same amount of space because it uses some magic called superposition - which is just ghost-speak for having two things occupy the same space. So because of this magic, the pirates can have their normal engine and a ghost engine at the same time.
The engineers are clever, and they saw this coming all along -- so they have a super-singular elliptic curve isogenous engine bartered from a passing submarine for a Ballmer of rum.
The moral being that the hypothetical pirate boat may gain some spooky magic engine, but the engineers build spooky magic engines for breakfast.
Silly stories aside, quantum computing is certainly a concern for systems secured by cryptography -- but there are many solutions to the proposed threats. On top of this, the block chain is naturally a revision control system -- and given catastrophic failure, it could be patched and rolled back.
There are a large number of people who would likely disagree with me that these solutions are not 100% sound proof, but I stipulate that they are closer to 99.99% than not.
Check out these white papers to see that awesome super-singular elliptic curve isogenous engine in action:
Towards Quantum-Resistant Cryptosystems from Supersingular Elliptic Curve Isogenies by De Feo, Jao, and Plˆut
Machine Level Software Optimization of Cryptographic Protocols by Dieter Fishbein
*To give an idea as to the scale of hashes it would take to produce a sha256 collision in Bitcoin:(2^256/9460800000000000000000)/13800000000 (Bitcoin hashing algorithm digest space, divided by the bitcoin hash rate for one year, divided by the age of the universe)
It would take 886894459681353320486815658331188003935001243 times the age of the universe to create a sha-256 collision with the current Bitcoin hash rate.