Interesting paper.
According to it, preimage searches can be faster on quantum computers than on classic computers. BTC mining can be expressed as preimage search, so the extended Grovers algorithm could be applied. The paper sais it is not clear what search complexity is required to reach the tip-over point at which a quantum computer is more efficient. Therefore it isnt clear on which side BTC sits. It may or may not be more efficient.
If BTC mining was more efficient on quantum computers, it wouldnt necessarily be the end of BTC. As long as the length of SHA2 hashes permit, quantum mining rigs will be dealt with by difficulty adjustments. Just like GPU, FPGA, ASIC technology each is so much more efficient than the previous generations. The network has compensated for all of them and is still running as designed.
There is a maximum possible difficulty though. Only when the network hashing power gets beyond that point, BTC mining is broken. Until then: business as usual.
Other areas of BTC (such as the public key crypto) are probably much more vulnerable to quantum computers than the mining process.