I believe this would be horribly bad for the mining community and for the concurrency itself. the concept and power of the block-chain is that it is spread across a very large amount of users (miners), I like to think of those users as witnesses in a crime scene the more you have the more certain you are of what really happened, If one decides to change the story he would have to convince a lot of people to do so a gain credibility.
In my example a quantum computer is on its own representative of millions of users (miners) because of the equivalent Hash rate power, In other words who ever owns a quantum computer owns a big pool (Group of miners) creating a huge imbalance in the consensus of the network and maybe impose his on own path on the block-chain. There are more reasons why this would be bad for the crypto-network including power consumption of QC and ordinary PC's for the same instructions or affordability, how much will it cost? who would have access to it? Will it create a deeper and wider wedge between the elite and the poor? I believe the QC makes the future of crypto-currency even more uncertain, at least as long as it is based on cryptography.