What positive effects can Quantum Computers have on the Blockchain technology and hence Bitcoin
A couple very hypothetical examples:


Quantum channels: These channels allow wiretap resistant transmission of data. Bitcoin users can share secret information such as keys over quantum channels in such a way that any wiretapping would be detectable.
Database queries: Quantum computers can search through a database in time O(N^(1/3)). This could potentially speed up lookups in a blockchain. Say I want to transactions that correspond to my public key. For one billion transactions this can be done in only a thousand steps (ignoring gigantic constants probably). 
Quantum simulation could perhaps lead to better hardware so that's always nice.


However, the biggest real impact that quantum computers have right now on cryptography and thus cryptocurrencies is something different: They encourage cryptographers to explore new and interesting schemes and cryptographic assumptions. The study of these new assumptions and schemes could lead to more useful cryptographic tools which we couldn't build from other assumptions. The prime example for this is fully homomorphic encryption which can be built from ideal lattices. These lattices were first used in cryptography to build quantum resistant cryptography.