misunderstood. the SHA256 is not broken in output. what I wrote above is about the weakness in providing input for the SHA256 - because of weakness in random number generation. this is much more about vulnerabilities that exist in implementation stages of a secure platform - not the Math behind it. so we need to know how QC could influences in the structure of providing (and predict) input for SHA256 (or any other hash algorithm).
UPDATE:
we all know several online/offline bitcoin address generators that only run random function in javascript / server-side script. better solutions make the user to move her mouse to reach better amount of randomness. as I know we have no control over quality of randomness in bitcoin protocol. hope the paper bellow help:
http://www.mixoftix.net/knowledge_base/security/Key_Generation_with_Verifiable_Randomness.pdf