Do you think there will be a period where bitcoin is still used, but big accounts are getting 'sniped' by fast computers? I guess with certain assumptions it might be possible. It's funny to think about the protections people would take, splitting down coins to many addresses to avoid being targeted, maybe moving them around quickly (might not help I guess).
Quantum computers will not be able to develop to a threating size without it escaping public knowledge.
When it becomes likely that a quantum computer of a attacking size will been developed within the next say - 10 years. A security update will be developed that will make Bitcoin much more difficult to attack.
This update will consist of three parts:
1. Increasing the length of the hashes used for the block chain. (maybe SHA256 => XXX8192)
2. Massively increasing the asymmetrical private/public key length used to secure transactions.
3. Massively increasing the length of a Bitcoin address (the hash of the public part of a key). (maybe the new address will be 1024 + 8 character long)
This security patch will be released well before a quantum computer is developed to a stage that can attack it. For anyones bitcoins to remain secure, they will need to 'spend' the coins to the new secure addresses.
Since 'lost' coins cannot be 'spent,' they will on day be collected (and moved to new secure addresses) by somebody who can take the effort to crack the old (insecure) addresses.
Once, quantum computers become common, bitcoin could even use cypto that requires quantum computers to do the calculations, otherwise it would be prohibitory slow.