I understand there are two ways Bitcoin is affected by a crypto quantum-computer:
1) A QC is able to derive the private-keys for a wallet's public address, allowing for the theft of bitcoin
2) A QC able to perform the proof-of-work algorithm to mine new blocks at an order-of-magnitude faster rate than currently possible.
Fortunately for 1) (I think) it currently takes 2^512 (?) operations to break the private/public algorithm which is unfeasible to brute-force on normal hardware but a QC brings it down to 2^128 - but that's still on-the-order-of unfeasible - and in the event it ever does happen the blockchain could be changed overnight to use a new keying algorithm. And for 2) it would cause the blockchain difficulty to be pushed-up so high that people with QC machines would see the same ROI as today's industrial GPU and ASIC miners see - plus given that QC computers are horrendously expensive (think: billions of USD for a 50-bit general-purpose QC) it questions why you'd ever try to break Bitcoin as you'd already be a billionaire.
> Fortunately for 1) (I think) it currently takes 2^512 (?) operations to break the private/public algorithm which is unfeasible to brute-force on normal hardware but a QC brings it down to 2^128
Where have you got that info? Quantum computers can break ECDSA in polynomial function of 512.
> the blockchain could be changed overnight to use a new keying algorithm.
> Will quantum computing kill Bitcoin by rendering the underlying cryptography obsolete?
No, as even if the current underlying crypto falls (for whatever reason), the ledger up to that point could very likely endure in a new form.
Outside of the blockchain concept of itself, the oft-ignored indirect gift of bitcoin's longevity is the way it is providing us a new digital mechanism for the international distribution of wealth as more people join, the ledger proceeds and mined coins are exchanged more widely.
1) A QC is able to derive the private-keys for a wallet's public address, allowing for the theft of bitcoin
2) A QC able to perform the proof-of-work algorithm to mine new blocks at an order-of-magnitude faster rate than currently possible.
Fortunately for 1) (I think) it currently takes 2^512 (?) operations to break the private/public algorithm which is unfeasible to brute-force on normal hardware but a QC brings it down to 2^128 - but that's still on-the-order-of unfeasible - and in the event it ever does happen the blockchain could be changed overnight to use a new keying algorithm. And for 2) it would cause the blockchain difficulty to be pushed-up so high that people with QC machines would see the same ROI as today's industrial GPU and ASIC miners see - plus given that QC computers are horrendously expensive (think: billions of USD for a 50-bit general-purpose QC) it questions why you'd ever try to break Bitcoin as you'd already be a billionaire.